Recent zbMATH articles in MSC 76 https://zbmath.org/atom/cc/76 2021-11-25T18:46:10.358925Z Werkzeug Stochastic approaches to Lagrangian coherent structures https://zbmath.org/1472.34111 2021-11-25T18:46:10.358925Z "Balasuriya, Sanjeeva" https://zbmath.org/authors/?q=ai:balasuriya.sanjeeva Summary: This note discusses a connection between deterministic Lagrangian coherent structures (robust fluid parcels which move coherently in unsteady fluid flows according to a deterministic ordinary differential equation), and the incorporation of noise or stochasticity which leads to the Fokker-Planck equation (a partial differential equation governing a probability density function). The link between these is via a stochastic ordinary differential equation. It is argued that a closer investigation of the stochastic differential equation offers additional insights to both the other approaches, and in particular to uncertainty quantification in Lagrangian coherent structures. For the entire collection see [Zbl 1462.35005]. Rigorous derivation of a mean field model for the Ostwald ripening of thin films https://zbmath.org/1472.35028 2021-11-25T18:46:10.358925Z "Dai, Shibin" https://zbmath.org/authors/?q=ai:dai.shibin During the late stages of the evolution of thin liquid films on a solid substrate, liquid droplets are connected by an ultra-thin residual film. Their number decreases due to migration and collision on the one hand, and exchange of matter through a diffusive field in the residual film on the other hand. Supposing that, at time $$t>0$$, there are $$N(t)\ge 1$$ droplets $$\{B(x_i,R_i(t))\ :\ 1\le i \le N(t)\}$$ in the square $$\Omega_{\mathcal{L}} =(0,\mathcal{L})^2$$ and neglecting the motion of the centers $$x_i$$ due to the no-slip boundary condition for the fluid at the substrate, the dynamics of the radii $$(R_i)$$ and the diffusive field $$u$$ may be described by \begin{align*} - \Delta u(t,x) &= 0, \qquad x\in \Omega_{\mathcal{L}}\setminus \bigcup_{i=1}^{N(t)} \bar{B}(x_i,R_i(t)), \ t>0, \\ u(t,x) &= \frac{1}{R_i(t)}, \qquad x\in B(x_i,R_i(t)), \ t>0, \\ \frac{dR_i}{dt}(t) &= \frac{1}{R_i(t)^2} \int_{\partial B(x_i,R_i(t))} [\nabla u(t,s)\cdot \mathbf{n}(s)]\ ds, \qquad t>0, \end{align*} supplemented with periodic boundary conditions on $$\partial\Omega_{\mathcal{L}}$$. In the above integral term, $$[\nabla u(t,s)\cdot \mathbf{n}(s)]$$ denotes the jump of the normal gradient of $$u$$ across the boundary of $$B(x_i,R_i(t))$$. After introducing a small parameter $$\varepsilon>0$$ and scaling $$\mathcal{L}$$, $$x$$, $$t$$, $$N$$, $$(R_i)$$, and $$u$$ in an appropriate way, homogeneization techniques are used to establish the convergence of the rescaled diffusion fields to a mean field $$u_*$$. The latter is a weak solution to \begin{align*} -\Delta u_*(t,y) + 2\pi\delta \int_0^\infty \left( u_*(t,y) - \frac{1}{r} \right) f(t,y,r)\ dr & = 0, \qquad r\in (0,\infty),\\ \partial_t f(t,y,r) + \partial_r \left( \frac{2\pi}{r^2} \left( u_*(t,y) - \frac{1}{r} \right) f(t,y,r) \right) & = 0, \qquad r\in (0,\infty), \end{align*} for $$t>0$$ and $$y\in \Omega_1$$, supplemented with periodic boundary conditions on $$\Omega_1$$. The parameter $$\delta$$ is prescribed by the scaling, while $$f$$ is in general a measure-valued solution to the above transport equation. Upscaling of a system of diffusion-reaction equations coupled with a system of ordinary differential equations originating in the context of crystal dissolution and precipitation of minerals in a porous medium https://zbmath.org/1472.35029 2021-11-25T18:46:10.358925Z "Mahato, Hari Shankar" https://zbmath.org/authors/?q=ai:mahato.hari-shankar "Kräutle, Serge" https://zbmath.org/authors/?q=ai:krautle.serge "Knabner, Peter" https://zbmath.org/authors/?q=ai:knabner.peter "Böhm, Michael" https://zbmath.org/authors/?q=ai:bohm.michael-j|bohm.michael-c Summary: In this paper, we consider diffusion and reaction of mobile chemical species, and dissolution and precipitation of immobile species present inside a porous medium. The transport of mobile species in the pores is modeled by a system of semilinear parabolic partial differential equations. The reactions amongst the mobile species are assumed to be reversible. i.e. both forward and backward reactions are considered. These reversible reactions lead to highly nonlinear reaction rate terms on the right-hand side of the partial differential equations. This system of equations for the mobile species is complemented by flux boundary conditions at the outer boundary. Furthermore, the dissolution and precipitation of immobile species on the surface of the solid parts are modeled by mass action kinetics which lead to a nonlinear precipitation term and a multivalued dissolution term. The model is posed at the pore (micro) scale. The contribution of this paper is two-fold: first we show the existence of a unique positive global weak solution for the coupled systems and then we upscale (homogenize) the model from the micro scale to the macro scale. For the existence of solution, some regularization techniques, Schaefer's fixed point theorem and Lyapunov type arguments have been used whereas the concepts of two-scale convergence and periodic unfolding are used for the homogenization. Existence of global steady subsonic Euler flows with collision through 2D infinitely long nozzles https://zbmath.org/1472.35129 2021-11-25T18:46:10.358925Z "Han, Fangyu" https://zbmath.org/authors/?q=ai:han.fangyu "Tan, Zhong" https://zbmath.org/authors/?q=ai:tan.zhong.1|tan.zhong Summary: In this paper, we study the global existence of steady subsonic flows with collision, where the collision is caused by a confluence of two semi-infinitely incoming flows that are nonmiscible steady subsonic irrotational Euler flows come from two different infinitely nozzles. First, we prove that when the total flux of two incoming flows is less that the critical mass flux, there exists a unique global smooth subsonic flow with collision. Meanwhile, the interface between two flows is a smooth free interface, which is determined uniquely by the mass fluxes of incoming flows. Second, by using the blowup argument, we establish the asymptotic behaviors for the stream function. Finally, we prove that the position of free interface can be determined uniquely by the mass fluxes of incoming flows. Moreover, we establish the monotonicity of the relation between the position of free interface and the mass fluxes of incoming flows. Compactness and sharp lower bound for a 2D smectics model https://zbmath.org/1472.35143 2021-11-25T18:46:10.358925Z "Novack, Michael" https://zbmath.org/authors/?q=ai:novack.michael-r "Yan, Xiaodong" https://zbmath.org/authors/?q=ai:yan.xiaodong Summary: We consider a 2D smectics model $E_{\epsilon}(u)=\frac{1}{2}\int_\varOmega\frac{1}{\varepsilon}\left(u_z-\frac{1}{2}u_x^2\right)^2+\varepsilon(u_{xx})^2\text{d}x\,\text{d}z.$ For $$\varepsilon_n\rightarrow 0$$ and a sequence $$\{u_n\}$$ with bounded energies $$E_{\varepsilon_n}(u_n)$$, we prove compactness of $$\{\partial_zu_n\}$$ in $$L^2$$ and $$\{\partial_xu_n\}$$ in $$L^q$$ for any $$1\le q<p$$ under the additional assumption $$\Vert\partial_xu_n\Vert_{L^p}\le C$$ for some $$p>6$$. We also prove a sharp lower bound on $$E_{\varepsilon}$$ when $$\varepsilon\rightarrow 0.$$ The sharp bound corresponds to the energy of a 1D ansatz in the transition region. Quantitative regularity for the Navier-Stokes equations via spatial concentration https://zbmath.org/1472.35266 2021-11-25T18:46:10.358925Z "Barker, Tobias" https://zbmath.org/authors/?q=ai:barker.tobias "Prange, Christophe" https://zbmath.org/authors/?q=ai:prange.christophe The authors consider the Cauchy problem for the 3D incompressible Navier-Stokes equations on $$\mathbb R^3$$. The aim is to get quantitative estimates for blow-up conditions. They develop a strategy for obtaining new quantitative estimates of the Navier-Stokes equations. The main novelty is that the strategy allows obtaining local quantitative estimates. Compressible Navier-Stokes equations with heterogeneous pressure laws https://zbmath.org/1472.35267 2021-11-25T18:46:10.358925Z "Bresch, Didier" https://zbmath.org/authors/?q=ai:bresch.didier "Jabin, Pierre-Emmanuel" https://zbmath.org/authors/?q=ai:jabin.pierre-emmanuel "Wang, Fei" https://zbmath.org/authors/?q=ai:wang.fei.1|wang.fei.2 On the Serrin-type condition on one velocity component for the Navier-Stokes equations https://zbmath.org/1472.35268 2021-11-25T18:46:10.358925Z "Chae, D." https://zbmath.org/authors/?q=ai:chae.dasom|chae.david|chae.dongho|chae.donghyun|chae.dongsuk "Wolf, J." https://zbmath.org/authors/?q=ai:wolf.jorg|wolf.jochen.3|wolf.joseph-a.1|wolf.jana|wolf.jurgen|wolf.jan|wolf.jamison|wolf.judith|wolf.julia|wolf.jesse|wolf.john-p|wolf.joel-l|wolf.jochen.2|wolf.jared-r|wolf.j-benedict A new local regularity criterion for the three-dimensional Navier-Stokes equations is derived. As a consequence a Serrin-type regularity condition imposed on one component of the velocity vector is proved. Boundary stabilizability of the linearized compressible Navier-Stokes system in one dimension by backstepping approach https://zbmath.org/1472.35269 2021-11-25T18:46:10.358925Z "Chowdhury, Shirshendu" https://zbmath.org/authors/?q=ai:chowdhury.shirshendu "Dutta, Rajib" https://zbmath.org/authors/?q=ai:dutta.rajib "Majumdar, Subrata" https://zbmath.org/authors/?q=ai:majumdar.subrata Corrigendum to: On the spatial asymptotic decay of a suitable weak solution to the Navier-Stokes Cauchy problem'' https://zbmath.org/1472.35270 2021-11-25T18:46:10.358925Z "Crispo, F." https://zbmath.org/authors/?q=ai:crispo.francesca "Maremonti, P." https://zbmath.org/authors/?q=ai:maremonti.paolo Misprints in the authors' paper [ibid. 29, No. 4, 1355--1383 (2016, Zbl 1342.35212)] are corrected. Global regularity for solutions of the Navier-Stokes equation sufficiently close to being eigenfunctions of the Laplacian https://zbmath.org/1472.35271 2021-11-25T18:46:10.358925Z "Miller, Evan" https://zbmath.org/authors/?q=ai:miller.evan Summary: In this paper, we will prove a new, scale critical regularity criterion for solutions of the Navier-Stokes equation that are sufficiently close to being eigenfunctions of the Laplacian. This estimate improves previous regularity criteria requiring control on the $$\dot{H}^\alpha$$ norm of $$u,$$ with $$2\leq \alpha <\frac{5}{2}$$, to a regularity criterion requiring control on the $$\dot{H}^\alpha$$ norm multiplied by the deficit in the interpolation inequality for the embedding of $$\dot{H}^{\alpha -2}\cap\dot{H}^{\alpha}\hookrightarrow \dot{H}^{\alpha -1}$$. This regularity criterion suggests, at least heuristically, the possibility of some relationship between potential blowup solutions of the Navier-Stokes equation and the Kolmogorov-Obhukov spectrum in the theory of turbulence. Probabilistic representation for mild solution of the Navier-Stokes equations https://zbmath.org/1472.35272 2021-11-25T18:46:10.358925Z "Olivera, Christian" https://zbmath.org/authors/?q=ai:olivera.christian The author extends the approach by \textit{P. Constantin} and \textit{G. Iyer} [Commun. Pure Appl. Math. 61, No. 3, 330--345 (2008; Zbl 1156.60048); Ann. Appl. Probab. 21, No. 4, 1466--1492 (2011; Zbl 1246.76018)] to the Navier-Stokes system that involves a probabilistic Lagrangian representation formula making use of stochastic flows. These results are applicable to a more natural class of mild solutions instead of the case of previous works related to classical ones. Global well-posedness and long time decay of fractional Navier-Stokes equations in Fourier-Besov spaces https://zbmath.org/1472.35273 2021-11-25T18:46:10.358925Z "Xiao, Weiliang" https://zbmath.org/authors/?q=ai:xiao.weiliang "Chen, Jiecheng" https://zbmath.org/authors/?q=ai:chen.jiecheng "Fan, Dashan" https://zbmath.org/authors/?q=ai:fan.dashan "Zhou, Xuhuan" https://zbmath.org/authors/?q=ai:zhou.xuhuan Summary: We study the Cauchy problem of the fractional Navier-Stokes equations in critical Fourier-Besov spaces $$F \dot{B}_{p, q}^{1 - 2 \beta + 3 / p'}$$. Some properties of Fourier-Besov spaces have been discussed, and we prove a general global well-posedness result which covers some recent works in classical Navier-Stokes equations. Particularly, our result is suitable for the critical case $$\beta = 1 / 2$$. Moreover, we prove the long time decay of the global solutions in Fourier-Besov spaces. Decay estimates for three-dimensional Navier-Stokes equations with damping https://zbmath.org/1472.35274 2021-11-25T18:46:10.358925Z "Zhao, Xiaopeng" https://zbmath.org/authors/?q=ai:zhao.xiaopeng The Navier-Stokes system with the damping term $$|u|^{\beta-1}u$$ is studied in the whole space $${\mathbb R}^3$$. Decay rates for solutions of the Cauchy problem are derived, together with some auxiliary estimates of negative order Sobolev norms. Low Mach and thin domain limit for the compressible Euler system https://zbmath.org/1472.35275 2021-11-25T18:46:10.358925Z "Caggio, Matteo" https://zbmath.org/authors/?q=ai:caggio.matteo "Ducomet, Bernard" https://zbmath.org/authors/?q=ai:ducomet.bernard "Nečasová, Šárka" https://zbmath.org/authors/?q=ai:necasova.sarka "Tang, Tong" https://zbmath.org/authors/?q=ai:tang.tong Summary: We consider the compressible Euler system describing the motion of an ideal fluid confined to a straight layer $$\Omega_{\delta}=(0,\delta)\times\mathbb{R}^2,\delta >0$$. In the framework of \textit{dissipative measure-valued solutions}, we show the convergence to the strong solution of the 2D incompressible Euler system when the Mach number tends to zero and $$\delta\rightarrow 0$$. Finite-time singularity formation for an active scalar equation https://zbmath.org/1472.35276 2021-11-25T18:46:10.358925Z "Elgindi, Tarek" https://zbmath.org/authors/?q=ai:elgindi.tarek-mohamed "Ibrahim, Slim" https://zbmath.org/authors/?q=ai:ibrahim.slim "Shen, Shengyi" https://zbmath.org/authors/?q=ai:shen.shengyi Stable self-similar blow-up for a family of nonlocal transport equations https://zbmath.org/1472.35277 2021-11-25T18:46:10.358925Z "Elgindi, Tarek M." https://zbmath.org/authors/?q=ai:elgindi.tarek-mohamed "Ghoul, Tej-Eddine" https://zbmath.org/authors/?q=ai:ghoul.tej-eddine "Masmoudi, Nader" https://zbmath.org/authors/?q=ai:masmoudi.nader Summary: We consider a family of nonlocal problems that model the effects of transport and vortex stretching in the incompressible Euler equations. Using modulation techniques, we establish \textit{stable} self-similar blow-up near a family of known self-similar blow-up solutions. Two-dimensional pseudosteady flows around a sharp corner https://zbmath.org/1472.35278 2021-11-25T18:46:10.358925Z "Lai, Geng" https://zbmath.org/authors/?q=ai:lai.geng "Sheng, Wancheng" https://zbmath.org/authors/?q=ai:sheng.wancheng Summary: We consider two-dimensional (2D) pseudosteady flows around a sharp corner. This problem can be seen as a 2D Riemann initial and boundary value problem (IBVP) for the compressible Euler system. The initial state is a combination of a uniform flow in one quadrant and vacuum in the remaining domain. The boundary condition on the wall of the sharp corner is a slip boundary condition. By a self-similar transformation, the 2D Riemann IBVP is converted into a boundary value problem (BVP) for the 2D self-similar Euler system. Existence of global piecewise smooth (or Lipshitz-continuous) solutions to the BVP are obtained. One of the main difficulties for the global existence is that the type of the 2D self-similar Euler system is a priori unknown. In order to use the method of characteristic analysis, we establish some a priori estimates for the hyperboliciy of the system. The other main difficulty is that when the uniform flow is sonic or subsonic, the hyperbolic system becomes degenerate at the origin. Moreover, there is a multi-valued singularity at the origin. To solve this degenerate hyperbolic boundary value problem, we establish some uniform interior $$C^{0, 1}$$ norm estimates for the solutions of a sequence of regularized hyperbolic boundary value problems, and then use the Arzela-Ascoli theorem and a standard diagonal procedure to construct a global Lipschitz continuous solution. The method used here may also be used to construct continuous solutions of some other degenerate hyperbolic boundary value problems and sonic-supersonic flow problems. Global solutions to the compressible Euler equations with heat transport by convection around Dyson's isothermal affine solutions https://zbmath.org/1472.35279 2021-11-25T18:46:10.358925Z "Rickard, Calum" https://zbmath.org/authors/?q=ai:rickard.calum Summary: Global solutions to the compressible Euler equations with heat transport by convection in the whole space are shown to exist through perturbations of \textit{F. J. Dyson}'s isothermal affine solutions [J. Math. Mech. 18, 91--101 (1968; Zbl 0197.24501)]. This setting presents new difficulties because of the vacuum at infinity behavior of the density. In particular, the perturbation of isothermal motion introduces a Gaussian function into our stability analysis and a novel finite propagation result is proven to handle potentially unbounded terms arising from the presence of the Gaussian. Crucial stabilization-in-time effects of the background motion are mitigated through the use of this finite propagation result however and a careful use of the heat transport formulation in conjunction with new time weight manipulations are used to establish global existence. The heat transport by convection offers unique physical insights into the model and mathematically, we use a controlled spatial perturbation in the analysis of this feature of our system which leads us to exploit source term estimates as part of our techniques. Isentropic approximation of the compressible Euler equations in Besov spaces https://zbmath.org/1472.35280 2021-11-25T18:46:10.358925Z "Wu, Xinglong" https://zbmath.org/authors/?q=ai:wu.xinglong Summary: The article mainly studies the isentropic approximation of the compressible Euler equations in Besov space $$B^s_{2,r}(\mathbb{R}^N)$$, provided the initial entropy $$\tilde{S}_0(x)$$ changes closing a constant $$\delta$$ in the Besov spaces, which extends and improves the result in Sobolev space $$L^2(\mathbb{R}^N)$$ by \textit{J. Jia} and \textit{R. Pan} [J. Sci. Comput. 64, No. 3, 745--760 (2015; Zbl 1330.35305)]. Integrable systems, multicomponent twisted Heisenberg-Virasoro algebra and its central extensions https://zbmath.org/1472.35281 2021-11-25T18:46:10.358925Z "Wu, Yemo" https://zbmath.org/authors/?q=ai:wu.yemo "Xu, Xiurong" https://zbmath.org/authors/?q=ai:xu.xiurong "Zuo, Dafeng" https://zbmath.org/authors/?q=ai:zuo.dafeng Summary: Let $$\mathscr{D}_N$$ be the multicomponent twisted Heisenberg-Virasoro algebra. We compute the second continuous cohomology group with coefficients in $$\mathbb{C}$$ and study the bihamiltonian Euler equations associated to $$\mathscr{D}_N$$ and its central extensions. Time-periodic weak solutions to incompressible generalized Newtonian fluids https://zbmath.org/1472.35282 2021-11-25T18:46:10.358925Z "Abbatiello, Anna" https://zbmath.org/authors/?q=ai:abbatiello.anna Summary: In this study we are interested in the Navier-Stokes-like system for generalized viscous fluids whose viscosity has a power-structure with exponent $$q$$. We develop an existence theory of time-periodic three-dimensional flows. Space-time fractional diffusion-advection equation with Caputo derivative https://zbmath.org/1472.35283 2021-11-25T18:46:10.358925Z "Aguilar, José Francisco Gómez" https://zbmath.org/authors/?q=ai:gomez-aguilar.jose-francisco "Hernández, Margarita Miranda" https://zbmath.org/authors/?q=ai:hernandez.margarita-miranda Summary: An alternative construction for the space-time fractional diffusion-advection equation for the sedimentation phenomena is presented. The order of the derivative is considered as $$0 < \beta$$, $$\gamma \leq 1$$ for the space and time domain, respectively. The fractional derivative of Caputo type is considered. In the spatial case we obtain the fractional solution for the underdamped, undamped, and overdamped case. In the temporal case we show that the concentration has amplitude which exhibits an algebraic decay at asymptotically large times and also shows numerical simulations where both derivatives are taken in simultaneous form. In order that the equation preserves the physical units of the system two auxiliary parameters $$\sigma_x$$ and $$\sigma_t$$ are introduced characterizing the existence of fractional space and time components, respectively. A physical relation between these parameters is reported and the solutions in space-time are given in terms of the Mittag-Leffler function depending on the parameters $$\beta$$ and $$\gamma$$. The generalization of the fractional diffusion-advection equation in space-time exhibits anomalous behavior. Kelvin-Voigt equations with anisotropic diffusion, relaxation and damping: blow-up and large time behavior https://zbmath.org/1472.35284 2021-11-25T18:46:10.358925Z "Antontsev, S." https://zbmath.org/authors/?q=ai:antontsev.stanislav-nikolaevich "De Oliveira, H. B." https://zbmath.org/authors/?q=ai:de-oliveira.hermenegildo-borges "Khompysh, Kh." https://zbmath.org/authors/?q=ai:khompysh.kh|khompysh.khonatbek Summary: A nonlinear initial and boundary-value problem for the Kelvin-Voigt equations with anisotropic diffusion, relaxation and absorption/damping terms is considered in this work. The global and local unique solvability of the problem was established by the first author et al. [J. Math. Anal. Appl. 473, No. 2, 1122--1154 (2019; Zbl 1458.74026)]. In the present work, we show how all the anisotropic exponents of nonlinearity and all anisotropic coefficients should interact with the problem data for the solutions of this problem display exponential and polynomial time-decays. We also establish the conditions for the solutions of this problem to blow-up in a finite time in three different cases: problem without convection, full anisotropic problem, and the problem with isotropic relaxation. Near-critical reflection of internal waves https://zbmath.org/1472.35286 2021-11-25T18:46:10.358925Z "Bianchini, Roberta" https://zbmath.org/authors/?q=ai:bianchini.roberta "Dalibard, Anne-Laure" https://zbmath.org/authors/?q=ai:dalibard.anne-laure "Saint-Raymond, Laure" https://zbmath.org/authors/?q=ai:saint-raymond.laure Summary: Internal waves describe the (linear) response of an incompressible stably stratified fluid to small perturbations. The inclination of their group velocity with respect to the vertical is completely determined by their frequency. Therefore the reflection on a sloping boundary cannot follow Descartes' laws, and it is expected to be singular if the slope has the same inclination as the group velocity. We prove that in this critical geometry the weakly viscous and weakly nonlinear wave equations have actually a solution which is well approximated by the sum of the incident wave packet, a reflected second harmonic and some boundary layer terms. This result confirms the prediction by Dauxois and Young, and provides precise estimates on the time of validity of this approximation. Equations of symmetric boundary layer for the Ladyzhenskaya model of a viscous medium in the Crocco variables https://zbmath.org/1472.35287 2021-11-25T18:46:10.358925Z "Bulatova, Regina R." https://zbmath.org/authors/?q=ai:bulatova.regina-r "Samokhin, V. N." https://zbmath.org/authors/?q=ai:samokhin.vyacheslav-n "Chechkin, G. A." https://zbmath.org/authors/?q=ai:chechkin.gregory-a In this paper authors consider the system of boundary layer equations governing a viscous medium subject to the nonlinear rheological law in the sense of Ladyzhenskaya, $\left\{\begin{array}{l} \nu \left(1+3d\left(\frac{\partial u}{\partial y}\right)^2\right)\frac{\partial^2u}{\partial y^2}-u\frac{\partial u}{\partial x}-v\frac{\partial u}{\partial y}=U\frac{\partial U}{\partial x}\\ \frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0, \end{array}\right. \tag{1}$ Owing to the use of the Crocco transformation for reducing the system (1) to a single quasilinear equation, $\left\{\begin{array}{ll} \nu(1+3dU^2\omega^2)\omega^2\omega_{\eta\eta}-\eta U\omega_{\xi}+(\eta^2 -1)U_{\xi}\omega_{\eta}-\eta U_{\xi}\omega +6\nu dU^2\omega^{2}_{\eta}\omega^{3}=0 & \hbox{in } 0<\xi<X, 0<\eta<1\\ \omega(\xi,1)=0, \left(\nu(1+3dU^2\omega^2)\omega\omega_{\eta}-v_{0}(\xi)\omega+U_{\xi}\right)|_{\eta=0}=0 & \hbox{in } 0<\xi<X, \end{array}\right. \tag{2}$ which becomes possible to study both stationary and nonstationary boundary layers. The authors obtain asymptotic estimates for the solution. In comparison, the von Mises transformation can only handle stationary boundary conditions. Global well-posedness of the 2-d magnetic Prandtl model in the Prandtl-Hartmann regime https://zbmath.org/1472.35288 2021-11-25T18:46:10.358925Z "Chen, Dongxiang" https://zbmath.org/authors/?q=ai:chen.dongxiang "Ren, Siqi" https://zbmath.org/authors/?q=ai:ren.siqi "Wang, Yuxi" https://zbmath.org/authors/?q=ai:wang.yuxi "Zhang, Zhifei" https://zbmath.org/authors/?q=ai:zhang.zhifei Summary: In this paper, we prove the global well-posedness of the 2-D magnetic Prandtl model in the mixed Prandtl/Hartmann regime when the initial data is a small perturbation of the Hartmann layer in Sobolev space. Rogue wave for the (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation https://zbmath.org/1472.35289 2021-11-25T18:46:10.358925Z "Chen, Hanlin" https://zbmath.org/authors/?q=ai:chen.hanlin "Xu, Zhenhui" https://zbmath.org/authors/?q=ai:xu.zhenhui "Dai, Zhengde" https://zbmath.org/authors/?q=ai:dai.zhengde Summary: A new method, homoclinic (heteroclinic) breather limit method (HBLM), for seeking rogue wave solution to nonlinear evolution equation (NEE) is proposed. (3+1)-dimensional Yu-Toda-Sasa-Fukuyama (YTSF) equation is used as an example to illustrate the effectiveness of the suggested method. A new family of two-wave solution, rational breather wave solution, is obtained by extended homoclinic test method, and it is just a rogue wave solution. This result shows rogue wave can come from extreme behavior of breather solitary wave for (3+1)-dimensional nonlinear wave fields. Erratum to: On the nonlocal Cahn-Hilliard-Brinkman and Cahn-Hilliard-Hele-Shaw systems'' https://zbmath.org/1472.35290 2021-11-25T18:46:10.358925Z "Della Porta, Francesco" https://zbmath.org/authors/?q=ai:della-porta.francesco "Grasselli, Maurizio" https://zbmath.org/authors/?q=ai:grasselli.maurizio From the text: In this note, we want to highlight and correct an error in our paper [ibid. 15, No. 2, 299--317 (2016; Zbl 1334.35226), Prop. 2.4] which has consequences on the proof of [loc. cit., Thm. 6.1]. Referring to [loc. cit.] for the notation, the correct statement in [loc. cit., Prop. 2.4] is that $$\mathbf{u} \in L^2(0, T; [H^1(\Omega)]^d)$$ and not $$\mathbf{u} \in L^2(0,T; V_{div})$$ as incorrectly written. Therefore we have $$\mathbf{v}(t)=\mathbf{u}(t)- \mathbf{u}_\nu(t)\in [H^1(\Omega)]^d$$ for almost any $$t\in (0,T)$$ and the boundary trace of $$\mathbf{v}(t)$$ is not necessarily zero. Estimates as the one in [loc. cit., Thm. 6.1] are in general difficult to obtain due to the presence of a boundary layer. A common approach to obtain such estimates is to introduce a corrector, so that the difference between the solution and the corrector itself has zero trace. Here we devise a simpler way to obtain an estimate quite similar to the one reported in [loc. cit., Thm. 6.1] without introducing a corrector. However, the order of convergence with respect to $$\nu$$ is no longer $$\frac12$$. Enhanced diffusivity in perturbed senile reinforced random walk models https://zbmath.org/1472.35291 2021-11-25T18:46:10.358925Z "Dinh, Thu" https://zbmath.org/authors/?q=ai:dinh.thu "Xin, Jack" https://zbmath.org/authors/?q=ai:xin.jack-x Summary: We consider diffusivity of random walks with transition probabilities depending on the number of consecutive traversals of the last traversed edge, the so called senile reinforced random walk (SeRW). In one dimension, the walk is known to be sub-diffusive with identity reinforcement function. We perturb the model by introducing a small probability $$\delta$$ of escaping the last traversed edge at each step. The perturbed SeRW model is diffusive for any $$\delta>0$$, with enhanced diffusivity $$(\gg O(\delta^2))$$ in the small $$\delta$$ regime. We further study stochastically perturbed SeRW models by having the last edge escape probability of the form $$\delta\xi_n$$ with $$\xi_n$$'s being independent random variables. Enhanced diffusivity in such models are logarithmically close to the so called residual diffusivity (positive in the zero $$\delta$$ limit), with diffusivity between $$O(\frac{1}{|\log\delta|})$$ and $$O(\frac{1}{\log |\log\delta|})$$. Finally, we generalize our results to higher dimensions where the unperturbed model is already diffusive. The enhanced diffusivity can be as much as $$O(\log^{-2}\delta)$$. Stability and exponential decay for the 2D anisotropic Boussinesq equations with horizontal dissipation https://zbmath.org/1472.35292 2021-11-25T18:46:10.358925Z "Dong, Boqing" https://zbmath.org/authors/?q=ai:dong.boqing "Wu, Jiahong" https://zbmath.org/authors/?q=ai:wu.jiahong "Xu, Xiaojing" https://zbmath.org/authors/?q=ai:xu.xiaojing "Zhu, Ning" https://zbmath.org/authors/?q=ai:zhu.ning Summary: The hydrostatic equilibrium is a prominent topic in fluid dynamics and astrophysics. Understanding the stability of perturbations near the hydrostatic equilibrium of the Boussinesq system helps gain insight into certain weather phenomena. The 2D Boussinesq system focused here is anisotropic and involves only horizontal dissipation and horizontal thermal diffusion. Due to the lack of the vertical dissipation, the stability and precise large-time behavior problem is difficult. When the spatial domain is $$\mathbb{R}^2$$, the stability problem in a Sobolev setting remains open. When the spatial domain is $$\mathbb{T}\times \mathbb{R}$$, this paper solves the stability problem and specifies the precise large-time behavior of the perturbation. By decomposing the velocity $$u$$ and temperature $$\theta$$ into the horizontal average $$(\bar{u}, \bar{\theta})$$ and the corresponding oscillation $$(\widetilde{u},\widetilde{\theta})$$, and deriving various anisotropic inequalities, we are able to establish the global stability in the Sobolev space $$H^2$$. In addition, we prove that the oscillation $$(\widetilde{u},\widetilde{\theta})$$ decays exponentially to zero in $$H^1$$ and $$(u,\theta)$$ converges to $$(\bar{u}, \bar{\theta})$$. This result reflects the stratification phenomenon of buoyancy-driven fluids. Blow up criterion for the 2D full compressible Navier-Stokes equations involving temperature in critical spaces https://zbmath.org/1472.35293 2021-11-25T18:46:10.358925Z "Fan, Jie" https://zbmath.org/authors/?q=ai:fan.jie "Jiu, Quansen" https://zbmath.org/authors/?q=ai:jiu.quansen "Wang, Yanqing" https://zbmath.org/authors/?q=ai:wang.yanqing "Xiao, Yuelong" https://zbmath.org/authors/?q=ai:xiao.yuelong The authors study the structural stability of conical shocks in the three-dimensional steady isothermal supersonic flows past Lipschitz perturbed cones with small enough vertex angles (less than the critical angle). The problem is symmetrical with respect to the cone's axes, so there remain just two spatial variables. The Bernoulli law serves as the equation of state. The incoming flow left to the obstacle has fixed constant density and supersonic velocity (parallel to the axes of symmetry). The cone is perturbed, with small perturbation in the sense of bounded variation. The main result is existence of global entropy solutions of bounded variation and asymptotic stability of this solution. On the long-time behavior of dissipative solutions to models of non-Newtonian compressible fluids https://zbmath.org/1472.35294 2021-11-25T18:46:10.358925Z "Feireisl, Eduard" https://zbmath.org/authors/?q=ai:feireisl.eduard "Kwon, Young-Sam" https://zbmath.org/authors/?q=ai:kwon.young-sam "Novotný, Antonín" https://zbmath.org/authors/?q=ai:novotny.antonin Summary: We identify a class \textit{maximal} dissipative solutions to models of compressible viscous fluids that maximize the energy dissipation rate. Then we show that any maximal dissipative solution approaches an equilibrium state for large times. The vanishing surface tension limit of the Muskat problem https://zbmath.org/1472.35295 2021-11-25T18:46:10.358925Z "Flynn, Patrick T." https://zbmath.org/authors/?q=ai:flynn.patrick-t "Nguyen, Huy Quang" https://zbmath.org/authors/?q=ai:nguyen.huy-quang The authors investigate the Muskat problem with surface tension. They proved that for any subcritical data satisfying the Rayleigh-Taylor condition, solutions of the Muskat problem with surface tension converge to the unique solution of the Muskat problem without surface tension locally in time. When the initial curvature is square integrable, they obtained the convergence with optimal rate. Erratum to: Volume viscosity and internal energy relaxation: symmetrization and Chapman-Enskog expansion'' https://zbmath.org/1472.35297 2021-11-25T18:46:10.358925Z "Giovangigli, Vincent" https://zbmath.org/authors/?q=ai:giovangigli.vincent "Yong, Wen-An" https://zbmath.org/authors/?q=ai:yong.wen-an Erratum to the authors' paper [ibid. 8, No. 1, 79--116 (2015; Zbl 1310.35196)]. Partial regularity of suitable weak solutions of the Navier-Stokes-Planck-Nernst-Poisson equation https://zbmath.org/1472.35298 2021-11-25T18:46:10.358925Z "Gong, Huajun" https://zbmath.org/authors/?q=ai:gong.huajun "Wang, Changyou" https://zbmath.org/authors/?q=ai:wang.changyou "Zhang, Xiaotao" https://zbmath.org/authors/?q=ai:zhang.xiaotao Large-time behavior of magnetohydrodynamics with temperature-dependent heat-conductivity https://zbmath.org/1472.35299 2021-11-25T18:46:10.358925Z "Huang, Bin" https://zbmath.org/authors/?q=ai:huang.bin "Shi, Xiaoding" https://zbmath.org/authors/?q=ai:shi.xiaoding "Sun, Ying" https://zbmath.org/authors/?q=ai:sun.ying Summary: For the strong solutions to the equations of a planar magnetohydrodynamic compressible flow with the heat conductivity proportional to a nonnegative power of the temperature, we first prove that both the specific volume and the temperature are proved to be bounded from below and above independently of time. Then, we also show that the global strong solution is nonlinearly exponentially stable as time tends to infinity. This is the first result obtaining the exponential stability behavior of strong solutions to the equations of a planar magnetohydrodynamic compressible flow without any smallness conditions on the data. Our result can be regarded as a natural generalization of the previous ones for the compressible Navier-Stokes system to MHD system with either constant heat-conductivity or nonlinear and temperature-depending heat-conductivity. As a direct consequence, it is shown that the global strong solution to the constant heat-conductivity MHD system whose existence is obtained by \textit{A. V. Kazhikhov} [A priori estimates for the solutions of equations of magnetic gas dynamics'' (Russian), in: Boundary-value problems for equations of mathematical physics. Krasnoyarsk. 84--94 (1987)] is nonlinearly exponentially stable. Weak solutions of Hopf type to 2D Maxwell flows with infinite number of relaxation times https://zbmath.org/1472.35300 2021-11-25T18:46:10.358925Z "Karazeeva, N. A." https://zbmath.org/authors/?q=ai:karazeeva.n-a Summary: A system of equations describing the motion of fluids of Maxwell type is considered: $\frac{\partial }{\partial t}v +v \cdot \nabla v -\underset{0}{\overset{t}{\int }}K\left(t-\tau \right) d\tau +\nabla p=f\left(x,t\right), \quad\mathrm{div}v =0.$ Here $$K(t)$$ is an exponential series $$K(t)=\sum \limits_{s=1}^{\infty }{\beta}_s{e}^{-{\alpha}_st}$$. The existence of a weak solution for the initial boundary value problem $v (x,0)=v_0(x),\quad v \cdot n|_{\partial \Omega }=0,\quad rot v |_{\partial \Omega }=0$ is proved. Some regularity criteria for the 3D generalized Navier-Stokes equations https://zbmath.org/1472.35301 2021-11-25T18:46:10.358925Z "Kim, Jae-Myoung" https://zbmath.org/authors/?q=ai:kim.jaemyoung Generalizations and improvements of Serrin's type regularity criterion for weak solutions of the three-dimensional Navier-Stokes system with the dissipation defined by fractional Laplacians are shown. These are conditions expressed in terms of the vorticity of solutions using Lorentz spaces. Global existence and time decay estimate of solutions to the compressible Navier-Stokes-Korteweg system under critical condition https://zbmath.org/1472.35302 2021-11-25T18:46:10.358925Z "Kobayashi, Takayuki" https://zbmath.org/authors/?q=ai:kobayashi.takayuki "Tsuda, Kazuyuki" https://zbmath.org/authors/?q=ai:tsuda.kazuyuki Summary: In this research, we study the global existence of solutions to the compressible Navier-Stokes-Korteweg system around a constant state. This system describes liquid-vapor type two-phase flow with a phase transition with diffuse interface. Previous works assume that pressure is a monotone function for change of density similarly to the usual compressible Navier-Stokes system. On the other hand, due to phase transition the pressure is in fact non-monotone function, and the linearized system loses symmetry in a critical case such that the derivative of pressure is 0 at the given constant state. We show that global $$L^2$$ solutions are available for the critical case of small data, whose momentum is in its derivative form, and obtain parabolic type decay rate of the solutions. This is proved based on the decomposition of solutions to a low frequency part and a high frequency part. Weak solutions for a sixth order Cahn-Hilliard type equation with degenerate mobility https://zbmath.org/1472.35303 2021-11-25T18:46:10.358925Z "Liu, Aibo" https://zbmath.org/authors/?q=ai:liu.aibo "Liu, Changchun" https://zbmath.org/authors/?q=ai:liu.chein-shan Summary: We study an initial-boundary problem for a sixth order Cahn-Hilliard type equation, which arises in oil-water-surfactant mixtures. An existence result for the problem with a concentration dependent diffusional mobility in three space dimensions is presented. Well-posedness of the MHD boundary layer system in Gevrey function space without structural assumption https://zbmath.org/1472.35304 2021-11-25T18:46:10.358925Z "Li, Wei-Xi" https://zbmath.org/authors/?q=ai:li.weixi "Yang, Tong" https://zbmath.org/authors/?q=ai:yang.tong.1|yang.tong Exact solutions and conservation laws of the Drinfel'd-Sokolov-Wilson system https://zbmath.org/1472.35306 2021-11-25T18:46:10.358925Z "Matjila, Catherine" https://zbmath.org/authors/?q=ai:matjila.catherine "Muatjetjeja, Ben" https://zbmath.org/authors/?q=ai:muatjetjeja.ben "Khalique, Chaudry Masood" https://zbmath.org/authors/?q=ai:khalique.chaudry-masood Summary: We study the Drinfel'd-Sokolov-Wilson system, which was introduced as a model of water waves. Firstly we obtain exact solutions of this system using the $$(G' / G)$$-expansion method. In addition to exact solutions we also construct conservation laws for the underlying system using Noether's approach. Global existence and the decay of solutions to the Prandtl system with small analytic data https://zbmath.org/1472.35307 2021-11-25T18:46:10.358925Z "Paicu, Marius" https://zbmath.org/authors/?q=ai:paicu.marius "Zhang, Ping" https://zbmath.org/authors/?q=ai:zhang.ping.3 Summary: In this paper, we prove the global existence and the large time decay estimate of solutions to Prandtl system with small initial data, which is analytical in the tangential variable. The key ingredient used in the proof is to derive a sufficiently fast decay-in-time estimate of some weighted analytic energy estimate to a quantity, which consists of a linear combination of the tangential velocity with its primitive one, and which basically controls the evolution of the analytical radius to the solutions. Our result can be viewed as a global-in-time Cauchy-Kowalevsakya result for the Prandtl system with small analytical data, which in particular improves the previous result in [\textit{M. Ignatova} and \textit{V. Vicol}, ibid. 220, No. 2, 809--848 (2016; Zbl 1334.35238)] concerning the almost global well-posedness of a two-dimensional Prandtl system. On evolutionary inverse problems for mathematical models of heat and mass transfer https://zbmath.org/1472.35309 2021-11-25T18:46:10.358925Z "Pyatkov, Sergeĭ Grigor'evich" https://zbmath.org/authors/?q=ai:pyatkov.sergei-g Summary: This article is a survey. The results on well-posedness of inverse problems for mathematical models of heat and mass transfer are presented. The unknowns are the coefficients of a system or the right-hand side (the source function). The overdetermination conditions are values of a solution of some manifolds or integrals of a solution with weight over the spatial domain. Two classes of mathematical models are considered. The former includes the Navier-Stokes system, the parabolic equations for the temperature of a fluid, and the parabolic system for concentrations of admixtures. The right-hand side of the system for concentrations is unknown and characterizes the volumetric density of sources of admixtures in a fluid. The unknown functions depend on time and some part of spacial variables and occur in the right-hand side of the parabolic system for concentrations. The latter class is just a parabolic system of equations, where the unknowns occur in the right-hand side and the system as coefficients. The well-posedness questions for these problems are examined, in particular, existence and uniqueness theorems as well as stability estimates for solutions are exposed. Hydrodynamic entrance region in a flat porous channel with a pressure head isothermal laminar flow of a Newtonian medium https://zbmath.org/1472.35310 2021-11-25T18:46:10.358925Z "Ryazhskikh, Aleksandr Viktorovich" https://zbmath.org/authors/?q=ai:ryazhskikh.aleksandr-viktorovich "Nikolenko, Aleksandr Vladimirovich" https://zbmath.org/authors/?q=ai:nikolenko.aleksandr-vladimirovich "Konovalov, Dmitriĭ Al'bertovich" https://zbmath.org/authors/?q=ai:konovalov.dmitrii-albertovich "Ryazhskih, Viktor Ivanovich" https://zbmath.org/authors/?q=ai:ryazhskih.viktor-ivanovich "Keller, Alevtina Viktorovna" https://zbmath.org/authors/?q=ai:keller.alevtina-viktorovna Summary: The problem of the hydrodynamic initial section of an isothermal pressure laminar flow of a Newtonian fluid in a horizontal flat porous channel of semi-infinite length, formulated in the initial-boundary formulation for the Darcy-Brinkman equation with partial consideration of the convective component, provided that the pressure depends only on the axial coordinate, is analytically solved. For a channel without a porous matrix, the results correlate with the classical data. An explicit relation was proposed for calculating the length of the hydrodynamic initial section, which does not contradict the results based on macroscopic boundary layer concepts. A remark on the regularity criterion for the 3D Boussinesq equations involving the pressure gradient https://zbmath.org/1472.35312 2021-11-25T18:46:10.358925Z "Zhang, Zujin" https://zbmath.org/authors/?q=ai:zhang.zujin Summary: We consider the three-dimensional Boussinesq equations and obtain a regularity criterion involving the pressure gradient in the Morrey-Companato space $$M_{p, q}$$. This extends and improves the result of \textit{S. Gala} [Appl. Anal. 92, No. 1, 96--103 (2013; Zbl 1284.35313)] for the Navier-Stokes equations. Remarks on the regularity criteria for the axisymmetric MHD system https://zbmath.org/1472.35313 2021-11-25T18:46:10.358925Z "Zhang, Zujin" https://zbmath.org/authors/?q=ai:zhang.zujin "Zhang, Yali" https://zbmath.org/authors/?q=ai:zhang.yali Summary: We show several weighted regularity criteria for the axisymmetric solutions to the three-dimensional magnetohydrodynamic equations, involving $$u^r, u^z; u^r, b^r$$, $$\partial_ru^z, \partial_rb^z$$; $$u^r,b^r, \partial_zu^\theta$$, $$\partial_zb^\theta; u^r, b^r$$, $$\partial_ru^\theta,\partial_rb^\theta$$; or $$\omega^\theta$$, where $$u^r,u^\theta,u^z$$ are the angular, swirl and axial components of the velocity respectively and $$\omega^\theta$$ denotes the swirl component of the vorticity. Global strong solution to the nonhomogeneous Bénard system with large initial data and vacuum https://zbmath.org/1472.35314 2021-11-25T18:46:10.358925Z "Zhong, Xin" https://zbmath.org/authors/?q=ai:zhong.xin Summary: We establish a unique global strong solution for nonhomogeneous Bénard system with zero density at infinity on the whole two-dimensional (2D) space. In particular, the initial data can be arbitrarily large and the initial density can contain vacuum states and even have compact support. Our method relies heavily on the structure of the system under consideration and spatial dimension. Global strong solution of nonhomogeneous Bénard system with large initial data and vacuum in a bounded domain https://zbmath.org/1472.35315 2021-11-25T18:46:10.358925Z "Zhong, Xin" https://zbmath.org/authors/?q=ai:zhong.xin Summary: We study an initial boundary value problem of two-dimensional nonhomogeneous Bénard system with nonnegative density. We derive the global existence of a unique strong solution. In particular, the initial data can be arbitrarily large. Whitham equations and phase shifts for the Korteweg-de Vries equation https://zbmath.org/1472.35330 2021-11-25T18:46:10.358925Z "Ablowitz, Mark J." https://zbmath.org/authors/?q=ai:ablowitz.mark-j "Cole, Justin T." https://zbmath.org/authors/?q=ai:cole.justin-t "Rumanov, Igor" https://zbmath.org/authors/?q=ai:rumanov.igor Summary: The semi-classical Korteweg-de Vries equation for step-like data is considered with a small parameter in front of the highest derivative. Using perturbation analysis, Whitham theory is constructed to the higher order. This allows the order one phase and the complete leading-order solution to be obtained; the results are confirmed by extensive numerical calculations. Dynamics of a 3D Benjamin-Bona-Mahony equations with sublinear operator https://zbmath.org/1472.35345 2021-11-25T18:46:10.358925Z "Zhao, Mingxia" https://zbmath.org/authors/?q=ai:zhao.mingxia "Yang, Xin-Guang" https://zbmath.org/authors/?q=ai:yang.xinguang "Yan, Xingjie" https://zbmath.org/authors/?q=ai:yan.xingjie "Cui, Xiaona" https://zbmath.org/authors/?q=ai:cui.xiaona Summary: This paper is concerned with the tempered pullback dynamics for a three dimensional Benjamin-Bona-Mahony equations with sublinear operator on bounded domain, which describes the long time behavior for long waves model in shallow water with friction. By virtue of a new retarded Gronwall inequality, and using the energy equation method from \textit{J. M. Ball} [Discrete Contin. Dyn. Syst. 10, No. 1--2, 31--52 (2004; Zbl 1056.37084)] to achieve asymptotic compactness for solution process, the minimal family of pullback attractors has been obtained, which reduces a single trajectory under a sufficient condition. Dynamics of nearly parallel vortex filaments for the Gross-Pitaevskii equation https://zbmath.org/1472.35358 2021-11-25T18:46:10.358925Z "Jerrard, R. L." https://zbmath.org/authors/?q=ai:jerrard.robert-leon "Smets, D." https://zbmath.org/authors/?q=ai:smets.didier Summary: \textit{R. Klein} et al. [J. Fluid Mech. 288, 201--248 (1995; Zbl 0846.76015)] have formally derived a simplified asymptotic motion law for the evolution of nearly parallel vortex filaments in the context of the three dimensional Euler equation for incompressible fluids. In the present work, we rigorously derive the corresponding asymptotic motion law in the context of the Gross-Pitaevskii equation. How to smooth a crinkled map of space-time: Uhlenbeck compactness for $$L^\infty$$ connections and optimal regularity for general relativistic shock waves by the Reintjes-Temple equations https://zbmath.org/1472.35377 2021-11-25T18:46:10.358925Z "Reintjes, Moritz" https://zbmath.org/authors/?q=ai:reintjes.moritz "Temple, Blake" https://zbmath.org/authors/?q=ai:temple.blake Summary: We present the authors' new theory of the RT-equations (regularity transformation' or Reintjes-Temple' equations), nonlinear elliptic partial differential equations which determine the coordinate transformations which smooth connections $$\Gamma$$ to optimal regularity, one derivative smoother than the Riemann curvature tensor Riem $$( \Gamma )$$. As one application we extend Uhlenbeck compactness from Riemannian to Lorentzian geometry; and as another application we establish that regularity singularities at general relativistic shock waves can always be removed by coordinate transformation. This is based on establishing a general multi-dimensional existence theory for the RT-equations by application of elliptic regularity theory in $$L^p$$ spaces. The theory and results announced in this paper apply to arbitrary $$L^\infty$$ connections on the tangent bundle $$T \mathcal{M}$$ of arbitrary manifolds $$\mathcal{M}$$, including Lorentzian manifolds of general relativity. Mathematical modeling of a temperature-sensitive and tissue-mimicking gel matrix: solving the Flory-Huggins equation for an elastic ternary mixture system https://zbmath.org/1472.35383 2021-11-25T18:46:10.358925Z "Sung, Baeckkyoung" https://zbmath.org/authors/?q=ai:sung.baeckkyoung Summary: Programmed to retain active responsivity to environmental stimuli, diverse types of synthetic gels have been attracting interests regarding various applications, such as elastomer biodevices. In a different approach, when the gels are made of tissue-derived biopolymers, they can act as an artificial extracellular matrix (ECM) for use as soft implants in medicine. To explore the physical properties of hydrogels in terms of statistical thermodynamics, the mean-field Flory-Huggins-Rehner theory has long been used with various analytical and numerical modifications. Here, we suggest a novel mathematical model on the phase transition of a biological hybrid gel that is sensitive to ambient temperature. To mimic acellular soft tissues, the ECM-like hydrogel is modeled as a network of biopolymers, such as type I collagen and gelatin, which are covalently crosslinked and swollen in aqueous solvents. Within the network, thermoresponsive synthetic polymer chains are doped by chemical conjugation. Based on the Flory-Huggins-Rehner framework, our analytical model phenomenologically illustrates a well-characterized volume phase behavior of engineered tissue mimics as a function of temperature by formulating the ternary mixing free energy of the polymer-solvent system and by generalizing the elastic free energy term. With this formalism, the decoupling of the Flory-Huggins interaction parameter between the thermoresponsive polymer and ECM biopolymer enables deriving a simple steady-state formula for the volume phase transition as a function of the structural and compositional parameters. We show that the doping ratio of thermoresponsive polymers and the Flory-Huggins interaction parameter between biopolymer and water affect the phase transition temperature of the ECM-like gels. Strong Feller property of the magnetohydrodynamics system forced by space-time white noise https://zbmath.org/1472.35389 2021-11-25T18:46:10.358925Z "Yamazaki, Kazuo" https://zbmath.org/authors/?q=ai:yamazaki.kazuo Invariant measures and global well posedness for the SQG equation https://zbmath.org/1472.35392 2021-11-25T18:46:10.358925Z "Földes, Juraj" https://zbmath.org/authors/?q=ai:foldes.juraj "Sy, Mouhamadou" https://zbmath.org/authors/?q=ai:sy.mouhamadou Summary: We construct an invariant measure $$\mu$$ for the Surface Quasi-Geostrophic (SQG) equation and show that almost all functions in the support of $$\mu$$ are initial conditions of global, unique solutions of SQG that depend continuously on the initial data. In addition, we show that the support of $$\mu$$ is infinite dimensional, meaning that it is not locally a subset of any compact set with finite Hausdorff dimension. Also, there are global solutions that have arbitrarily large initial condition. The measure a $$\mu$$ is obtained via fluctuation-dissipation method, that is, as a limit of invariant measures for stochastic SQG with a carefully chosen dissipation and random forcing. Local well-posedness of strong solutions to the three-dimensional compressible primitive equations https://zbmath.org/1472.35393 2021-11-25T18:46:10.358925Z "Liu, Xin" https://zbmath.org/authors/?q=ai:liu.xin.4|liu.xin.3|liu.xin.2|liu.xin|liu.xin.1|liu.xin.5 "Titi, Edriss S." https://zbmath.org/authors/?q=ai:titi.edriss-saleh Summary: This work is devoted to establishing the local-in-time well-posedness of strong solutions to the three-dimensional compressible primitive equations of atmospheric dynamics. It is shown that strong solutions exist, are unique, and depend continuously on the initial data, for a short time in two cases: with gravity but without vacuum, and with vacuum but without gravity. Toward understanding the boundary propagation speeds in tumor growth models https://zbmath.org/1472.35404 2021-11-25T18:46:10.358925Z "Liu, Jian-Guo" https://zbmath.org/authors/?q=ai:liu.jian-guo "Tang, Min" https://zbmath.org/authors/?q=ai:tang.min "Wang, Li" https://zbmath.org/authors/?q=ai:wang.li.6 "Zhou, Zhennan" https://zbmath.org/authors/?q=ai:zhou.zhennan Free boundary problem in a polymer solution model https://zbmath.org/1472.35423 2021-11-25T18:46:10.358925Z "Petrova, A. G." https://zbmath.org/authors/?q=ai:petrova.anna-georgevna "Pukhnachev, V. V." https://zbmath.org/authors/?q=ai:pukhnachov.vladislav-v The authors consider the integro-differential equation $\frac{\partial w}{\partial t}+\frac{\partial w}{\partial y}\int_{0}^{y}w(z,t)dz-w^{2}=\frac{\partial^{2}w}{\partial y^{2}}+\gamma (\frac{\partial^{3}w}{\partial y^{2}\partial t}+\frac{\partial^{3}w}{\partial y^{3}}\int_{0}^{y}w(z,t)dz- \frac{\partial^{2}w}{\partial y^{2}}),$ posed in the domain $$\Omega_{T} = \{y,t:0 < y < h(t)$$, $$0\leq t\leq T\}$$. This model accounts for the flow of a mixture of water and polymer. This equation is completed with: $$\frac{dh}{dt}=\int_{0}^{h}w(y,t)dy$$. The boundary conditions $$w(0,t)=0$$ and $$\frac{\partial w}{\partial y}+\gamma (\frac{\partial^{2}w}{\partial y\partial t}+ \frac{\partial^{2}w}{\partial y^{2}}\int_{0}^{h}w(y,t)dy-w\frac{\partial w}{\partial y})(h(t),t)=0$$ are added, together with the initial conditions $$w(y,0)=w_{0}(y)$$, $$0\leq y\leq 1$$, $$h(0)=1$$. Here $$\gamma >0$$ is a constant and $$w_{0}$$ is a smooth ($$C^{3}$$) function of $$y$$ satisfying the conditions $$w_{0}(0)=w_{0}^{\prime}(1)=0$$. The first main result proves the existence of a local in time strong solution ($$h\in C^{1}([0,t^{\ast}])$$, $$w\in C^{3,1}([0,h(t)]\times \lbrack 0,t^{\ast}])$$) to this problem. If the initial condition further satisfies $$w_{0}(y)\leq 0$$, $$w_{0}(y)-\gamma w_{0}^{\prime \prime}(y)\leq 0$$, the authors prove the existence of a classical solution $$h\in C^{1}([0,T])$$, $$w\in C^{3,1}([0,h(t)]\times \lbrack 0,T])$$ to the above problem. Both existence results are obtained through appropriate transformations and using Schauder's theorem. The authors then consider the case where $$\gamma$$ tends to 0 and they observe that the problem turns into that of the deformation of a strip of viscous fluid. They here prove that the solution to this problem is destructed in finite time. They finally introduce asymptotic expansions with respect to $$\gamma$$ and they express the second term of this asymptotic expansion. Existence and regularity of inverse problem for the nonlinear fractional Rayleigh-Stokes equations https://zbmath.org/1472.35448 2021-11-25T18:46:10.358925Z "Bao, Ngoc Tran" https://zbmath.org/authors/?q=ai:bao.ngoc-tran "Hoang, Luc Nguyen" https://zbmath.org/authors/?q=ai:hoang.luc-nguyen "Van, Au Vo" https://zbmath.org/authors/?q=ai:van.au-vo "Nguyen, Huy Tuan" https://zbmath.org/authors/?q=ai:nguyen-huy-tuan. "Zhou, Yong" https://zbmath.org/authors/?q=ai:zhou.yong Summary: This paper investigates an inverse problem for fractional Rayleigh-Stokes equations with nonlinear source. The fractional derivative in time is taken in the sense of Riemann-Liouville. The proposed problem has many applications in some non-Newtonian fluids. We obtain some results on the existence and regularity of mild solutions. On the identification of the nonlinearity parameter in the Westervelt equation from boundary measurements https://zbmath.org/1472.35453 2021-11-25T18:46:10.358925Z "Kaltenbacher, Barbara" https://zbmath.org/authors/?q=ai:kaltenbacher.barbara "Rundell, William" https://zbmath.org/authors/?q=ai:rundell.william Summary: We consider an undetermined coefficient inverse problem for a nonlinear partial differential equation occurring in high intensity ultrasound propagation as used in acoustic tomography. In particular, we investigate the recovery of the nonlinearity coefficient commonly labeled as $$B/A$$ in the literature which is part of a space dependent coefficient $$\kappa$$ in the Westervelt equation governing nonlinear acoustics. Corresponding to the typical measurement setup, the overposed data consists of time trace measurements on some zero or one dimensional set $$\Sigma$$ representing the receiving transducer array. After an analysis of the map from $$\kappa$$ to the overposed data, we show injectivity of its linearisation and use this as motivation for several iterative schemes to recover $$\kappa$$. Numerical simulations will also be shown to illustrate the efficiency of the methods. $$L^q$$-solvability for an equation of viscoelasticity in power type material https://zbmath.org/1472.45002 2021-11-25T18:46:10.358925Z "de Andrade, Bruno" https://zbmath.org/authors/?q=ai:de-andrade.bruno "Silva, Clessius" https://zbmath.org/authors/?q=ai:silva.clessius "Viana, Arlúcio" https://zbmath.org/authors/?q=ai:viana.arlucio The authors study the existence, uniqueness, regularity, continuous dependence, unique continuation, a blow-up alternative for mild solutions, and global well-posedness of the nonlinear Volterra equation $u_t = \int_0^t dg_\alpha(s) \Delta u(t-s,x)- \nabla p +h - (u\cdot \nabla u),\quad \textrm{div}(u)=0,$ in $$(0,\infty)\times \Omega$$, where $$u=0$$ on $$(0,\infty)\times \partial \Omega$$ and $$u(0,x)=u_0(x)$$ in $$\Omega$$. Here the kernel is taken to be $$g_\alpha (t)= t^{\alpha}/\Gamma(\alpha+1)$$ with $$0\leq \alpha <1$$ and a mild solution is a solution to the equation $u(t)= S_\alpha (tA)u_0 + \int_0^t S_\alpha((t-s)A)(F(u)(s)+Ph(s))\, ds,$ where $$P$$ is the Leray projection on divergence free functions, $$F(u)= P(u\cdot \nabla)u$$, $$A=P\Delta$$ and $S_\alpha(tA)= \frac 1{2\pi i} \int_{Ha}e^{\lambda t}\lambda^\alpha(\lambda^{\alpha+1}I+A)^{-1}\, d\lambda,$ where $$t>0$$ and $$Ha$$ is a suitable path. The existence results show that the mild solutions have more spatial regularity in terms of estimates on norms in fractional power spaces when $$\alpha$$ is closer to $$0$$, the case of the Navier-Stokes equations. The linear estimates needed are stated in an abstract setting for sectorial operators which makes it possible to restate the results for some other equations as well. Boundary control for optimal mixing via Navier-Stokes flows https://zbmath.org/1472.49005 2021-11-25T18:46:10.358925Z "Hu, Weiwei" https://zbmath.org/authors/?q=ai:hu.weiwei "Wu, Jiahong" https://zbmath.org/authors/?q=ai:wu.jiahong On the unique solvability of the optimal starting control problem for the linearized equations of motion of a viscoelastic medium https://zbmath.org/1472.49068 2021-11-25T18:46:10.358925Z "Artemov, M. A." https://zbmath.org/authors/?q=ai:artemov.mikhail-anatolevich Summary: We study an optimization problem for the linearized evolution equations of the Oldroyd model of motion of a viscoelastic medium. The equations are given in a bounded three-dimensional domain. The velocity distribution at the initial time is used as a control function. The objective functional is terminal. The existence of a unique optimal control is proved for a given set of admissible controls. A variational inequality characterizing the optimal control is derived. Differential invariants for spherical layer flows of viscid fluids https://zbmath.org/1472.53020 2021-11-25T18:46:10.358925Z "Duyunova, Anna" https://zbmath.org/authors/?q=ai:duyunova.anna-andreevna "Lychagin, Valentin" https://zbmath.org/authors/?q=ai:lychagin.valentin-v "Tychkov, Sergey" https://zbmath.org/authors/?q=ai:tychkov.sergey-n Summary: Symmetries and the corresponding algebras of differential invariants of viscid fluids on a spherical layer are given. Their dependence on thermodynamical states of media is studied, and a classification of thermodynamical states is given. A Björling representation for Jacobi fields on minimal surfaces and soap film instabilities https://zbmath.org/1472.53066 2021-11-25T18:46:10.358925Z "Alexander, Gareth P." https://zbmath.org/authors/?q=ai:alexander.gareth-p "Machon, Thomas" https://zbmath.org/authors/?q=ai:machon.thomas Summary: We develop a general framework for the description of instabilities on soap films using the Björling representation of minimal surfaces. The construction is naturally geometric and the instability has the interpretation as being specified by its amplitude and transverse gradient along any curve lying in the minimal surface. When the amplitude vanishes, the curve forms part of the boundary to a critically stable domain, while when the gradient vanishes the Jacobi field is maximal along the curve. In the latter case, we show that the Jacobi field is maximally localized if its amplitude is taken to be the lowest eigenfunction of a one-dimensional Schrödinger operator. We present examples for the helicoid, catenoid, circular helicoids and planar Enneper minimal surfaces, and emphasize that the geometric nature of the Björling representation allows direct connection with instabilities observed in soap films. Local existence and uniqueness of skew mean curvature flow https://zbmath.org/1472.53100 2021-11-25T18:46:10.358925Z "Song, Chong" https://zbmath.org/authors/?q=ai:song.chong Summary: The Skew Mean Curvature Flow (SMCF) is a Schrödinger-type geometric flow canonically defined on a co-dimension two submanifold, which generalizes the famous vortex filament equation in fluid dynamics. In this paper, we prove the local existence and uniqueness of general-dimensional SMCF in Euclidean spaces. Ambit stochastics https://zbmath.org/1472.60002 2021-11-25T18:46:10.358925Z "Barndorff-Nielsen, Ole E." https://zbmath.org/authors/?q=ai:barndorff-nielsen.ole-eiler "Benth, Fred Espen" https://zbmath.org/authors/?q=ai:benth.fred-espen "Veraart, Almut E. D." https://zbmath.org/authors/?q=ai:veraart.almut-e-d This is a monograph on stochastic modelling of complex phenomena which are random and evolve in both time and space. The word ambit' used as a part of the title appears for the first time in the literature. Available are only a few ambit' papers and one weekly Ambit magazine'. Relying on advanced probability the authors define and intensively use the notions ambit sets' and ambit fields'. Important applied problems lead to the necessity to develop a systematic and adequate theory. In order to build up good mathematical models, one needs a general theory of non-semimartingale stochastic integration with respect to Volterra processes followed by a detailed analytical study. The author pays a great attention to diverse methods of numerical integration and simulation algorithms. All these are successfully used to suggest and analyze stochastic models in complex areas such as turbulence and stochastic volatility. The reader will get a good sense of the contents of the book by looking at the chapter names and, in brackets, the names of two randomly chosen sections. Part I. The purely temporally case: 1. Volatility modulated Volterra processes (Lévy processes, semimartingale and non-semimartingale settings). 2. Simulation (a stepwise simulation scheme based on the Laplace representation, simulation based on numerically solving stochastic PDEs). 3. Asymptotic theory for power variation of LSS processes (convergence concept, Asymptotic theory in the non-semimartingale setting). 4. Integration with respect to volatility modulated Volterra processes (integration with respect to VMBV processes, discussion of stochastic integration based on an infinite dimensional approach). Part II. The spatio-temporal case: 5. The ambit framework (integration concepts with respect to a Lévy basis, general aspects of the theory of ambit fields and processes). 6. Representation and simulation of ambit fields (Fourier transformation of ambit fields, representations of ambit fields in Hilbert space). 7. Stochastic integration with ambit fields as integrators (definition of the stochastic integral, relationships to semimartingale integration). 8. Trawl processes (choices for the marginal distribution, inference for trawl processes). Part III. Applications: 9. Turbulence modelling (exponentiated ambit fields and correlators, some remarks on dynamic intermittency). 10. Stochastic modelling on energy spot prices by LSS processes (case study: electricity spot prices from the European energy exchange market, pricing electricity derivatives). 11. Forward curve modelling by ambit fields (properties of the ambit model, application to spread options). Two appendices: A. Bessel functions. B. Generalized hyperbolic distribution. A comprehensive list of References and Index. The authors have written a fundamental book on contemporary probability theory and its applications. The book can be strongly recommended to theorists and applied scientists. Locally robust random attractors in stochastic non-autonomous magneto-hydrodynamics https://zbmath.org/1472.60104 2021-11-25T18:46:10.358925Z "Li, Fuzhi" https://zbmath.org/authors/?q=ai:li.fuzhi "Yangrong, Li" https://zbmath.org/authors/?q=ai:yangrong.li This paper shows the local robustness result of random attractors (towards a deterministic attractor), which generalizes some related results in the literature. The main results are illustrated in the content of stochastic non-autonomous magneto-hydrodynamics (MHD) equations. By using joint convergence of the cocycles, collective local compactness and deterministic recurrence of the random attractors, the authors prove that the family of pullback random attractors is locally uniform convergent to the pullback attractor of the deterministic MHD equation when the density of random noise tends to 0. Model reduction for kinetic equations: moment approximations and hierarchical approximate proper orthogonal decomposition https://zbmath.org/1472.65004 2021-11-25T18:46:10.358925Z "Leibner, Tobias" https://zbmath.org/authors/?q=ai:leibner.tobias (no abstract) Convergence of time-splitting approximations for degenerate convection-diffusion equations with a random source https://zbmath.org/1472.65099 2021-11-25T18:46:10.358925Z "Díaz-Adame, Roberto" https://zbmath.org/authors/?q=ai:diaz-adame.roberto "Jerez, Silvia" https://zbmath.org/authors/?q=ai:jerez.silvia In this paper authors propose a time-splitting method for degenerate convectionś-diffusion equations perturbed stochastically by white noise. This work generalizes previous results on splitting operator techniques for stochastic hyperbolic conservation laws for the degenerate parabolic case. The convergence in $$L_{\mathrm{loc}}^p$$ of the time-splitting operator scheme to the unique weak entropy solution is proven. Moreover, we analyze the performance of the splitting approximation by computing its convergence rate and showing numerical simulations for some benchmark examples, including a luid low application in porous media. Kernel based high order explicit'' unconditionally stable scheme for nonlinear degenerate advection-diffusion equations https://zbmath.org/1472.65107 2021-11-25T18:46:10.358925Z "Christlieb, Andrew" https://zbmath.org/authors/?q=ai:christlieb.andrew-j "Guo, Wei" https://zbmath.org/authors/?q=ai:guo.wei "Jiang, Yan" https://zbmath.org/authors/?q=ai:jiang.yan "Yang, Hyoseon" https://zbmath.org/authors/?q=ai:yang.hyoseon In the present article, authors propose a high-order numerical scheme for solving a class of nonlinear degenerate parabolic equations written as $\partial_t u+\partial_x f(u)=\partial_{xx}g(u),$ where $$g'(u)\geq 0$$ and $$g'(u)$$ can vanish for some values of $$u$$. This type of equations arises in a wide range of applications, containing for example radiative transport or porous medium flow. It has similar properties as hyperbolic conservation laws, including in particular possible existence of nonsmooth solutions. It is therefore important to consider a high order approximation for this type of equations. Moreover, since the problem is parabolic, a classical explicit time discretization would imply a constraining restriction on the time step to ensure stability, while classical implicit methods would lead to invert some operator at each time steps. To overcome these issues, an approach based on the method of lines transpose ($$MOL^T$$) is considered. The idea is to first discretize the time, here with an explicit strong-stability-preserving Runge-Kutta (SSP RK) method, and then to solve a boundary value problem at each discrete time levels. Let us mention that the same ideas where used in [\textit{A. Christlieb} et al., J. Comput. Phys. 327, 337--367 (2016; Zbl 1422.65432)] for advection equations, the main difference being that in this previous article, an implicit SSP RK method was used instead of an explicit one. Then, the spatial derivatives are represented as infinite series, in which each term relies on a special kernel based formulation of the solution. This approach makes the method effectively implicit at each stage of the explicit SSP RK method, but without the need of invert any operator. Finally, a WENO methodology is applied, but may not be sufficient to suppress solution overshoots in the case of nonsmooth problems. To enhance robustness of the method, a nonlinear filter is introduced, constructed thanks to the smoothness indicators provided by the WENO methodology, and then not increasing the computational cost. Unconditional stability of the proposed numerical scheme is rigorously proved in the linear case with periodic boundary conditions, for order $$k=1,\,2,\,3$$. The stability for the more general nonlinear case is not theoretically established, but numerically confirmed. Several numerical 1D and 2D test cases, including porous medium equation, Buckley-Leverett equation and strongly degenerate parabolic problems, are presented. Numerical results demonstrate efficiency of the proposed method, high order accuracy and ability to produce nonoscillatory shock transitions. Moreover, it appears that the CFL number can be chosen arbitrarily large, leading only to a loss of accuracy and not a stability issue. Analysis of the parareal method with spectral deferred correction method for the Stokes/Darcy equations https://zbmath.org/1472.65109 2021-11-25T18:46:10.358925Z "Xue, Dandan" https://zbmath.org/authors/?q=ai:xue.dandan "Hou, Yanren" https://zbmath.org/authors/?q=ai:hou.yanren "Liu, Wenjia" https://zbmath.org/authors/?q=ai:liu.wenjia Summary: In this paper, we analyze a second-order numerical algorithm for the non-stationary mixed Stokes/Darcy equations with Beavers-Joseph-Saffman's interface condition. The scheme is based on a finite element method in space and the parareal method with spectral deferred correction in time. We present the unconditional stability and the optimal error estimate of the full-discrete scheme. Finally, some numerical experiments are given to verify the effectiveness. Analytical and Rothe time-discretization method for a Boussinesq-type system over an uneven bottom https://zbmath.org/1472.65113 2021-11-25T18:46:10.358925Z "Mejía, Luis Fernando" https://zbmath.org/authors/?q=ai:mejia.luis-fernando "Muñoz Grajales, Juan Carlos" https://zbmath.org/authors/?q=ai:munoz-grajales.juan-carlos The authors consider the analytical and numerical resolution of a 2D version of a Boussinesq-type model which occur in the water wave propagation. The time discretization is performed using a finite-difference second-order Crank-Nicholson-type scheme, and then, at each time step, the spatial variables are discretized with an efficient Galerkin/Finite Element Method (FEM) using triangular-finite elements based on 2D piecewise-linear Lagrange interpolation. Some numerical tests are presented to support the theoretical results. Affine invariant interacting Langevin dynamics for Bayesian inference https://zbmath.org/1472.65118 2021-11-25T18:46:10.358925Z "Garbuno-Inigo, Alfredo" https://zbmath.org/authors/?q=ai:garbuno-inigo.alfredo "Nüsken, Nikolas" https://zbmath.org/authors/?q=ai:nusken.nikolas "Reich, Sebastian" https://zbmath.org/authors/?q=ai:reich.sebastian This paper proposes a computational method for generating samples from a given high-dimensional target distribution of the form $\pi(u) = \frac1Z \exp(-\Phi(u))$ where $$\Phi$$ is a suitable potential and $$Z$$ is a normalization constant; this is a fundamental task in, e.g., Bayesian inverse problems. As an alternative to the widely known (Markov chain) Monte Carlo methods, the proposed method is based on Langevin dynamics under which the target distribution is invariant. Specifically, they propose a stochastic process of $$N$$ interacting particles given by $d u^{(i)}_t = -C(U_t) \nabla_{u^{(i)}}\Phi(u^{(i)}_t)dt + \frac{D+1}{N}(u^{(i)}_t - m(U_t))dt + \sqrt2 C^{1/2}(U_t)dW_t^{(i)},$ where $$u^{(i)}_t\in\mathbb{R}^D$$ denotes position of the $$i$$th particle at time $$t$$ (which are all collected into the vector $$U_t$$), $$C(U_t)$$ is the empirical covariance matrix, $$m(U_t)$$ is the empirical mean, and $$C^{1/2}(U_t)$$ is a generalized square root than can be directly computed using the deviations of the particles from the empirical mean. The second term here is a correction term that guarantees for $$N>D+1$$ (under suitable assumptions on the potential and the initial ensemble) that these dynamics are invariant under affine transformations, which prevents inefficient sampling if the empirical covariance matrix is a poor approximation of the target covariance measure in Bayesian inverse problems with Gaussian posteriors. They also provide a gradient-free variant that replaces $$\nabla_{u^{(i)}}\Phi(u^{(i)}_t)$$ by an approximation that is exact for Bayesian inverse problems with affine forward operators and is related to classical Ensemble Kalman-Bucy Filter as well as to the more recent Ensemble Kalman inversion. The performance of this method is illustrated for the typical model problem of Darcy flow inversion. Preconditioning high order $$H^2$$ conforming finite elements on triangles https://zbmath.org/1472.65138 2021-11-25T18:46:10.358925Z "Ainsworth, Mark" https://zbmath.org/authors/?q=ai:ainsworth.mark "Parker, Charles" https://zbmath.org/authors/?q=ai:parker.charles The authors are concerned with the p-version of FEM approximation of some fourth order linear elliptic problems on regular triangulations. As the condition number of the stiffness matrix typically grows rapidly with the polynomial degree p and the numbers of elements, the authors develop a preconditioner which ameliorates this bleak situation. The preconditioner is based on a smart decomposition of the global finite element space into local subspaces augmented with a global lower order vertex space. The analysis of the preconditioner on a single triangular element and the implementation aspects, including the construction of the vertex basis functions, is thoroughly performed. Three classical problems, namely ; Airy stress tensor, Stokes in a cavity domain with parabolic inflow and outflow velocity profiles and the plate one on a L-shaped domain with point loading are solved in order to underline the performances of the preconditioning technique. An adaptive multiscale hybrid-mixed method for the Oseen equations https://zbmath.org/1472.65139 2021-11-25T18:46:10.358925Z "Araya, Rodolfo" https://zbmath.org/authors/?q=ai:araya.rodolfo-a "Cárcamo, Cristian" https://zbmath.org/authors/?q=ai:carcamo.cristian "Poza, Abner H." https://zbmath.org/authors/?q=ai:poza.abner-h "Valentin, Frédéric" https://zbmath.org/authors/?q=ai:valentin.frederic Summary: A novel residual a posteriori error estimator for the Oseen equations achieves efficiency and reliability by including multilevel contributions in its construction. Originates from the Multiscale Hybrid Mixed (MHM) method, the estimator combines residuals from the skeleton of the first-level partition of the domain, along with the contributions from element-wise approximations. The second-level estimator is local and infers the accuracy of multiscale basis computations as part of the MHM framework. Also, the face-degrees of freedom of the MHM method shape the estimator and induce a new face-adaptive procedure on the mesh's skeleton only. As a result, the approach avoids re-meshing the first-level partition, which makes the adaptive process affordable and straightforward on complex geometries. Several numerical tests assess theoretical results. Correction to: Finite element solvers for Biot's poroelasticity equations in porous media'' https://zbmath.org/1472.65145 2021-11-25T18:46:10.358925Z "Kadeethum, T." https://zbmath.org/authors/?q=ai:kadeethum.t "Lee, S." https://zbmath.org/authors/?q=ai:lee.seungjae.1|lee.seongil|lee.soonmook|lee.shinae|lee.sungyoon|lee.sangyun|lee.seewoo|lee.seunghak|lee.seokho|lee.sanghwan|lee.seunghyun|lee.sangmok|lee.sangjik|lee.sungkee|lee.seunghee|lee.soonkyu|lee.sanggon|lee.sungjun|lee.shongleigh|lee.sangjeen|lee.soonyoung|lee.soojeong|lee.soodong|lee.seungkyu|lee.seri|lee.sangjin|lee.sangyeol|lee.sangyop|lee.sau|lee.shiowjen|lee.soojin|lee.seungjoon|lee.seonmi|lee.seungjae|lee.sanghyeon|lee.sangin|lee.seekeong|lee.seonjoo|lee.seungchul|lee.saebom|lee.sunju|lee.soojung|lee.seyoung|lee.sangbok|lee.seunghye|lee.seungho|lee.sangryun|lee.sunggeun|lee.shaun|lee.seokcheon|lee.sangmin|lee.sokbae|lee.soyoon|lee.seongwon|lee.sujin|lee.seunggwan|lee.sanghun|lee.susan|lee.sungro|lee.sangheon|lee.soyoung|lee.sangjune|lee.sangkyun|lee.suwon|lee.sunmi|lee.seungjun|lee.stanley|lee.sungyun|lee.sungim|lee.sungwon|lee.seungyong|lee.seyeon|lee.sukyoung|lee.seungyun|lee.sik-yum|lee.seung-yeoun|lee.suekyung|lee.sanboh|lee.sanghack|lee.seongkee|lee.sunmin|lee.seungrae|lee.somin|lee.sangwoo|lee.sungjae|lee.sinmin|lee.sojung|lee.sangwook|lee.seungkwang|lee.sangyoun|lee.sangyoon|lee.sangkeon|lee.seunghoon|lee.sangwon|lee.seungwon|lee.sukhan|lee.sangmoon|lee.sunyoung|lee.sangmoo|lee.seoklae|lee.sungryul|lee.sangjun|lee.sangkeun|lee.seulip|lee.sangmin.1|lee.seoungsoo|lee.seungkoo|lee.soungdouk|lee.seungjoo|lee.singling|lee.seungduck|lee.sunggu|lee.sangjae|lee.sanghyun|lee.sangyeob|lee.sungji|lee.sunhong|lee.sungwook|lee.sujeong|lee.sanguk|lee.sieun|lee.sanghan|lee.suyeon|lee.soojoon|lee.sungsu|lee.seongu|lee.sungmun|lee.soogab|lee.shernita|lee.sookyoung|lee.sangkon|lee.sunah|lee.sunho|lee.soonhui|lee.sangmi|lee.sanghyuk|lee.sungyon|lee.sabine|lee.shiwoo|lee.sungho|lee.sangchul|lee.suchang|lee.sanha|lee.seunghwan|lee.sanghyup|lee.soomin|lee.sungyoung|lee.sanghoon|lee.sangseung|lee.seongwhan|lee.sangil|lee.soonhee|lee.seunghun|lee.sokjoon|lee.sunghee|lee.siyul|lee.sichang|lee.seongjin|lee.seonhee|lee.seonghun|lee.swungho|lee.sunnyeo|lee.seungsoo|lee.seungjai|lee.sungju|lee.sungjin|lee.sangjong|lee.sean|lee.sangkyu|lee.sooyong|lee.shinyoung|lee.seojeong|lee.shawin|lee.sukhoon|lee.sangyum|lee.sanghyeok|lee.sangki|lee.sihun|lee.seungwoo|lee.seunghwa|lee.sunghan|lee.sangho|lee.sungjay|lee.sooyeon|lee.soyeon|lee.soocheol|lee.soowon|lee.sheldon|lee.sungwoo|lee.soonchil|lee.seungmin|lee.seunggeun|lee.sori|lee.sungchang|lee.sangbae|lee.seungsin|lee.seungjin|lee.sangbum|lee.sang-hyuk|lee.seungri|lee.sangpil|lee.seonjeong|lee.sophia|lee.seunghan|lee.sungduck|lee.sungjoo|lee.shunching|lee.seongno|lee.sangyong|lee.sungjune|lee.seounghwan|lee.shufen|lee.shinjae|lee.sunjung|lee.sora|lee.sukho|lee.sungyeol|lee.sungchul|lee.subin|lee.sangman|lee.seokhyoung|lee.sangsan "Nick, H. M." https://zbmath.org/authors/?q=ai:nick.h-m From the text: The original version of this paper [the authors, ibid. 52, No. 8, 977--1015 (2020; Zbl 1451.76070)] was inadvertently published with an incorrect formula. The correct formula is $\nabla \cdot \, {\boldsymbol{\sigma}}^{\prime } ({\boldsymbol{u}}) - \alpha \nabla \cdot p{\boldsymbol{I}} = {\boldsymbol{f}}\quad {\text{in }}\Omega \times {\mathbb{T}},$ The original article has been corrected. We apologise for any inconvenience caused to our readers. A local and parallel Uzawa finite element method for the generalized Navier-Stokes equations https://zbmath.org/1472.65148 2021-11-25T18:46:10.358925Z "Shu, Yu" https://zbmath.org/authors/?q=ai:shu.yu "Li, Jian" https://zbmath.org/authors/?q=ai:li.jian.1 "Zhang, Chong" https://zbmath.org/authors/?q=ai:zhang.chong Summary: In this paper, we propose and develop a local and parallel Uzawa finite element method for the generalized Navier-Stokes equations. The Uzawa finite element method is no need to deal with the saddle point problem, and only solves one vector-valued elliptic equation and one simple scalar-valued equation. It has the geometric convergence with a crispation number $$\gamma$$ what has nothing to do with the mesh size $$h$$. As for the local and parallel Uzawa finite element method, each subproblem is a global problem, but most of degrees of freedom originate from the subdomain. Moreover, the presented method is easy to be applied with less communication requirements and has good parallelism. Finally, numerical results verify the performance of the proposed method. Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method https://zbmath.org/1472.65152 2021-11-25T18:46:10.358925Z "Pintore, Moreno" https://zbmath.org/authors/?q=ai:pintore.moreno "Pichi, Federico" https://zbmath.org/authors/?q=ai:pichi.federico "Hess, Martin" https://zbmath.org/authors/?q=ai:hess.martin-wilfried "Rozza, Gianluigi" https://zbmath.org/authors/?q=ai:rozza.gianluigi "Canuto, Claudio" https://zbmath.org/authors/?q=ai:canuto.claudio Summary: The majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities. Such features lead to the coexistence of multiple solutions studied by the bifurcation theory. Unfortunately, in practical scenarios, one has to exploit numerical methods to compute the solutions of systems of PDEs, even if the classical techniques are usually able to compute only a single solution for any value of a parameter when more branches exist. In this work, we implemented an elaborated deflated continuation method that relies on the spectral element method (SEM) and on the reduced basis (RB) one to efficiently compute bifurcation diagrams with more parameters and more bifurcation points. The deflated continuation method can be obtained combining the classical continuation method and the deflation one: the former is used to entirely track each known branch of the diagram, while the latter is exploited to discover the new ones. Finally, when more than one parameter is considered, the efficiency of the computation is ensured by the fact that the diagrams can be computed during the online phase while, during the offline one, one only has to compute one-dimensional diagrams. In this work, after a more detailed description of the method, we will show the results that can be obtained using it to compute a bifurcation diagram associated with a problem governed by the Navier-Stokes equations. A Reynolds-robust preconditioner for the Scott-Vogelius discretization of the stationary incompressible Navier-Stokes equations https://zbmath.org/1472.65155 2021-11-25T18:46:10.358925Z "Farrell, Patrick E." https://zbmath.org/authors/?q=ai:farrell.patrick-e|farrell.patrick-emmet "Mitchell, Lawrence" https://zbmath.org/authors/?q=ai:mitchell.lawrence "Scott, L. Ridgway" https://zbmath.org/authors/?q=ai:scott.larkin-ridgway "Wechsung, Florian" https://zbmath.org/authors/?q=ai:wechsung.florian Summary: Augmented Lagrangian preconditioners have successfully yielded Reynolds-robust preconditioners for the stationary incompressible Navier-Stokes equations, but only for specific discretizations. The discretizations for which these preconditioners have been designed possess error estimates which depend on the Reynolds number, with the discretization error deteriorating as the Reynolds number is increased. In this paper we present an augmented Lagrangian preconditioner for the Scott-Vogelius discretization on barycentrically-refined meshes. This achieves both Reynolds-robust performance and Reynolds-robust error estimates. A key consideration is the design of a suitable space decomposition that captures the kernel of the grad-div term added to control the Schur complement; the same barycentric refinement that guarantees inf-sup stability also provides a local decomposition of the kernel of the divergence. The robustness of the scheme is confirmed by numerical experiments in two and three dimensions. The multiscale perturbation method for second order elliptic equations https://zbmath.org/1472.65158 2021-11-25T18:46:10.358925Z "Ali, Alsadig" https://zbmath.org/authors/?q=ai:ali.alsadig "Mankad, Het" https://zbmath.org/authors/?q=ai:mankad.het "Pereira, Felipe" https://zbmath.org/authors/?q=ai:pereira.felipe-de-c|pereira.felipe|pereira.felipe-a-c "Sousa, Fabrício S." https://zbmath.org/authors/?q=ai:sousa.fabricio-s Summary: In the numerical solution of elliptic equations, multiscale methods typically involve two steps: the solution of families of local solutions or multiscale basis functions (an embarrassingly parallel task) associated with subdomains of a domain decomposition of the original domain, followed by the solution of a global problem. In the solution of multiphase flow problems approximated by an operator splitting method one has to solve an elliptic equation every time step of a simulation, that would require that all multiscale basis functions be recomputed. In this work, we focus on the development of a novel method that replaces a full update of local solutions by reusing multiscale basis functions that are computed at an earlier time of a simulation. The procedure is based on classical perturbation theory. It can take advantage of both an offline stage (where multiscale basis functions are computed at the initial time of a simulation) as well as of a good initial guess for velocity and pressure. The formulation of the method is carefully explained and several numerical studies are presented and discussed. They provide an indication that the proposed procedure can be of value in speeding-up the solution of multiphase flow problems by multiscale methods. Numerical solution of scattering problems using a Riemann-Hilbert formulation https://zbmath.org/1472.65176 2021-11-25T18:46:10.358925Z "Smith, Stefan G. Llewellyn" https://zbmath.org/authors/?q=ai:llewellyn-smith.stefan-g "Luca, Elena" https://zbmath.org/authors/?q=ai:luca.elena Summary: A fast and accurate numerical method for the solution of scalar and matrix Wiener-Hopf (WH) problems is presented. The WH problems are formulated as Riemann-Hilbert problems on the real line, and a numerical approach developed for these problems is used. It is shown that the known far-field behaviour of the solutions can be exploited to construct numerical schemes providing spectrally accurate results. A number of scalar and matrix WH problems that generalize the classical Sommerfeld problem of diffraction of plane waves by a semi-infinite plane are solved using the approach. Control of chaotic systems by deep reinforcement learning https://zbmath.org/1472.68171 2021-11-25T18:46:10.358925Z "Bucci, M. A." https://zbmath.org/authors/?q=ai:bucci.michele-alessandro "Semeraro, O." https://zbmath.org/authors/?q=ai:semeraro.onofrio "Allauzen, A." https://zbmath.org/authors/?q=ai:allauzen.alexandre "Wisniewski, G." https://zbmath.org/authors/?q=ai:wisniewski.grzegorz "Cordier, L." https://zbmath.org/authors/?q=ai:cordier.laurent "Mathelin, L." https://zbmath.org/authors/?q=ai:mathelin.lionel Summary: Deep reinforcement learning (DRL) is applied to control a nonlinear, chaotic system governed by the one-dimensional Kuramoto-Sivashinsky (KS) equation. DRL uses reinforcement learning principles for the determination of optimal control solutions and deep neural networks for approximating the value function and the control policy. Recent applications have shown that DRL may achieve superhuman performance in complex cognitive tasks. In this work, we show that using restricted localized actuation, partial knowledge of the state based on limited sensor measurements and model-free DRL controllers, it is possible to stabilize the dynamics of the KS system around its unstable fixed solutions, here considered as target states. The robustness of the controllers is tested by considering several trajectories in the phase space emanating from different initial conditions; we show that DRL is always capable of driving and stabilizing the dynamics around target states. The possibility of controlling the KS system in the chaotic regime by using a DRL strategy solely relying on local measurements suggests the extension of the application of RL methods to the control of more complex systems such as drag reduction in bluff-body wakes or the enhancement/diminution of turbulent mixing. Shallow neural networks for fluid flow reconstruction with limited sensors https://zbmath.org/1472.68172 2021-11-25T18:46:10.358925Z "Erichson, N. Benjamin" https://zbmath.org/authors/?q=ai:erichson.n-benjamin "Mathelin, Lionel" https://zbmath.org/authors/?q=ai:mathelin.lionel "Yao, Zhewei" https://zbmath.org/authors/?q=ai:yao.zhewei "Brunton, Steven L." https://zbmath.org/authors/?q=ai:brunton.steven-l "Mahoney, Michael W." https://zbmath.org/authors/?q=ai:mahoney.michael-w "Kutz, J. Nathan" https://zbmath.org/authors/?q=ai:kutz.j-nathan Summary: In many applications, it is important to reconstruct a fluid flow field, or some other high-dimensional state, from limited measurements and limited data. In this work, we propose a shallow neural network-based learning methodology for such fluid flow reconstruction. Our approach learns an end-to-end mapping between the sensor measurements and the high-dimensional fluid flow field, without any heavy preprocessing on the raw data. No prior knowledge is assumed to be available, and the estimation method is purely data-driven. We demonstrate the performance on three examples in fluid mechanics and oceanography, showing that this modern data-driven approach outperforms traditional modal approximation techniques which are commonly used for flow reconstruction. Not only does the proposed method show superior performance characteristics, it can also produce a comparable level of performance to traditional methods in the area, using significantly fewer sensors. Thus, the mathematical architecture is ideal for emerging global monitoring technologies where measurement data are often limited. Deep neural networks for waves assisted by the Wiener-Hopf method https://zbmath.org/1472.68174 2021-11-25T18:46:10.358925Z "Huang, Xun" https://zbmath.org/authors/?q=ai:huang.xun Summary: In this work, the classical Wiener-Hopf method is incorporated into the emerging deep neural networks for the study of certain wave problems. The essential idea is to use the first-principle-based analytical method to efficiently produce a large volume of datasets that would supervise the learning of data-hungry deep neural networks, and to further explain the working mechanisms on underneath. To demonstrate such a combinational research strategy, a deep feed-forward network is first used to approximate the forward propagation model of a duct acoustic problem, which can find important aerospace applications in aeroengine noise tests. Next, a convolutional type U-net is developed to learn spatial derivatives in wave equations, which could help to promote computational paradigm in mathematical physics and engineering applications. A couple of extensions of the U-net architecture are proposed to further impose possible physical constraints. Finally, after giving the implementation details, the performance of the neural networks are studied by comparing with analytical solutions from the Wiener-Hopf method. Overall, the Wiener-Hopf method is used here from a totally new perspective and such a combinational research strategy shall represent the key achievement of this work. The relationship between viscoelasticity and elasticity https://zbmath.org/1472.74038 2021-11-25T18:46:10.358925Z "Snoeijer, J. H." https://zbmath.org/authors/?q=ai:snoeijer.jacco-h "Pandey, A." https://zbmath.org/authors/?q=ai:pandey.anupam "Herrada, M. A." https://zbmath.org/authors/?q=ai:herrada.miguel-angel "Eggers, J." https://zbmath.org/authors/?q=ai:eggers.jens-g Summary: Soft materials that are subjected to large deformations exhibit an extremely rich phenomenology, with properties lying in between those of simple fluids and those of elastic solids. In the continuum description of these systems, one typically follows either the route of solid mechanics (Lagrangian description) or the route of fluid mechanics (Eulerian description). The purpose of this review is to highlight the relationship between the theories of viscoelasticity and of elasticity, and to leverage this connection in contemporary soft matter problems. We review the principles governing models for viscoelastic liquids, for example solutions of flexible polymers. Such materials are characterized by a relaxation time $$\lambda$$, over which stresses relax. We recall the kinematics and elastic response of large deformations, and show which polymer models do (and which do not) correspond to a nonlinear elastic solid in the limit $$\lambda \rightarrow \infty$$. With this insight, we split the work done by elastic stresses into reversible and dissipative parts, and establish the general form of the conservation law for the total energy. The elastic correspondence can offer an insightful tool for a broad class of problems; as an illustration, we show how the presence or absence of an elastic limit determines the fate of an elastic thread during capillary instability. Violations of the Clausius-Duhem inequality in Couette flows of granular media https://zbmath.org/1472.74047 2021-11-25T18:46:10.358925Z "Ostoja-Starzewski, Martin" https://zbmath.org/authors/?q=ai:ostoja-starzewski.martin "Laudani, Rossella" https://zbmath.org/authors/?q=ai:laudani.rossella Summary: Spontaneous violations of the Clausius-Duhem (CD) inequality in Couette-type collisional flows of model granular media are studied. Planar systems of monosized circular discs (with disc numbers from 10 to 204, and disc diameters from 0.001 m to 1 m) with frictional-Hookean contacts are simulated under periodic boundary conditions by a molecular dynamics. The scale-dependent homogenization of micropolar media is used to determine the energy balances and mechanical entropy production. The dissipation function exhibits spontaneous negative entropy increments described by the fluctuation theorem. The boundary between violations and non-violations of the CD inequality is mapped in the parameter space, where the probability of such events diminishes with the disc diameter, the disc number and the area fraction increasing. The dissipation function is a random process, tending to Gaussian as the number of discs increases, and possessing non-trivial fractal and anti-persistent Hurst properties. Aerothermoelastic flutter analysis of pre-twisted thin-walled rotating blades reinforced with functionally graded carbon nanotubes https://zbmath.org/1472.74060 2021-11-25T18:46:10.358925Z "Bahaadini, Reza" https://zbmath.org/authors/?q=ai:bahaadini.reza "Saidi, Ali Reza" https://zbmath.org/authors/?q=ai:saidi.ali-reza Summary: In this study, the aerothermoelastic flutter analysis of pre-twisted tapered rotating blades reinforced with functionally graded carbon nanotubes (FG-CNTs) under supersonic flow is investigated. Based on the thin-walled Timoshenko beam theory and quasi-steady supersonic linear piston theory, the dynamic model of the supersonic rotating blades reinforced with FG-CNTs has been developed. The CNTs are considered to be either uniformly or non-uniformly distributed in the matrix along the thickness direction. Three various CNTs distribution patterns namely, UD, FG-X and FG-O have been assumed. The properties of CNTs and polymer matrix are considered to be temperature-dependent. Based on the extended Hamilton's principle, the equations of motion as a system of coupled linear partial deferential equations are found. The extended Galerkin method (EGM) is utilized to transform these coupled partial deferential equations to a set of coupled ordinary deferential equations. The influences of rotating speed, CNTs distribution, CNTs weight fraction, temperature, pre-twist and pre-setting angels, hub radius ratio, taper ratios and Mach number on the aerothermoelastic flutter responses of the system have been analyzed. The results indicate that the FG-X distribution pattern have predicted more strengthening the total bending of blade and the greatest flutter frequency for the composite blades. Furthermore, the pre-twist and pre-setting angles as well as taper ratio have significant effects on the flutter frequency of the thin-walled blade reinforced with CNTs. Computational homogenisation of acoustic metafoams https://zbmath.org/1472.74063 2021-11-25T18:46:10.358925Z "Lewińska, M. A." https://zbmath.org/authors/?q=ai:lewinska.m-a "Kouznetsova, V. G." https://zbmath.org/authors/?q=ai:kouznetsova.varvara-g "van Dommelen, J. A. W." https://zbmath.org/authors/?q=ai:van-dommelen.j-a-w "Geers, M. G. D." https://zbmath.org/authors/?q=ai:geers.marc-g-d Summary: Acoustic metafoams are novel materials recently proposed for low frequency sound attenuation. The design of their microstructure is based on the combination of standard acoustic foams with locally resonant acoustic metamaterials. This results in improved sound attenuation properties due to the interaction between viscothermal dissipation effects and the local resonance effects at the pore level. In this paper, the non-standard behaviour of such a metafoam with a complex two-phase microstructure is analysed through a multiscale approach. The macroscopic problem is described by general balance equations and at the microscopic scale a detailed representation of the microstructure is considered. The frequency dependent effective properties are used to explain the extraordinary acoustic performance. The homogenisation approach is also validated using direct numerical simulations, showing that the homogenisation technique is adequate in modelling both viscothermal dissipation and the local resonance effect within the metafoam microstructure. Effects of structural damping on acoustic scattering by flexible plates https://zbmath.org/1472.74064 2021-11-25T18:46:10.358925Z "Nilton, M. M." https://zbmath.org/authors/?q=ai:nilton.m-m "De Montesquieu, A. S." https://zbmath.org/authors/?q=ai:de-montesquieu.a-s "Cavalieri, A. V. G." https://zbmath.org/authors/?q=ai:cavalieri.andre-v-g "Donadon, M. V." https://zbmath.org/authors/?q=ai:donadon.mauricio-v "Wolf, W. R." https://zbmath.org/authors/?q=ai:wolf.william-r Summary: We investigate the effects of structural damping on the interaction of a turbulent eddy with flexible plates with respect to the efficiency of aerodynamic noise generation. Potential benefits are studied using a model based on a point-reacting compliant semi-infinite plate on a spring-damper foundation. This scattering problem is solved using the Wiener-Hopf technique. We compare results for semi-infinite compliant plates with finite ones. In both cases, plate vibration lead to reductions of sound radiation, especially at resonance; damping tends to reduce such acoustic benefits. We also present a formulation that considers the effect of structural damping on the acoustic properties of finite elastic plates. Numerical results are obtained by applying a boundary element method to solve the Helmholtz equation subject to the boundary conditions imposed by the plate vibration. Under specific conditions, such as high fluid loading factor and low bending-wave Mach number, the acoustic power scattered by an edge tends to be smaller than that which propagates over the plate as bending waves. Results show that structural damping attenuates these waves and may modify the far-field acoustic pressure, mostly by reducing the scattered sound at structural resonances. All models show that large damping coefficients lead to locally over-damped responses. There is thus an ideal range of structural damping to reduce both plate vibration and acoustic scattering. Free and forced vibrations of a composite plate in a perfect compressible fluid, taking into account energy dissipation in the plate and fluid https://zbmath.org/1472.74090 2021-11-25T18:46:10.358925Z "Paimushin, V. N." https://zbmath.org/authors/?q=ai:paimushin.vitaliy-n "Gazizullin, R. K." https://zbmath.org/authors/?q=ai:gazizullin.ruslan-kamilevich Summary: The problem of the passage of a monoharmonic plane sound wave through a thin composite rectangular plate hingly supported in the aperture of an absolutely rigid partition has been considered. In this work, two-dimensional equations of motion constructed by reduction of three-dimensional equations were used. These equations were based on a discrete structural model of multilayer plates deformation at small displacements and deformations. Additionally there were taken into account the internal friction of layer materials according to the Kelvin-Voigt model. The behavior of acoustic media is described by the generalized Helmholtz wave equations, composed with the introduction of the complex sound velocity according to [\textit{E. Skudrzyk}, The foundations of acoustics. Basic mathematics and basic acoustics. Wien: Springer-Verlag. (1971; Zbl 0251.76052)] to take into account the dissipation of energy. An exact analytical solution of the formulated problem has been obtained. On this basis, this work studies the insulation properties and the stress-strain parameters of a composite plate reinforced with carbon textile depending on the incident sound wave frequency. In addition to this, the laws that represent the change in the sound pressure in an acoustic medium with a distance from the plate were established. Elastic shocks in relativistic rigid rods and balls https://zbmath.org/1472.74124 2021-11-25T18:46:10.358925Z "Costa, João L." https://zbmath.org/authors/?q=ai:costa.joao-lopes "Natário, José" https://zbmath.org/authors/?q=ai:natario.jose Summary: We study the free boundary problem for the hard phase' material introduced by \textit{D. Christodoulou} [Arch. Ration. Mech. Anal. 130, No. 4, 343--400 (1995; Zbl 0841.76097)], both for rods in $$(1 + 1)$$-dimensional Minkowski space-time and for spherically symmetric balls in $$(3 + 1)$$-dimensional Minkowski space-time. Unlike Christodoulou, we do not consider a soft phase', and so we regard this material as an elastic medium, capable of both compression and stretching. We prove that shocks must be null hypersurfaces, and derive the conditions to be satisfied at a free boundary. We solve the equations of motion of the rods explicitly, and we prove existence of solutions to the equations of motion of the spherically symmetric balls for an arbitrarily long (but finite) time, given initial conditions sufficiently close to those for the relaxed ball at rest. In both cases we find that the solutions contain shocks if and only if the pressure or its time derivative do not vanish at the free boundary initially. These shocks interact with the free boundary, causing it to lose regularity. Comprehensive vibrational dynamics of half-open fluid-filled shells https://zbmath.org/1472.74145 2021-11-25T18:46:10.358925Z "Lendermann, Markus" https://zbmath.org/authors/?q=ai:lendermann.markus "Koh, Jin Ming" https://zbmath.org/authors/?q=ai:koh.jin-ming "Tan, Joel Shi Quan" https://zbmath.org/authors/?q=ai:tan.joel-shi-quan "Cheong, Kang Hao" https://zbmath.org/authors/?q=ai:cheong.kang-hao Summary: Fluid-filled shells are near-ubiquitous in natural and engineered structures---a familiar example is that of glass harps comprising partially filled wineglasses or glass bowls, whose acoustic properties are readily noticeable. Existing theories modelling the mechanical properties of such systems under vibrational load either vastly simplify shell geometry and oscillatory modal shapes to admit analytical solutions or rely on finite-element black-box computations for general cases, the former yielding poor accuracy and the latter offering limited tractability and physical insight. In the present study, we derive a theoretical framework encompassing elastic shell deformation with structural and viscous dissipation, accommodating arbitrary axisymmetric shell geometries and fluid levels; reductions to closed-form solutions under specific assumptions are shown to be possible. The theory is extensively verified against a range of geometries, fluid levels and fluid viscosities in experiments; an extension of the model encompassing additional solid objects within the fluid-filled shell is also considered and verified. The presented theoretical advance in describing vibrational response is relevant in performance evaluation for engineered structures and quality validation in manufacturing. Explosion problems for surface charges https://zbmath.org/1472.74159 2021-11-25T18:46:10.358925Z "Maksimenko, V. A." https://zbmath.org/authors/?q=ai:maksimenko.vasilii-aleksandrovich "Tolokonnikov, S. L." https://zbmath.org/authors/?q=ai:tolokonnikov.sergei-lvovich Summary: A plane problem of the formation of a crater as a result of the explosion of a line charge on the surface of the ground is investigated within the solid-liquid formulation. The explosion crater is supposed to be a polygonal line with two angular points. The exact solution to the problem is constructed. A parametric analysis is performed. The calculated profiles of the explosion crater are presented for some governing parameters of the problem. Restrictions on the governing parameters are given, and limiting cases are considered. Capillary imbibition of non-Newtonian fluids in a microfluidic channel: analysis and experiments https://zbmath.org/1472.76001 2021-11-25T18:46:10.358925Z "Gorthi, Srinivas R." https://zbmath.org/authors/?q=ai:gorthi.srinivas-r "Meher, Sanjaya Kumar" https://zbmath.org/authors/?q=ai:meher.sanjaya-kumar "Biswas, Gautam" https://zbmath.org/authors/?q=ai:biswas.gautam "Mondal, Pranab Kumar" https://zbmath.org/authors/?q=ai:mondal.pranab-kumar Summary: We have presented an experimental analysis on the investigations of capillary filling dynamics of inelastic non-Newtonian fluids in the regime of surface tension dominated flows. We use the Ostwald-de Waele power-law model to describe the rheology of the non-Newtonian fluids. Our analysis primarily focuses on the experimental observations and revisits the theoretical understanding of the capillary dynamics from the perspective of filling kinematics at the interfacial scale. Notably, theoretical predictions of the filling length into the capillary largely endorse our experimental results. We study the effects of the shear-thinning nature of the fluid on the underlying filling phenomenon in the capillary-driven regime through a quantitative analysis. We further show that the dynamics of contact line motion in this regime plays an essential role in advancing the fluid front in the capillary. Our experimental results on the filling in a horizontal capillary re-establish the applicability of the Washburn analysis in predicting the filling characteristics of non-Newtonian fluids in a vertical capillary during early stage of filling [\textit{R. M. Digilov}, Capillary rise of a non-Newtonian power law liquid: impact of the fluid rheology and dynamic contact angle'', Langmuir 24, 13663--13667 (2008; \url{doi:10.1021/la801807j})]. Finally, through a scaling analysis, we suggest that the late stage of filling by the shear-thinning fluids closely follows the variation $$x \sim \sqrt{t}$$. Such a regime can be called the modified Washburn regime [\textit{E. W. Washburn}, The dynamics of capillary flow'', Phys. Rev.17, No. 3, 273--283 (1921; \url{doi:10.1103/PhysRev.17.273})]. Corrigendum to: Heat and mass mixed convection for MHD viscoelastic fluid past a stretching sheet with ohmic dissipation'' https://zbmath.org/1472.76002 2021-11-25T18:46:10.358925Z "Hsiao, Kai-Long" https://zbmath.org/authors/?q=ai:hsiao.kai-long Corrigendum to the author's paper [ibid. 15, No. 7, 1803--1812 (2010; Zbl 1222.76013)]. Initial boundary value problems for the three-dimensional compressible elastic Navier-Stokes-Poisson equations https://zbmath.org/1472.76003 2021-11-25T18:46:10.358925Z "Wang, Yong" https://zbmath.org/authors/?q=ai:wang.yong.6 "Wu, Wenpei" https://zbmath.org/authors/?q=ai:wu.wenpei The paper in question deals with compressible viscoelastic electrical conducting fluids. Their flows are governed by the elastic Navier-Stokes-Poisson system \begin{align*} \partial_t\rho + \nabla\cdot(\rho u) & = 0,\\ \partial_t(\rho u) + \nabla\cdot (\rho u \otimes u) + \nabla P(\rho) & = \mu\Delta u + (\mu + \lambda)\nabla\nabla\cdot u + c^2 \nabla\cdot(\rho \mathbb F\mathbb F^T) + \rho\nabla\Phi,\\ \partial_t\mathbb F + u \cdot \nabla \mathbb F & = \nabla u \mathbb F,\\ \Delta \Phi & = \rho - \overline\rho, \end{align*} which holds true on a certain bounded domain $$\Omega\subset \mathbb R^3$$. Here the unknowns are the density $$\rho$$, the velocity $$u,$$ the deformation gradient $$\mathbb F,$$ and the electrostatic potential $$\Phi$$. The system is endowed with an initial condition $(\rho, u, \mathbb F)(x,0) = (\rho_0,u_0,\mathbb F_0)(x),$ with the homogeneous Dirichlet bouundary condition for $$u$$ and with either $\Phi|_{\partial\Omega} = 0\qquad \mbox{or }\quad \nabla\Phi\cdot \nu|_{\partial\Omega} = 0.$ The main theorem of this paper provides the global-in-time existence of a unique global solution. This result is obtained under additional assumption on the smallness of initial data $$(\rho_0 - \overline\rho,u_0,\mathbb F_0)$$. In order to obtain the necessary estimates allowing multiple usage of the local-in-time existence theorem, the authors work with the deformation $$\varphi$$ rather than with the deformation gradient $$\mathbb F$$. Here the deformation is defined as $$\varphi:= X(x,t) - x$$, where $$X$$ is the Lagrangian coordinate, i.e., an inverse to a function $$x(X,t)$$ defined by the following ordinary differential equation \begin{align*} \frac{\mathrm{d}x(X,t)}{\mathrm{d}t} & = u(x(X,t),t),\\ x(X,0) & = X. \end{align*} A pseudo-anelastic model for stress softening in liquid crystal elastomers https://zbmath.org/1472.76004 2021-11-25T18:46:10.358925Z "Mihai, L. Angela" https://zbmath.org/authors/?q=ai:mihai.l-angela "Goriely, Alain" https://zbmath.org/authors/?q=ai:goriely.alain Summary: Liquid crystal elastomers exhibit stress softening with residual strain under cyclic loads. Here, we model this phenomenon by generalizing the classical pseudo-elastic formulation of the Mullins effect in rubber. Specifically, we modify the neoclassical strain-energy density of liquid crystal elastomers, depending on the deformation and the nematic director, by incorporating two continuous variables that account for stress softening and the associated set strain. As the material behaviour is governed by different forms of the strain-energy density on loading and unloading, the model is referred to as pseudo-anelastic. We then analyse qualitatively the mechanical responses of the material under cyclic uniaxial tension, which is easier to reproduce in practice, and further specialize the model in order to calibrate its parameters to recent experimental data at different temperatures. The excellent agreement between the numerical and experimental results confirms the suitability of our approach. Since the pseudo-energy function is controlled by the strain-energy density for the primary deformation, it is valid also for materials under multiaxial loads. Our study is relevant to mechanical damping applications and serves as a motivation for further experimental tests. Analysis and computations of a non-local thin-film model for two-fluid shear driven flows https://zbmath.org/1472.76005 2021-11-25T18:46:10.358925Z "Papageorgiou, D. T." https://zbmath.org/authors/?q=ai:papageorgiou.demetrios-t "Tanveer, S." https://zbmath.org/authors/?q=ai:tanveer.shakera|tanveer.saleh Summary: This paper is concerned with analysis and computations of a non-local thin-film model developed in Kalogirou \& Papageorgiou (\textit{J. Fluid Mech.}802, 5-36, 2016) for a perturbed two-layer Couette flow when the thickness of the more viscous fluid layer next to the stationary wall is small compared to the thickness of the less viscous fluid. Travelling wave solutions and their stability are determined numerically, and secondary bifurcation points are identified in the process. We also determine regions in parameter space where bistability is observed with two branches being linearly stable at the same time. The travelling wave solutions are mathematically justified through a \textit{quasi-solution} analysis in a neighbourhood of an empirically constructed approximate solution. This relies in part on precise asymptotics of integrals of Airy functions for large wave numbers. The primary bifurcation about the trivial state is shown rigorously to be supercritical, and the dependence of bifurcation points, as a function of Reynolds number $$R$$ and the primary wavelength $$2 \pi \nu^{-1/2}$$ of the disturbance, is determined analytically. A geometric diffuse-interface method for droplet spreading https://zbmath.org/1472.76006 2021-11-25T18:46:10.358925Z "Holm, Darryl D." https://zbmath.org/authors/?q=ai:holm.darryl-d "Náraigh, Lennon Ó." https://zbmath.org/authors/?q=ai:naraigh.lennon-o "Tronci, Cesare" https://zbmath.org/authors/?q=ai:tronci.cesare Summary: This paper exploits the theory of geometric gradient flows to introduce an alternative regularization of the thin-film equation valid in the case of large-scale droplet spreading---the geometric diffuse-interface method. The method possesses some advantages when compared with the existing models of droplet spreading, namely the slip model, the precursor-film method and the diffuse-interface model. These advantages are discussed and a case is made for using the geometric diffuse-interface method for the purpose of numerical simulations. The mathematical solutions of the geometric diffuse interface method are explored via such numerical simulations for the simple and well-studied case of large-scale droplet spreading for a perfectly wetting fluid---we demonstrate that the new method reproduces Tanner's Law of droplet spreading via a simple and robust computational method, at a low computational cost. We discuss potential avenues for extending the method beyond the simple case of perfectly wetting fluids. Corrigendum to: Hydrodynamic-driven morphogenesis of karst draperies: spatio-temporal analysis of the two-dimensional impulse response'' https://zbmath.org/1472.76007 2021-11-25T18:46:10.358925Z "Ledda, P. G." https://zbmath.org/authors/?q=ai:ledda.pier-giuseppe "Balestra, G." https://zbmath.org/authors/?q=ai:balestra.gioele "Lerisson, G." https://zbmath.org/authors/?q=ai:lerisson.gaetan "Scheid, B." https://zbmath.org/authors/?q=ai:scheid.benoit "Wyart, M." https://zbmath.org/authors/?q=ai:wyart.matthieu "Gallaire, F." https://zbmath.org/authors/?q=ai:gallaire.francois From the text: We found an error in (2.4) of our paper [ibid. 910, Paper No. A53, 33 p. (2021; Zbl 1461.76044)]. The correct non-dimensional expression for the curvature of the free surface is $\kappa=\boldsymbol{\nabla}\cdot\left(\frac{\nabla(h+h^0)}{\sqrt{1+\left(\frac{h_N}{l^\ast_c}\right)^2|\nabla(h+h^0)|^2}}\right).$ While this error does not bear any consequence in the linear analysis at the core of this paper, the value $$h_N/l^\ast_c=1$$ has to be specified in figures 15, 16, 17, 21, without altering the discussion. On the dynamics of thin layers of viscous flows inside another viscous fluid https://zbmath.org/1472.76008 2021-11-25T18:46:10.358925Z "Pernas Castaño, Tania" https://zbmath.org/authors/?q=ai:pernas-castano.tania "Velázquez, Juan J. L." https://zbmath.org/authors/?q=ai:velazquez.juan-j-l Summary: In this work we will study the dynamics of a thin layer of a viscous fluid which is embedded in the interior of another viscous fluid. The resulting flow can be approximated by means of the solutions of a free boundary problem for the Stokes equation in which one of the unknowns is the shape of a curve which approximates the geometry of the thin layer of fluid. We also derive the equation yielding the thickness of this fluid. This model, that will be termed as the \textit{Geometric Free Boundary Problem}, will be derived using matched asymptotic expansions. We will prove that the Geometric Free Boundary Problem is well posed and the solutions of the thickness equation are well defined (in particular they do not yield breaking of fluid layers) as long as the solutions of the Geometric Free Boundary Problem exist. Optimization of consistent two-equation models for thin film flows https://zbmath.org/1472.76009 2021-11-25T18:46:10.358925Z "Richard, G. L." https://zbmath.org/authors/?q=ai:richard.gael-loic "Gisclon, M." https://zbmath.org/authors/?q=ai:gisclon.marguerite "Ruyer-Quil, C." https://zbmath.org/authors/?q=ai:ruyer-quil.christian "Vila, J. P." https://zbmath.org/authors/?q=ai:vila.jean-paul Summary: A general study of consistent two-equation models for thin film flows is presented. In all models derived by the energy integral method or by an equivalent method, the energy of the system, apart from the kinetic energy of the mean flow, depends on the mean velocity. We show that in this case the model does not satisfy the principle of Galilean invariance. All consistent models derived by the momentum integral method are Galilean invariant but they admit an energy equation and a capillary energy only if the Galilean-invariant part of the first-order momentum flux does not depend on the mean velocity. We show that, both for theoretical and numerical reasons, two-equations models should be derived by a momentum integral method admitting an energy equation leading to the structure of the equations of fluids endowed with internal capillarity. Among all models fulfilling these conditions, those having the best properties are selected. The nonlinear properties are tested from the speed of solitary waves at the high Reynolds number limit while the linear properties are studied from the neutral stability curves and from the celerity of the kinematic waves along these curves. The latter criterion gives the best consistent way to write the second-order diffusive terms of the model. Optimized consistent two-equation models are then proposed and numerical results are compared to numerical and experimental results of the literature. Swelling and shrinking in prestressed polymer gels: an incremental stress-diffusion analysis https://zbmath.org/1472.76010 2021-11-25T18:46:10.358925Z "Rossi, Marco" https://zbmath.org/authors/?q=ai:rossi.marco|rossi.marco.1 "Nardinocchi, Paola" https://zbmath.org/authors/?q=ai:nardinocchi.paola "Wallmersperger, Thomas" https://zbmath.org/authors/?q=ai:wallmersperger.thomas Summary: Polymer gels are porous fluid-saturated materials which can swell or shrink triggered by various stimuli. The swelling/shrinking-induced deformation can generate large stresses which may lead to the failure of the material. In the present research, a nonlinear stress-diffusion model is employed to investigate the stress and the deformation state arising in hydrated constrained polymer gels when subject to a varying chemical potential. Two different constraint configurations are taken into account: (i) elastic constraint along the thickness direction and (ii) plane elastic constraint. The first step entirely defines a compressed/tensed configuration. From there, an incremental chemo-mechanical analysis is presented. The derived model extends the classical linear poroelastic theory with respect to a prestressed configuration. Finally, the comparison between the analytical results obtained by the proposed model and a particular problem already discussed in literature for a stress-free gel membrane (one-dimensional test case) will highlight the relevance of the derived model. A variational principle for fluid sloshing with vorticity, dynamically coupled to vessel motion https://zbmath.org/1472.76011 2021-11-25T18:46:10.358925Z "Ardakani, H. Alemi" https://zbmath.org/authors/?q=ai:alemi-ardakani.h|ardakani.hamid-alemi "Bridges, T. J." https://zbmath.org/authors/?q=ai:bridges.thomas-j "Gay-Balmaz, F." https://zbmath.org/authors/?q=ai:gay-balmaz.francois "Huang, Y. H." https://zbmath.org/authors/?q=ai:huang.youhong|huang.yunhu|huang.yonghao|huang.yihong|huang.yunhong|huang.yong-huai|huang.yanhong|huang.yuan-hao|huang.yonghui|huang.yehui|huang.yu-hsi|huang.yunhan|huang.yanhu|huang.yuehua|huang.you-heng|huang.yahui|huang.yao-hung|huang.yao-hsien|huang.yuheng|huang.yongheng|huang.yi-hsiang|huang.ying-hui|huang.yonghong|huang.yuhan|huang.yanhe|huang.yuhao|huang.yuehui|huang.yihui|huang.yuhui|huang.yanghong|huang.yanhao|huang.yunhua|huang.yuhua|huang.yanhua|huang.yi-hsiung|huang.yong-hu|huang.yu-hsiung|huang.yih-huei|huang.yuhai|huang.yihai|huang.yihua|huang.yu-hsuan|huang.yen-hui|huang.yao-huei|huang.yonghang|huang.yanhui|huang.yung-hsiang|huang.yu-hsiu|huang.yu-hsih|huang.yuhong|huang.yueh-hung "Tronci, C." https://zbmath.org/authors/?q=ai:tronci.cesare Summary: A variational principle is derived for two-dimensional incompressible rotational fluid flow with a free surface in a moving vessel when both the vessel and fluid motion are to be determined. The fluid is represented by a stream function and the vessel motion is represented by a path in the planar Euclidean group. Novelties in the formulation include how the pressure boundary condition is treated, the introduction of a stream function into the Euler-Poincaré variations, the derivation of free surface variations and how the equations for the vessel path in the Euclidean group, coupled to the fluid motion, are generated automatically. Two-point wavepacket modelling of jet noise https://zbmath.org/1472.76012 2021-11-25T18:46:10.358925Z "Maia, I. A." https://zbmath.org/authors/?q=ai:maia.igor-a "Jordan, P." https://zbmath.org/authors/?q=ai:jordan.peter "Cavalieri, A. V. G." https://zbmath.org/authors/?q=ai:cavalieri.andre-v-g "Jaunet, V." https://zbmath.org/authors/?q=ai:jaunet.vincent Summary: This paper is focused on the study of a kinematic wavepacket model for jet noise based on two-point statistics. The model contains physical parameters that define its structure in terms of wavenumber, envelope shape and coherence decay. These parameters, which are necessary to estimate the sound pressure levels radiated by the source, were educed from a large-eddy simulation database of a Mach 0.4, fully turbulent jet. The sound pressure levels predicted by the model were compared with acoustic data and the results show that when the parameters are carefully educed from the data, the sound pressure levels generated are in good agreement with experimentally measured values for low Strouhal numbers and polar angles. Furthermore, here we show that a correct representation of both coherence decay and wavepacket envelope shape are key aspects to an accurate sound prediction. A Spectral Proper Orthogonal Decomposition (SPOD) of the model source was also performed motivated by the search for a low-rank model capable of capturing the acoustic efficiency of the full source. It is shown that only a few SPOD modes are necessary to recover acoustically important wavepacket traits. An alternative view on the Bateman-Luke variational principle https://zbmath.org/1472.76013 2021-11-25T18:46:10.358925Z "Alemi Ardakani, Hamid" https://zbmath.org/authors/?q=ai:ardakani.hamid-alemi Summary: A new derivation of the Bernoulli equation for water waves in three-dimensional rotating and translating coordinate systems is given. An alternative view on the Bateman-Luke variational principle is presented. The variational principle recovers the boundary value problem governing the motion of \textit{potential water waves} in a container undergoing prescribed rigid-body motion in three dimensions. A mathematical theory is presented for the problem of three-dimensional interactions between \textit{potential surface waves} and a floating structure with interior \textit{potential fluid sloshing}. The complete set of equations of motion for the exterior gravity-driven water waves, and the exact nonlinear hydrodynamic equations of motion for the linear momentum and angular momentum of the floating structure containing fluid, are derived from a second variational principle. Trapped modes in a multi-layer fluid https://zbmath.org/1472.76014 2021-11-25T18:46:10.358925Z "Cal, F. S." https://zbmath.org/authors/?q=ai:cal.filipe-s "Dias, G. A. S." https://zbmath.org/authors/?q=ai:dias.goncalo-a-s "Pereira, B. M. M." https://zbmath.org/authors/?q=ai:pereira.b-m-m "Videman, J. H." https://zbmath.org/authors/?q=ai:videman.juha-hans Summary: In this article, we study the existence of solutions for the problem of interaction of linear water waves with an array of three-dimensional fixed structures in a density-stratified multi-layer fluid, where in each layer the density is assumed to be constant. Considering time-harmonic small-amplitude motion, we present recursive formulae for the coefficients of the eigenfunctions of the spectral problem associated with the water-wave problem in the absence of obstacles and for the corresponding dispersion relation. We derive a variational and operator formulation for the problem with obstacles and introduce a sufficient condition for the existence of propagating waves trapped in the vicinity of the array of obstacles. We present several (arrays of) structures supporting trapped waves and discuss the possibility of approximating the continuously stratified fluid by a multi-layer model. Capillary-gravity waves on a dielectric fluid of finite depth under normal electric field https://zbmath.org/1472.76015 2021-11-25T18:46:10.358925Z "Gao, Tao" https://zbmath.org/authors/?q=ai:gao.tao "Doak, Alex" https://zbmath.org/authors/?q=ai:doak.alex "Vanden-Broeck, Jean-Marc" https://zbmath.org/authors/?q=ai:vanden-broeck.jean-marc "Wang, Zhan" https://zbmath.org/authors/?q=ai:wang.zhan Summary: In this work, we consider two-dimensional capillary-gravity waves propagating under the influence of a vertical electric field on a dielectric of finite depth bounded above by a perfectly conducting and hydrodynamically passive fluid. Both linear and weakly nonlinear theories are developed, and long-wave model equations are derived based on the analyticity of the Dirichlet-Neumann operator. Fully nonlinear computations are carried out by using a time-dependent conformal mapping method. Solitary waves are found, and their stability characteristics subject to longitudinal perturbations are studied numerically. The shedding of stable solitary waves is achieved by moving a Gaussian pressure on the free surface with the speed close to a phase speed minimum and removing the pressure after a period of time. The novel result shows that a depression bright solitary wave and an elevation generalized solitary wave co-exist in the solitary-wave excitation. Scattering and radiation of water waves by a submerged rigid disc in a two-layer fluid https://zbmath.org/1472.76016 2021-11-25T18:46:10.358925Z "Islam, Najnin" https://zbmath.org/authors/?q=ai:islam.najnin "Kundu, Souvik" https://zbmath.org/authors/?q=ai:kundu.souvik "Gayen, Rupanwita" https://zbmath.org/authors/?q=ai:gayen.rupanwita Summary: Interaction of water waves with a horizontal rigid disc submerged in the lower layer of a two-layer fluid is studied in three dimensions using linear theory. The governing boundary value problem is reduced to a two-dimensional hypersingular integral equation. This integral equation is further reduced to a one-dimensional Fredholm integral equation of the second kind in terms of a newly defined function. The solution to the latter integral equation is used to compute the total scattering cross section and the hydrodynamic force for the scattering problem and the added mass and the damping coefficient for the radiation problem. Haskind relations connecting the solutions of the radiation and the scattering problems are also derived. The effects of variations of the submergence depth of the disc and the depth of the upper layer on different physical quantities are investigated. We observe amplification of the added mass and the damping coefficient, the total scattering cross section and the hydrodynamic force when the disc goes near the interface or when the height of the upper layer decreases. Known results for a horizontal disc submerged in a single-layer fluid of infinite depth are recovered from the present analysis. A class of exact nonlinear traveling wave solutions for shallow water with a non-stationary bottom surface https://zbmath.org/1472.76017 2021-11-25T18:46:10.358925Z "Kogelbauer, F." https://zbmath.org/authors/?q=ai:kogelbauer.florian "Rubin, M. B." https://zbmath.org/authors/?q=ai:rubin.miles-b Summary: The GN nonlinear shallow water wave equations developed by \textit {A. E. Green} and \textit {P. M. Naghdi} [Proc. R. Soc. Lond., Ser. A 347, 447--473 (1976; Zbl 0333.76003); J. Fluid Mech. 78, 237--246 (1976; Zbl 0351.76014)] are valid for a non-stationary, non-uniform bottom surface and a non-uniform pressure on the top surface. In contrast, the S nonlinear shallow water wave equations developed by \textit{F. Serre} [Contribution à l'étude des écoulements permanents et variables dans les canaux'', Houille Blanche 6, 830--872 (1953; \url{doi:10.1051/lhb/1953058}); Contribution à l'étude des écoulements permanents et variables dans les canaux'', Houille Blanche 3, 374--388 (1953)] for uniform depth and later generalized by \textit{F. J. Seabra-Santos} et al. [Numerical and experimental study of the transformation of a solitary wave over a shelf or isolated obstacle'', J. Fluid Mech. 176, No. 1, 117--134 (1987; \url{doi:10.1017/s0022112087000594})] for non-uniform depth are limited to a stationary bottom surface and a uniform pressure applied to the top surface. This paper develops a class of exact nonlinear traveling wave solutions of the GN equations for a non-stationary, non-uniform bottom surface. Also, the explicit expressions for the pressure acting on the bottom surface and the average pressure through the depth in the GN equations are used to place physical restrictions on the motion which ensure that these pressures remain non-negative preventing cavitation. Kernel representation of long-wave dynamics on a uniform slope https://zbmath.org/1472.76018 2021-11-25T18:46:10.358925Z "Shimozono, T." https://zbmath.org/authors/?q=ai:shimozono.takenori Summary: Long-wave propagation on a uniformly sloping beach is formulated as a transient-response problem, with initially stationary water subjected to an incident wave. Both the water surface elevation and the horizontal flow velocity on the slope can be represented as convolutions of the rate of displacement of the water surface at the toe of the slope with a singular kernel function of time and space. The kernel, which is typically expressed in the form of an infinite series, accommodates the dynamic processes of long waves, such as shoaling, reflection, and multiple reflections over the slope and yields exact solutions of the linear shallow water equations for any smooth incident wave. The kernel convolution can be implemented numerically by using double exponential formulas to avoid the kernel singularity. The kernel formulation can be extended readily to nonlinear dynamics \textit{via} the hodograph transform, which in turn enables the instantaneous prediction of nonlinear wave properties and of the occurrence of wave breaking in the near-shore area. This general description of long-wave dynamics provides new insights into the long-studied problem. On the Wiener-Hopf solution of water-wave interaction with a submerged elastic or poroelastic plate https://zbmath.org/1472.76019 2021-11-25T18:46:10.358925Z "Smith, M. J. A." https://zbmath.org/authors/?q=ai:smith.michael-j-a "Peter, M. A." https://zbmath.org/authors/?q=ai:peter.malte-andreas "Abrahams, I. D." https://zbmath.org/authors/?q=ai:abrahams.i-david "Meylan, M. H." https://zbmath.org/authors/?q=ai:meylan.michael-h Summary: A solution to the problem of water-wave scattering by a semi-infinite submerged thin elastic plate, which is either porous or non-porous, is presented using the Wiener-Hopf technique. The derivation of the Wiener-Hopf equation is rather different from that which is used traditionally in water-waves problems, and it leads to the required equations directly. It is also shown how the solution can be computed straightforwardly using Cauchy-type integrals, which avoids the need to find the roots of the highly non-trivial dispersion equations. We illustrate the method with some numerical computations, focusing on the evolution of an incident wave pulse which illustrates the existence of two transmitted waves in the submerged plate system. The effect of the porosity is studied, and it is shown to influence the shorter-wavelength pulse much more strongly than the longer-wavelength pulse. General rogue wave solutions of the coupled Fokas-Lenells equations and non-recursive Darboux transformation https://zbmath.org/1472.76020 2021-11-25T18:46:10.358925Z "Ye, Yanlin" https://zbmath.org/authors/?q=ai:ye.yanlin "Zhou, Yi" https://zbmath.org/authors/?q=ai:zhou.yi "Chen, Shihua" https://zbmath.org/authors/?q=ai:chen.shihua "Baronio, Fabio" https://zbmath.org/authors/?q=ai:baronio.fabio "Grelu, Philippe" https://zbmath.org/authors/?q=ai:grelu.philippe Summary: We formulate a non-recursive Darboux transformation technique to obtain the general $$n$$ th-order rational rogue wave solutions to the coupled Fokas-Lenells system, which is an integrable extension of the noted Manakov system, by considering both the double-root and triple-root situations of the spectral characteristic equation. Based on the explicit fundamental and second-order rogue wave solutions, we demonstrate several interesting rogue wave dynamics, among which are coexisting rogue waves and anomalous Peregrine solitons. Our solutions are generalized to include the complete background-field parameters and therefore helpful for future experimental study. A fluid mechanic's analysis of the teacup singularity https://zbmath.org/1472.76021 2021-11-25T18:46:10.358925Z "Barkley, Dwight" https://zbmath.org/authors/?q=ai:barkley.dwight Summary: The mechanism for singularity formation in an inviscid wall-bounded fluid flow is investigated. The incompressible Euler equations are numerically simulated in a cylindrical container. The flow is axisymmetric with the swirl. The simulations reproduce and corroborate aspects of prior studies reporting strong evidence for a finite-time singularity. The analysis here focuses on the interplay between inertia and pressure, rather than on vorticity. The linearity of the pressure Poisson equation is exploited to decompose the pressure field into independent contributions arising from the meridional flow and from the swirl, and enforcing incompressibility and enforcing flow confinement. The key pressure field driving the blowup of velocity gradients is that confining the fluid within the cylinder walls. A model is presented based on a primitive-variables formulation of the Euler equations on the cylinder wall, with closure coming from how pressure is determined from velocity. The model captures key features in the mechanics of the blowup scenario. The Godbillon-Vey invariant as topological vorticity compression and obstruction to steady flow in ideal fluids https://zbmath.org/1472.76022 2021-11-25T18:46:10.358925Z "Machon, Thomas" https://zbmath.org/authors/?q=ai:machon.thomas Summary: If the vorticity field of an ideal fluid is tangent to a foliation, additional conservation laws arise. For a class of zero-helicity vorticity fields, the Godbillon-Vey (GV) invariant of foliations is defined and is shown to be an invariant purely of the vorticity, becoming a higher-order helicity-type invariant of the flow. GV $$\neq 0$$ gives both a global topological obstruction to steady flow and, in a particular form, a local obstruction. GV is interpreted as helical compression and stretching of vortex lines. Examples are given where the value of GV is determined by a set of distinguished closed vortex lines. Exact solution to a Liouville equation with Stuart vortex distribution on the surface of a torus https://zbmath.org/1472.76023 2021-11-25T18:46:10.358925Z "Sakajo, Takashi" https://zbmath.org/authors/?q=ai:sakajo.takashi Summary: A steady solution of the incompressible Euler equation on a toroidal surface $$\mathbb{T}_{R , r}$$ of major radius $$R$$ and minor radius $$r$$ is provided. Its streamfunction is represented by an exact solution to the modified Liouville equation, $$\nabla_{\mathbb{T}_{R , r}}^2 \psi = c \text{e}^{d \psi} +( 8 / d) \kappa$$, where $$\nabla_{\mathbb{T}_{R , r}}^2$$ and $$\kappa$$ denote the Laplace-Beltrami operator and the Gauss curvature of the toroidal surface respectively, and $$c, d$$ are real parameters with \textit{cd} < 0. This is a generalization of the flows with smooth vorticity distributions owing to [\textit{J. T. Stuart}, J. Fluid Mech. 29, 417--440 (1967; Zbl 0152.45403)] in the plane and [\textit{D. G. Crowdy}, J. Fluid Mech. 498, 381--402 (2004; Zbl 1059.76012)] on the spherical surface. The flow consists of two point vortices at the innermost and the outermost points of the toroidal surface on the same line of a longitude, and a smooth vorticity distribution centred at their antipodal position. Since the surface of a torus has non-constant curvature and a handle structure that are different geometric features from the plane and the spherical surface, we focus on how these geometric properties of the torus affect the topological flow structures along with the change of the aspect ratio $$\alpha = R/r$$. A comparison with the Stuart vortex on the flat torus is also made. Desingularization of multiscale solutions to planar incompressible Euler equations https://zbmath.org/1472.76024 2021-11-25T18:46:10.358925Z "Wan, Jie" https://zbmath.org/authors/?q=ai:wan.jie Summary: In this paper, we consider the desingularization of multiscale solutions to 2D steady incompressible Euler equations. When the background flow $$\psi_0$$ is nontrivial, we construct a family of solutions which has nonzero vorticity in small neighborhoods of a given collection of points. One prescribed set of points comprises minimizers of the Kirchhoff-Routh function, while another part of points is on the boundary determined by both $$\psi_0$$ and Green's function. Moreover, heights and circulation of solutions have two kinds of scale. We prove the results by considering maximization problem for the vorticity and analyzing the asymptotic behavior of the maximizers. Capillary-gravity waves on the interface of two dielectric fluid layers under normal electric fields https://zbmath.org/1472.76025 2021-11-25T18:46:10.358925Z "Doak, A." https://zbmath.org/authors/?q=ai:doak.alex|doak.alexander "Gao, T." https://zbmath.org/authors/?q=ai:gao.tao "Vanden-Broeck, J.-M." https://zbmath.org/authors/?q=ai:vanden-broeck.jean-marc "Kandola, J. J. S." https://zbmath.org/authors/?q=ai:kandola.j-j-s Summary: In this article, we consider capillary-gravity waves propagating on the interface of two dielectric fluids under the influence of normal electric fields. The density of the upper fluid is assumed to be much smaller than the lower one. Linear and weakly nonlinear theories are studied. The connection to the results in other limit configurations is discussed. Fully nonlinear computations for travelling wave solutions are achieved via a boundary integral equation method. Periodic waves, solitary waves and generalised solitary waves are presented. The bifurcation of generalised solitary waves is discussed in detail. Nonlinear stability of two-layer shallow water flows with a free surface https://zbmath.org/1472.76026 2021-11-25T18:46:10.358925Z "Viríssimo, Francisco De Melo" https://zbmath.org/authors/?q=ai:virissimo.francisco-de-melo "Milewski, Paul A." https://zbmath.org/authors/?q=ai:milewski.paul-a Summary: The problem of two layers of immiscible fluid, bordered above by an unbounded layer of passive fluid and below by a flat bed, is formulated and discussed. The resulting equations are given by a first-order, four-dimensional system of PDEs of mixed-type. The relevant physical parameters in the problem are presented and used to write the equations in a non-dimensional form. The conservation laws for the problem, which are known to be only six, are explicitly written and discussed in both non-Boussinesq and Boussinesq cases. Both dynamics and nonlinear stability of the Cauchy problem are discussed, with focus on the case where the upper unbounded passive layer has zero density, also called the free surface case. We prove that the stability of a solution depends only on two baroclinic' parameters (the shear and the difference of layer thickness, the former being the most important one) and give a precise criterion for the system to be well-posed. It is also numerically shown that the system is nonlinearly unstable, as hyperbolic initial data evolves into the elliptic region before the formation of shocks. We also discuss the use of simple waves as a tool to bound solutions and preventing a hyperbolic initial data to become elliptic and use this idea to give a mathematical proof for the nonlinear instability. Optimum shapes of supercavitating hydrofoils at zero cavitation number https://zbmath.org/1472.76027 2021-11-25T18:46:10.358925Z "Gazizova, S. E." https://zbmath.org/authors/?q=ai:gazizova.s-e "Maklakov, D. V." https://zbmath.org/authors/?q=ai:maklakov.dimitri-v Summary: We investigate the problem of the flow around a supercavitating hydrofoils at zero cavitation number. Making use of formulas for the lift and drag, derived in the work by \textit{D. V. Maklakov} [J. Fluid Mech. 687, 360--375 (2011; Zbl 1241.76113)], we dtermine the hydrofoil shape that provides the minimum drag coefficient at a given lift coefficient. This ensures the maximum lift-to-drag ratio. Dynamical stability of water distribution networks https://zbmath.org/1472.76028 2021-11-25T18:46:10.358925Z "Masuda, Naoki" https://zbmath.org/authors/?q=ai:masuda.naoki "Meng, Fanlin" https://zbmath.org/authors/?q=ai:meng.fanlin Summary: Water distribution networks are hydraulic infrastructures that aim to meet water demands at their various nodes. Water flows through pipes in the network create nonlinear dynamics on networks. A desirable feature of water distribution networks is high resistance to failures and other shocks to the system. Such threats would at least transiently change the flow rate in various pipes, potentially undermining the functionality of the whole water distribution system. Here we carry out a linear stability analysis for a nonlinear dynamical system representing the flow rate through pipes that are interconnected through an arbitrary pipe network with reservoirs and consumer nodes. We show that the steady state is always locally stable and develop a method to calculate the eigenvalue that corresponds to the mode that decays the most slowly towards the equilibrium, which we use as an index for resilience of the system. We show that the proposed index is positively correlated with the recovery rate of the pipe network, which was derived from a realistic and industrially popular simulator. The present analytical framework is expected to be useful for deploying tools from nonlinear dynamics and network analysis in the design, resilience management and scenario testing of water distribution networks. A drop does not fall in a straight line: a rationale for the width of stalagmites https://zbmath.org/1472.76029 2021-11-25T18:46:10.358925Z "Parmentier, J." https://zbmath.org/authors/?q=ai:parmentier.jeanne|parmentier.j-f "Lejeune, S." https://zbmath.org/authors/?q=ai:lejeune.s "Maréchal, M." https://zbmath.org/authors/?q=ai:marechal.matthieu|marechal.michel-andre "Bourges, F." https://zbmath.org/authors/?q=ai:bourges.f "Genty, D." https://zbmath.org/authors/?q=ai:genty.d "Terrapon, V." https://zbmath.org/authors/?q=ai:terrapon.vincent-e "Maréchal, J.-C." https://zbmath.org/authors/?q=ai:marechal.j-c "Gilet, T." https://zbmath.org/authors/?q=ai:gilet.tristan Summary: Drops loaded in calcium ions detach from stalactites and impact the underlying stalagmites, thereby allowing these latter to grow through calcite precipitation. Nevertheless, little is known about the influence of the drop free fall and splash dynamics on stalagmite shape and width. Through high-speed imaging of impacting drops on stalagmites from several caves, we observed that the impact point position of the drops is scattered, sometimes over several centimetres. We show that this dispersal has no external cause and must, therefore, be self-induced. Using a Langevin-like equation, we then propose a prediction of the impact point dispersal as a function of the falling height travelled by the drops. We finally show that measured stalagmite widths are correlated to the dispersal in the impact point position of the drop. Stokes and Navier-Stokes equations subject to partial slip on uniform $$C^{2,1}$$-domains in $$L_q$$-spaces https://zbmath.org/1472.76030 2021-11-25T18:46:10.358925Z "Hobus, Pascal" https://zbmath.org/authors/?q=ai:hobus.pascal "Saal, Jürgen" https://zbmath.org/authors/?q=ai:saal.jurgen The article presents a comprehensive investigation of the well-posedness of the Stokes and Navier-Stokes initial-value problems subject to certain partial slip boundary conditions on uniform $$C^{2,1}$$-domains, including a class of non-Helmholtz domains, that is, domains where $$L_q$$ is not equal to the direct sum of solenoidal fields and gradient fields. For this purpose, the authors introduce a generalized version of the Helmholtz decomposition, which exists for a large class of domains. Moreover, its existence is shown to be necessary and sufficient for the well-posedness of the Stokes resolvent problem under consideration. The very detailed analysis is based on the resolvent problem of the heat equation subject to perfect slip boundary conditions, which is treated by a localization procedure and perturbation arguments. Since the associated resolvent operator commutes with the generalized Helmholtz decomposition, its properties can be transferred to the Stokes resolvent problem in the case of perfect slip. Subsequently, the more general partial slip boundary conditions are treated by a Neumann series argument. The authors conclude that the associated Stokes operator generates an analytic semigroup, and they derive suitable $$L_p$$-$$L_q$$ estimates. Finally, the contraction mapping principle leads to the existence of local-in-time mild solutions to the associated Navier-Stokes problem. Self-sustaining critical layer/shear layer interaction in annular Poiseuille-Couette flow at high Reynolds number https://zbmath.org/1472.76031 2021-11-25T18:46:10.358925Z "Kumar, Rishi" https://zbmath.org/authors/?q=ai:kumar.rishi "Walton, Andrew" https://zbmath.org/authors/?q=ai:walton.andrew-g Summary: The nonlinear stability of annular Poiseuille-Couette flow through a cylindrical annulus subjected to axisymmetric and helical disturbances is analysed theoretically at asymptotically large Reynolds number $$R$$ based on the radius of the outer cylinder and the constant axial pressure gradient applied. The inner cylinder moves with a prescribed positive or negative velocity in the axial direction. A distinguished scaling for the disturbance size $$\Delta = O(R^{-4/9})$$ is identified at which the jump in vorticity across the fully nonlinear critical layer is in tune with that induced across a near-wall shear layer. The disturbance propagates at close to the velocity of the inner cylinder and possesses a wavelength comparable to the radius of the outer cylinder. The dynamics of the critical layer, shear layer and the Stokes layer adjacent to the stationary wall are discussed in detail. In the majority of the pipe, the disturbance is governed predominantly by inviscid dynamics with the pressure perturbation satisfying a form of Rayleigh's equation. For a radius ratio $$\delta$$ in the range $$0 < \delta < 1$$ and a positive sliding velocity $$V$$, a numerical solution of the Rayleigh equation exists for sliding velocities in the range $$0 < V < 1 - \delta^2 + 2 \delta^2$$ ln $$\delta$$, whereas if $$V < 0$$, solutions exist for $$1 - \delta^2 + 2$$ ln $$\delta < V < 0$$. The amplitude equations for both these situations are derived analytically, and we further find that the corresponding asymptotic structures break down when the maximum value of the basic flow becomes located at the inner and outer walls, respectively. The acoustic emission from asperity interactions in mixed lubrication https://zbmath.org/1472.76032 2021-11-25T18:46:10.358925Z "Hutt, S." https://zbmath.org/authors/?q=ai:hutt.steven|hutt.steve "Clarke, A." https://zbmath.org/authors/?q=ai:clarke.a-c-m|clarke.andrew-j|clarke.allan-j|clarke.andrew-s|clarke.a-bruce|clarke.anthony|clarke.a-p|clarke.aaron|clarke.annemarie|clarke.andy|clarke.andrew-l "Pullin, R." https://zbmath.org/authors/?q=ai:pullin.r "Evans, H. P." https://zbmath.org/authors/?q=ai:evans.h-p.1 Summary: Gears typically operate in mixed lubrication conditions, where the lubricant film is too thin to prevent opposing surface asperities from interacting with each other. The likelihood/intensity of interactions is indicated by the $$\Lambda$$ ratio: the ratio of smooth surface film thickness to surface roughness. Researchers have asserted that asperity interactions are the predominant cause of acoustic emission (AE) in healthy gear contacts. However, direct experiments on gears have yet to yield a clear relationship between the Asperity AE (AAE) and $$\Lambda$$ ratio, this is in part due to the complexity of gear tooth contacts. In this paper, a disc rig was used to simulate a simplified gear contact so that the fundamental relationship between AAE and $$\Lambda$$ could be investigated more effectively. By varying oil temperature and entrainment speed, a wide spectrum of lubrication conditions was generated. In contrast to other published studies, an independent measurement technique, the contact voltage (CV), was used to verify the amount of interactions, and repeated roughness measurements were used to confirm minimal surface wear. A simple, consistent and precise relationship between AAE amplitude and $$\Lambda$$ was identified and defined for changes from full-film to mixed lubrication. Within the mixed lubrication regime, the AAE amplitude increased exponentially as $$\Lambda$$ decreased at all speeds tested. It was also observed that an increase in speed always resulted in an increase in AAE amplitude, independently of any changes in $$\Lambda$$. This direct effect of speed was modelled so that the AAE could be predicted for any combination of speed and $$\Lambda$$ within the tested envelope. This paper links gear contact tribology and AE with new precision and clearly demonstrates the potential of using AAE as a sensitive monitoring technique for the lubrication condition of gears. Some similarity solutions for three-dimensional boundary layers https://zbmath.org/1472.76033 2021-11-25T18:46:10.358925Z "Vaz, R. H." https://zbmath.org/authors/?q=ai:vaz.r-h "Mestel, A. J." https://zbmath.org/authors/?q=ai:mestel.a-jonathan Summary: A similarity solution of a three-dimensional boundary layer is investigated. The outer flow is given by $$U = ( - xz , - yz , z^2)$$, corresponding to an axisymmetric poloidal circulation with constant potential vorticity. This flow is an exact solution of the Navier-Stokes. A wall is introduced at $$y = 0$$ along which a boundary layer develops towards $$x = 0$$. We show that a similarity reduction to a system of ODEs is possible. Two distinct solutions are found, one of them through numerical path-continuation, and their stability is investigated. A second three-dimensional solution is also identified for two-dimensional outer flow. The solutions are generalized for outer flows scaling with different powers of $$z$$ and similar results are found. This behaviour is related to the non-uniqueness of the Falkner-Skan flows in a three-dimensional sense, with a transverse wall-jet. Spatial decay of the vorticity field of time-periodic viscous flow past a body https://zbmath.org/1472.76034 2021-11-25T18:46:10.358925Z "Eiter, Thomas" https://zbmath.org/authors/?q=ai:eiter.thomas|eiter.thomas-walter "Galdi, Giovanni P." https://zbmath.org/authors/?q=ai:galdi.giovanni-paolo The three-dimensional exterior problem for the Navier-Stokes equations is considered for time-periodic flows. The exponential decay of the vorticity outside the wake region is shown, uniformly in time. Moreover, the time fluctuation of the vorticity in the wake region decays algebraically and faster that the vorticity itself. This means that far from the body, the vorticity field behaves like that of the steady state exterior problem. Spectral analysis of a vortex wake behind a circular cylinder in a channel at moderate Reynolds numbers https://zbmath.org/1472.76035 2021-11-25T18:46:10.358925Z "Kalinin, E." https://zbmath.org/authors/?q=ai:kalinin.evgeniy "Mazo, A." https://zbmath.org/authors/?q=ai:mazo.alexander "Molochnikov, V." https://zbmath.org/authors/?q=ai:molochnikov.valeriy "Dushina, O." https://zbmath.org/authors/?q=ai:dushina.olga Summary: Direct numerical simulation is employed to study the complex vortical flow in the wake of a circular cylinder in a rectangular channel at $$\text{{Re}}\approx 10^2$$. Formation and development of vortices behind bodies are governed by two phenomena: Karman street in the central part of the channel and a pair of spiral peripheral vortices near the channel sidewalls. Both of these phenomena introduce their own disturbances to the flow and can be essential depending on the Reynolds number and geometry of the cross section. Fourier transform yielded spectral density of kinetic energy of velocity fluctuations at fixed sample points in the flow and also revealed the patterns in formation of vortical properties of the wake, including the transition to turbulence and self- oscillations of aerodynamics coefficients of the streamlined body. Quantitative classification of vortical flows based on topological features using graph matching https://zbmath.org/1472.76036 2021-11-25T18:46:10.358925Z "Krueger, Paul S." https://zbmath.org/authors/?q=ai:krueger.paul-s "Hahsler, Michael" https://zbmath.org/authors/?q=ai:hahsler.michael "Olinick, Eli V." https://zbmath.org/authors/?q=ai:olinick.eli-v "Williams, Sheila H." https://zbmath.org/authors/?q=ai:williams.sheila-h "Zharfa, Mohammadreza" https://zbmath.org/authors/?q=ai:zharfa.mohammadreza Summary: Vortical flow patterns generated by swimming animals or flow separation (e.g. behind bluff objects such as cylinders) provide important insight to global flow behaviour such as fluid dynamic drag or propulsive performance. The present work introduces a new method for quantitatively comparing and classifying flow fields using a novel graph-theoretic concept, called a weighted Gabriel graph, that employs critical points of the velocity vector field, which identify key flow features such as vortices, as graph vertices. The edges (connections between vertices) and edge weights of the weighted Gabriel graph encode local geometric structure. The resulting graph exhibits robustness to minor changes in the flow fields. Dissimilarity between flow fields is quantified by finding the best match (minimum difference) in weights of matched graph edges under relevant constraints on the properties of the edge vertices, and flows are classified using hierarchical clustering based on computed dissimilarity. Application of this approach to a set of artificially generated, periodic vortical flows demonstrates high classification accuracy, even for large perturbations, and insensitivity to scale variations and number of periods in the periodic flow pattern. The generality of the approach allows for comparison of flows generated by very different means (e.g. different animal species). Steady axisymmetric vortices in radial stagnation flows https://zbmath.org/1472.76037 2021-11-25T18:46:10.358925Z "Rajamanickam, Prabakaran" https://zbmath.org/authors/?q=ai:rajamanickam.prabakaran "Weiss, Adam D." https://zbmath.org/authors/?q=ai:weiss.adam-d Summary: A class of axisymmetric vortex solutions superposed upon radial stagnation flows is described. The new vortex solutions generalize the classical Burgers' vortex and Sullivan's vortex solutions in the presence of a volumetric line source at the symmetry axis, the former approaching the Burgers' vortex sheet when the source strength becomes very large. The stability of the generalized Burgers' vortex is studied. In a different manner from the classical solution, the generalized Burgers' vortices are found to be unstable for two-dimensional disturbances when the vortex Reynolds number is increased above a critical value, for a fixed strength of the volumetric source. A neutrally stable shell in a Stokes flow: a rotational Taylor's sheet https://zbmath.org/1472.76038 2021-11-25T18:46:10.358925Z "Corsi, G." https://zbmath.org/authors/?q=ai:corsi.giovanna "De Simone, A." https://zbmath.org/authors/?q=ai:de-simone.andrea|desimone.antonio|de-simone.anna "Maurini, C." https://zbmath.org/authors/?q=ai:maurini.corrado "Vidoli, S." https://zbmath.org/authors/?q=ai:vidoli.stefano Summary: In a seminal paper published in 1951, Taylor studied the interactions between a viscous fluid and an immersed flat sheet which is subjected to a travelling wave of transversal displacement. The net reaction of the fluid over the sheet turned out to be a force in the direction of the wave phase-speed. This effect is a key mechanism for the swimming of micro-organisms in viscous fluids. Here, we study the interaction between a viscous fluid and a special class of nonlinear morphing shells. We consider pre-stressed shells showing a one-dimensional set of neutrally stable equilibria with almost cylindrical configurations. Their shape can be effectively controlled through embedded active materials, generating a large-amplitude shape-wave associated with precession of the axis of maximal curvature. We show that this shape-wave constitutes the rotational analogue of a Taylor's sheet, where the translational swimming velocity is replaced by an angular velocity. Despite the net force acting on the shell vanishes, the resultant torque does not. A similar mechanism can be used to manoeuver in viscous fluids. The linearly stretching wall jet https://zbmath.org/1472.76039 2021-11-25T18:46:10.358925Z "Jafarimoghaddam, Amin" https://zbmath.org/authors/?q=ai:jafarimoghaddam.amin Summary: It is constructed a set-up comprising a jet from a slit at the leading edge, discharged over a linearly stretching wall. The non-similar flow can be interpreted as a combination of two distinct similarity regions; Akatnow-Glauert flow at the leading edge and Crane flow far away from it. In this respect, it is employed appropriate coordinate expansions to explore perturbatively the behavior of the flow near the similarity regions. A suitable composite transformation amalgamated with an abridgment of the stream-wise coordinate, facilitated an immaculate numerical simulation of the involved nonlinear partial differential equation over the entire spatial domain $$(0\leq \mathbf{X} < \infty , 0 \leq \hat{\boldsymbol{\eta}} < \infty )$$ followed by quasi-linearization technique together with an implicit algorithm of a tridiagonal form. As a result, shear stress at the wall is accurately predicted through a proposed formulation, valid all the way along the wall. It is also exhibited that there exists a transition region with a critical coordinate in the stream-wise direction in which the shear stress at the wall becomes zero. This universal coordinate (namely, the turning point) is determined as, reasonably close to, $$\mathbf{X}_{\mathbf{c} \mathbf{r.}} \approx \frac{ \mathbf{13}}{ \mathbf{23}}$$ ($$\mathbf{X}$$ is a dimensionless coordinate measuring distance along the wall and $$\hat{\boldsymbol{\eta}}$$ is the dimensionless non-similarity variable). Unsteady flow in a flattened tube https://zbmath.org/1472.76040 2021-11-25T18:46:10.358925Z "Wang, C. Y." https://zbmath.org/authors/?q=ai:wang.chengyue|wang.chuyuan|wang.canyou|wang.chenyu|wang.chenyan|wang.chaoyong|wang.chongyang.1|wang.chuan-yun|wang.chuyue|wang.chih-yueh|wang.cen-yang|wang.chuang-yun|wang.chaoyang|wang.chengyuan|wang.cuiying|wang.cangyuan|wang.chun-yen|wang.caiyun|wang.chuanyi|wang.chunyun|wang.chang-yi.1|wang.chuanyu|wang.ching-yuan|wang.chong-yu|wang.chunyin|wang.changying|wang.changyuan|wang.chunyue|wang.chinying|wang.cunyou|wang.chun-yi|wang.cun-yun|wang.chanyu|wang.cuiyun|wang.chih-yu|wang.changyuan.2|wang.chung-yue|wang.chun-yao|wang.chunying|wang.chang-yi|wang.changyou.1|wang.cheng-yeh|wang.chih-ying|wang.china-yuan|wang.canyun|wang.chuanyong|wang.changyun|wang.chung-yung|wang.chunyuan|wang.chengyi|wang.changyou|wang.c-y|wang.chengyu|wang.chuangyu|wang.chunyong|wang.chuanyou|wang.chih-yi|wang.chaoyi|wang.changyuan.1|wang.changyu|wang.congyin|wang.ching-yao|wang.chengying|wang.chuan-yin|wang.chengyong|wang.chunyang|wang.chengyou|wang.chenying|wang.cuiyu|wang.chenyong|wang.chuanyuan|wang.chien-yi|wang.chunyan|wang.chung-yi|wang.chenyang|wang.ching-yun|wang.chuyang|wang.chunyu|wang.chi-yu|wang.caiyuan|wang.chengyao|wang.chaoyue Summary: The study of the flow in a tube flattened by parallel plates is important in the transport of fluids in laterally restricted conduits. The \textit{unsteady} (starting and oscillatory) flows are solved using the method of eigenfunction superposition. The necessary eigenvalues and eigenfunctions of the Helmholtz equation are determined, for the first time, by accurate one-region or two-region point match collocations. The starting times for the starting transient depends on the aspect ratio of the duct. For oscillatory flows, the velocity maximum shifts towards the walls at higher normalized frequencies. Large-scale structures in stratified turbulent Couette flow and optimal disturbances https://zbmath.org/1472.76041 2021-11-25T18:46:10.358925Z "Zasko, Grigory V." https://zbmath.org/authors/?q=ai:zasko.grigory-v "Glazunov, Andrey V." https://zbmath.org/authors/?q=ai:glazunov.andrey-v "Mortikov, Evgeny V." https://zbmath.org/authors/?q=ai:mortikov.evgeny-v "Nechepurenko, Yuri M." https://zbmath.org/authors/?q=ai:nechepurenko.yuri-m Summary: Direct numerical simulation data of a stratified turbulent Couette flow contains two types of organized structures: rolls arising at neutral and close to neutral stratifications, and layered structures which manifest themselves as static stability increases. It is shown that both types of structures have spatial scales and forms that coincide with the scales and forms of the optimal disturbances of the simplified linear model of the Couette flow with the same Richardson numbers. On the problem of resonant incompressible flow in ventilated double glazing https://zbmath.org/1472.76042 2021-11-25T18:46:10.358925Z "Akinaga, T." https://zbmath.org/authors/?q=ai:akinaga.takeshi "Harvey-Ball, T. M." https://zbmath.org/authors/?q=ai:harvey-ball.t-m "Itano, T." https://zbmath.org/authors/?q=ai:itano.tomoaki "Generalis, S. C." https://zbmath.org/authors/?q=ai:generalis.s-c "Aifantis, E. C." https://zbmath.org/authors/?q=ai:aifantis.elias-c Summary: We employ a homotopy method, rather than conventional stability theory, in order to resolve the degeneracy due to resonance, which exists in fluid motion associated with a channel of infinite extent in ventilated double glazing. The introduction of a symmetry breaking perturbation, in the form of a Poiseuille flow component, alters substantially the resonant bifurcation tree of the original flow. Previously unknown resonant higher order nonlinear solutions, i.e. after the removal of the perturbative Poiseuille flow component, are discovered. A possible extension of the methodology to consider non-Newtonian gradient enhanced incompressible viscous fluids is also briefly discussed. Absolute and convective instabilities of semi-bounded spatially developing flows https://zbmath.org/1472.76043 2021-11-25T18:46:10.358925Z "Brevdo, Leo" https://zbmath.org/authors/?q=ai:brevdo.leo Summary: We analyse the absolute and convective instabilities of, and spatially amplifying waves in, semi-bounded spatially developing flows and media by applying the Laplace transform in time to the corresponding initial-value linear stability problem and treating the resulting boundary-value problem on $$\mathbb{R}^+$$ for a vector equation as a dynamical system. The analysis is an extension of our recently developed linear stability theory for spatially developing open flows and media with algebraically decaying tails and for fronts to flows in a semi-infinite domain. We derive the global normal-mode dispersion relations for different domains of frequency and treat absolute instability, convectively unstable wave packets and signalling. It is shown that when the limit state at infinity, i.e. the associated uniform state, is stable, the inhomogeneous flow is either stable or absolutely unstable. The inhomogeneous flow is absolutely stable but convectively unstable if and only if the flow is globally stable and the associated uniform state is convectively unstable. In such a case signalling in the inhomogeneous flow is identical with signalling in the associated uniform state. Onset and limiting amplitude of yaw instability of a submerged three-tethered buoy https://zbmath.org/1472.76044 2021-11-25T18:46:10.358925Z "Orszaghova, J." https://zbmath.org/authors/?q=ai:orszaghova.jana "Wolgamot, H." https://zbmath.org/authors/?q=ai:wolgamot.hugh-a "Draper, S." https://zbmath.org/authors/?q=ai:draper.scott "Taylor, P. H." https://zbmath.org/authors/?q=ai:taylor.paul-h "Rafiee, A." https://zbmath.org/authors/?q=ai:rafiee.ali|rafiee.ashkan|rafiee.aysan Summary: In this paper the dynamics of a submerged axi-symmetric wave energy converter are studied, through mathematical models and wave basin experiments. The device is disk-shaped and taut-moored via three inclined tethers which also act as a power take-off. We focus on parasitic yaw motion, which is excited parametrically due to coupling with heave. Assuming linear hydrodynamics throughout, but considering both linear and nonlinear tether geometry, governing equations are derived in 6 degrees of freedom (DOF). From the linearized equations, all motions, apart from yaw, are shown to be contributing to the overall power absorption. At higher orders, the yaw governing equation can be recast into a classical Mathieu equation (linear in yaw), or a nonlinear Mathieu equation with cubic damping and stiffness terms. The well-known stability diagram for the classical Mathieu equation allows prediction of onset/occurrence of yaw instability. From the nonlinear Mathieu equation, we develop an approximate analytical solution for the amplitude of the unstable motions. Comparison with regular wave experiments confirms the utility of both models for making relevant predictions. Additionally, irregular wave tests are analysed whereby yaw instability is successfully correlated to the amount of parametric excitation and linear damping. This study demonstrates the importance of considering all modes of motion in design, not just the power-producing ones. Our simplified 1 DOF yaw model provides fundamental understanding of the presence and severity of the instability. The methodology could be applied to other wave-activated devices. Stochastic modelling in fluid dynamics: Itô versus Stratonovich https://zbmath.org/1472.76045 2021-11-25T18:46:10.358925Z "Holm, Darryl D." https://zbmath.org/authors/?q=ai:holm.darryl-d Summary: Suppose the observations of Lagrangian trajectories for fluid flow in some physical situation can be modelled sufficiently accurately by a spatially correlated Itô stochastic process (with zero mean) obtained from data which is taken in fixed Eulerian space. Suppose we also want to apply Hamilton's principle to derive the stochastic fluid equations for this situation. Now, the variational calculus for applying Hamilton's principle requires the Stratonovich process, so we must transform from Itô noise in the \textit{data frame} to the equivalent Stratonovich noise. However, the transformation from the Itô process in the data frame to the corresponding Stratonovich process shifts the drift velocity of the transformed Lagrangian fluid trajectory out of the data frame into a non-inertial frame obtained from the Itô correction. The issue is, Will non-inertial forces arising from this transformation of reference frames make a difference in the interpretation of the solution behaviour of the resulting stochastic equations?' This issue will be resolved by elementary considerations. Fluctuation theorem and extended thermodynamics of turbulence https://zbmath.org/1472.76046 2021-11-25T18:46:10.358925Z "Porporato, Amilcare" https://zbmath.org/authors/?q=ai:porporato.amilcare "Hooshyar, Milad" https://zbmath.org/authors/?q=ai:hooshyar.milad "Bragg, Andrew D." https://zbmath.org/authors/?q=ai:bragg.andrew-d "Katul, Gabriel" https://zbmath.org/authors/?q=ai:katul.gabriel-g Summary: Turbulent flows are out-of-equilibrium because the energy supply at large scales and its dissipation by viscosity at small scales create a net transfer of energy among all scales. This energy cascade is modelled by approximating the spectral energy balance with a nonlinear Fokker-Planck equation consistent with accepted phenomenological theories of turbulence. The steady-state contributions of the drift and diffusion in the corresponding Langevin equation, combined with the killing term associated with the dissipation, induce a stochastic energy transfer across wavenumbers. The fluctuation theorem is shown to describe the scale-wise statistics of forward and backward energy transfer and their connection to irreversibility and entropy production. The ensuing turbulence entropy is used to formulate an extended turbulence thermodynamics. Modeling the third-order velocity structure function in the scaling range at finite Reynolds numbers https://zbmath.org/1472.76047 2021-11-25T18:46:10.358925Z "Djenidi, L." https://zbmath.org/authors/?q=ai:djenidi.lyazid "Antonia, R. A." https://zbmath.org/authors/?q=ai:antonia.robert-anthony Summary: A model for the third-order velocity structure function, $$S_3$$, is proposed for closing the transport equation of the second-order velocity structure function, $$S_2$$, in the scaling range of finite Reynolds number homogeneous and isotropic turbulence (HIT). The model is based on a gradient type hypothesis with an eddy-viscosity formulation. The present model differs from previous ones in that no assumptions are made with regard to the behaviors of $$S_2$$ and $$S_3$$ in the scaling range. This allows $$S_3$$ to be modeled whether the intermittency of the energy dissipation $$\epsilon$$ (as modeled by the intermittency phenomenology) is considered or not. In both cases, the model predicts the same (infinite Reynolds number) asymptotic behavior for $$S_2$$. This corresponds to the K41 prediction, i.e., $$S_2 \sim r^{2/3}$$. The model yields good agreement against direct numerical simulation data for forced HIT at all scales of motion except in the transition region between the dissipative and scaling ranges. The introduction of a simple bridging function in the model improves significantly the agreement in this region. Furthermore, the model illustrates the effect of the finite Reynolds number on the scaling range and shows that this effect is responsible for the deviation from a power-law behavior. {\copyright 2021 American Institute of Physics} Extreme dissipation and intermittency in turbulence at very high Reynolds numbers https://zbmath.org/1472.76048 2021-11-25T18:46:10.358925Z "Elsinga, Gerrit E." https://zbmath.org/authors/?q=ai:elsinga.gerrit-e "Ishihara, Takashi" https://zbmath.org/authors/?q=ai:ishihara.takashi "Hunt, Julian C. R." https://zbmath.org/authors/?q=ai:hunt.julian-c-r Summary: Extreme dissipation events in turbulent flows are rare, but they can be orders of magnitude stronger than the mean dissipation rate. Despite its importance in many small-scale physical processes, there is presently no accurate theory or model for predicting the extrema as a function of the Reynolds number. Here, we introduce a new model for the dissipation probability density function (PDF) based on the concept of significant shear layers, which are thin regions of elevated local mean dissipation. At very high Reynolds numbers, these significant shear layers develop layered substructures. The flow domain is divided into the different layer regions and a background region, each with their own PDF of dissipation. The volume-weighted regional PDFs are combined to obtain the overall PDF, which is subsequently used to determine the dissipation variance and maximum. The model yields Reynolds number scalings for the dissipation maximum and variance, which are in agreement with the available data. Moreover, the power law scaling exponent is found to increase gradually with the Reynolds numbers, which is also consistent with the data. The increasing exponent is shown to have profound implications for turbulence at atmospheric and astrophysical Reynolds numbers. The present results strongly suggest that intermittent significant shear layer structures are key to understanding and quantifying the dissipation extremes, and, more generally, extreme velocity gradients. On features of penetration of vertical free turbulent jets into surface of liquid in narrow channels of different lengths https://zbmath.org/1472.76049 2021-11-25T18:46:10.358925Z "Karlikov, V. P." https://zbmath.org/authors/?q=ai:karlikov.v-p.1 "Nechaev, A. T." https://zbmath.org/authors/?q=ai:nechaev.a-t "Tolokonnikov, S. L." https://zbmath.org/authors/?q=ai:tolokonnikov.sergei-lvovich Summary: The article presents new experimental results on the penetration of vertical plane and circular turbulent jets through a free surface of a liquid in relatively narrow channels of different extent with a overflow weir runoff mode. The behavior of the obtained experimental correlations for the period of arising self-oscillating flow modes is discussed. The analysis of a number of discovered features of the considered flows is carried out. Numerical simulations of turbulent thermal convection with a free-slip upper boundary https://zbmath.org/1472.76050 2021-11-25T18:46:10.358925Z "Hay, W. A." https://zbmath.org/authors/?q=ai:hay.william-a "Papalexandris, M. V." https://zbmath.org/authors/?q=ai:papalexandris.miltiadis-v Summary: In this paper, we report on direct numerical and large-eddy simulations of turbulent thermal convection without invoking the Oberbeck-Boussinesq approximation. The working medium is liquid water and we employ a free-slip upper boundary condition. This flow is a simplified model of thermal convection of water in a cavity heated from below with heat loss at its free surface. Analysis of the flow statistics suggests similarities in spatial structures to classical turbulent Rayleigh-Bénard convection but with turbulent fluctuations near the free-slip boundary. One important observation is the asymmetry in the thermal boundary layer heights at the lower and upper boundaries. Similarly, the budget of the turbulent kinetic energy shows different behaviour at the free-slip and at the lower wall. Interestingly, the work of the mean pressure is dominant due to the hydrostatic component of the mean-pressure gradient but also depends on the density fluctuations which are small but, critically, non-zero. As expected the boundary-layer heights decrease with the Rayleigh number, due to increased turbulence intensity. However, independent of the Rayleigh number, the height of the thermal boundary layer at the upper boundary is always smaller than that on the lower wall. Comparison between compressible, dilatable and incompressible fluid hypotheses efficiency in liquid conditions at high pressure and large temperature differences https://zbmath.org/1472.76051 2021-11-25T18:46:10.358925Z "Rodio, Maria Giovanna" https://zbmath.org/authors/?q=ai:rodio.maria-giovanna "Bieder, Ulrich" https://zbmath.org/authors/?q=ai:bieder.ulrich Summary: This work is devoted to comparing the compressible, dilatable and incompressible modeling approach for reproducing the unsteady TOPFLOW test case PTS TSW 3-4. For this comparison, we use two codes: NEPTUNE\_CFD and TRIO. In one hand, NEPTUNE\_CFD allows adopting the compressible hypothesis with a URANS turbulence approach. On the other hand, TRIO can reproduce the other two assumptions with a LES turbulence approach. At first, the computations have been validated by comparing the numerical results with the experimental data concerning temperature evolution in time. The comparison shows that the incompressible hypothesis presents a more critical error than the other ones. Then, the velocity profiles obtained by the two codes are shown and compared with a twofold objective: first of all, showing a comparison between two turbulence modeling approaches and then to observe the turbulence structure and fluid dynamic developments. The velocity comparison shows an excellent agreement between the two codes. 2D turbulence closures for the barotropic jet instability simulation https://zbmath.org/1472.76052 2021-11-25T18:46:10.358925Z "Perezhogin, Pavel A." https://zbmath.org/authors/?q=ai:perezhogin.pavel-aleksandrovich Summary: In the present work the possibility of turbulence closure applying to improve barotropic jet instability simulation at coarse grid resolutions is considered. This problem is analogous to situations occurring in eddy-permitting ocean models when Rossby radius of deformation is partly resolved on a computational grid. We show that the instability is slowed down at coarse resolutions. As follows from the spectral analysis of linearized equations, the slowdown is caused by the small-scale normal modes damping arising due to numerical approximation errors and nonzero eddy viscosity. In order to accelerate instability growth, stochastic and deterministic kinetic energy backscatter (KEBs) parameterizations and scale-similarity model were applied. Their utilization led to increase of the growth rates of normal modes and thus improve characteristic time and spatial structure of the instability. On URANS congruity with time averaging: analytical laws suggest improved models https://zbmath.org/1472.76053 2021-11-25T18:46:10.358925Z "Layton, W." https://zbmath.org/authors/?q=ai:layton.william-j "McLaughlin, M." https://zbmath.org/authors/?q=ai:mclaughlin.michael Summary: The standard 1-equation model of turbulence was first derived by Prandtl and has evolved to be a common method for practical flow simulations. Five fundamental laws that any URANS model should satisfy are \begin{itemize} \item[1.] Time window: $$\tau \downarrow 0$$ implies $$v_{\text{URANS}}\rightarrow u_{\text{NSE}} \& \tau \uparrow$$ implies $$\nu_T\uparrow$$ \item[2.] $$l(x)=0$$ at walls: $$l(x)\rightarrow 0$$ as $$x\rightarrow walls$$, \item[3.] Bounded energy: $$\sup_t\int \frac{1}{2}|v(x,t)|^2+k(x,t)dx<\infty$$ \item[4.] Statistical equilibrium: $$\lim \sup_{T\rightarrow \infty }\frac{1}{T}\int_0^T\varepsilon_{\text{model}}(t)dt=\mathcal{O}\left( \frac{U^3}{L}\right)$$ \item[5.] Backscatter possible: (without negative viscosities) \end{itemize} This report proves that a kinematic specification of the model's turbulence lengthscale by $l(x,t)=\sqrt{2}k^{1/2}(x,t)\tau,$ where $$\tau$$ is the time filter window, results in a 1-equation model satisfying Conditions 1, 2, 3, 4 without model tweaks, adjustments or wall damping multipliers. For the entire collection see [Zbl 1467.34001]. Reynolds stress anisotropy in flow over two-dimensional rigid dunes https://zbmath.org/1472.76054 2021-11-25T18:46:10.358925Z "Dey, Subhasish" https://zbmath.org/authors/?q=ai:dey.subhasish "Paul, Prianka" https://zbmath.org/authors/?q=ai:paul.prianka "Ali, Sk Zeeshan" https://zbmath.org/authors/?q=ai:ali.sk-zeeshan "Padhi, Ellora" https://zbmath.org/authors/?q=ai:padhi.ellora Summary: Characteristics of turbulence anisotropy in flow over two-dimensional rigid dunes are analysed. The Reynolds stress anisotropy is envisaged from the perspective of the stress ellipsoid shape. The spatial evolutions of the anisotropic invariant map (AIM), anisotropic invariant function, eigenvalues of the scaled Reynolds stress tensor and eccentricities of the stress ellipsoid are investigated at various streamwise distances along the vertical. The data plots reveal that the oblate spheroid axisymmetric turbulence appears near the top of the crest, whereas the prolate spheroid axisymmetric turbulence dominates near the free surface. At the dune trough, the axisymmetric contraction to the oblate spheroid diminishes, as the vertical distance below the crest increases. At the reattachment point and one-third of the stoss-side, the oblate spheroid axisymmetric turbulence formed below the crest appears to be more contracted, as the vertical distance increases. The AIMs suggest that the turbulence anisotropy up to edge of the boundary layer follows a looping pattern. As the streamwise distance increases, the turbulence anisotropy at the edge of the boundary layer approaches the plane-strain limit up to two-thirds of the stoss-side, intersecting the plane-strain limit at the top of the crest and thereafter moving towards the oblate spheroid axisymmetric turbulence. Terminal fall velocity: the legacy of Stokes from the perspective of fluvial hydraulics https://zbmath.org/1472.76055 2021-11-25T18:46:10.358925Z "Dey, Subhasish" https://zbmath.org/authors/?q=ai:dey.subhasish "Ali, Sk Zeeshan" https://zbmath.org/authors/?q=ai:ali.sk-zeeshan "Padhi, Ellora" https://zbmath.org/authors/?q=ai:padhi.ellora Summary: This review article, dedicated to the bicentenary celebration of Sir George Gabriel Stokes' birthday, presents the state-of-the-science of terminal fall velocity, highlighting his rich legacy from the perspective of fluvial hydraulics. It summarizes the fluid drag on a particle and the current status of the drag coefficient from both the theoretical and empirical formulations, highlighting the three major realms -- Stokesian, transitional and Newtonian realms. The force system that drives the particle motion falling through a fluid is described. The response of terminal fall velocity to key factors, which include particle shape, hindered settling and turbulence (nonlinear drag, vortex trapping, fast tracking and effects of loitering), is delineated. The article puts into focus the impact of terminal fall velocity on fluvial hydraulics, discussing the salient role that the terminal fall velocity plays in governing the hydrodynamics of the sediment threshold, bedload transport and suspended load transport. Finally, an innovative perspective is presented on the subject's future research track, emphasizing open questions. Aerodynamic analysis of basic and extended lead-trail formation using numerical technique https://zbmath.org/1472.76056 2021-11-25T18:46:10.358925Z "Gunasekaran, M." https://zbmath.org/authors/?q=ai:gunasekaran.m "Mukherjee, Rinku" https://zbmath.org/authors/?q=ai:mukherjee.rinku Summary: This paper uses a numerical post-stall predictive tool based on decambering' approach to study the aerodynamic characteristics of a lead-trail formation in pre and post-stall flow conditions. A basic lead-trail formation consisting of 2 wings and an extended formation consisting of 5 wings are studied with a view to the possibility of fuel savings, increase in range of operation, delayed flow separation and efficient positioning of the wings with respect to each other. Whether increasing the number of wings in a configuration is more useful is also looked into. The optimum operational angles of attack for maximum advantage in terms of fuel efficiency of all wings is studied including post-stall angles of attack. Numerical results for $$C_L, C_{D_i}$$, section $$C_l$$ distribution and their dependence on vertical offsets and angle of attack are reported. Calculation of small deformations of a radially convergent shock wave inside a cavitation bubble https://zbmath.org/1472.76057 2021-11-25T18:46:10.358925Z "Aganin, A. A." https://zbmath.org/authors/?q=ai:aganin.aleksandr-alekseevich "Khalitova, T. F." https://zbmath.org/authors/?q=ai:khalitova.t-f Summary: The possibility of increasing the efficiency of calculation of small axisymmetric non-sphericity of a radially convergent shock wave in a collapsing cavitation bubble by the Godunov method of increased order of accuracy is shown in the case the surfaces of the bubble and the shock wave are presented as a combination of the spherical component and its small perturbation in the form of a spherical harmonic of some degree $$n$$. The dynamics of the vapor in the bubble and the surrounding liquid in the final high-speed stage of collapse is governed by the equations of gas dynamics closed by wide-range equations of state. Non-uniform moving radially-divergent grids are applied, condensing to the bubble surface. An increase in the calculation efficiency is achieved by decreasing the apex angle of the computational domain from (normally accepted) $$\pi/2$$ to a value that is the minimum among nonzero angles $$\theta$$ corresponding to the local extrema of the Legendre polynomial of degree $$n$$ in $$\cos{\theta}$$. This way of increasing the calculation efficiency was used to study the growth of small axisymmetric non-sphericity of a radially convergent shock wave in a collapsing cavitation bubble in acetone with a temperature of 273.15 K and a pressure of 15 bar in the case of the initial non-sphericity of the bubble in the form of even harmonics of degree $$n=6-18$$. It was found that in the initial stage of convergence of the shock wave, where it turns into a strong one, its non-sphericity increases more slowly than during the subsequent convergence. In the initial stage, the growth rate of non-sphericity decreases with increasing $$n$$. During the subsequent convergence, the non-sphericity of the shock wave grows, independently of $$n$$, proportionally to its radius to the power of $$-1.12$$. Impact of dust in the decay of blast waves produced by a nuclear explosion https://zbmath.org/1472.76058 2021-11-25T18:46:10.358925Z "Chadha, Meera" https://zbmath.org/authors/?q=ai:chadha.meera "Jena, J." https://zbmath.org/authors/?q=ai:jena.j Summary: In this paper, we have studied the impact created by the introduction of up to 5\% dust particles in enhancing the decay of blast waves produced by a nuclear explosion. A mathematical model is designed and modified using appropriate assumptions, the most important being treating a nuclear explosion as a point source of energy. A system of partial differential equations describing the one-dimensional, adiabatic, unsteady flow of a relaxing gas with dust particles and radiation effects is considered. The symmetric nature of an explosion is captured using the Lie group invariance and self-similar solutions obtained for the gas undergoing strong shocks. The enhancements in decay caused by varying the quantity of dust are studied. The energy released and the damage radius are found to decrease with time with an increase in the dust parameters. Converging shock waves in a Van der Waals gas of variable density https://zbmath.org/1472.76059 2021-11-25T18:46:10.358925Z "Chauhan, Antim" https://zbmath.org/authors/?q=ai:chauhan.antim "Arora, Rajan" https://zbmath.org/authors/?q=ai:arora.rajan "Tomar, Amit" https://zbmath.org/authors/?q=ai:tomar.amit Summary: The converging problem of cylindrically or spherically symmetric strong shock wave collapsing at the axis/centre of symmetry, is studied in a non-ideal inhomogeneous gaseous medium. Here, we assume that the undisturbed medium is spatially variable and the density of a gas is decreasing towards the axis/centre according to a power law. In the present work, we have used the perturbation technique to the implosion problem and obtained a global solution that also admits Guderley's asymptotic solution in a very good agreement which holds only in the vicinity of the axis/centre of implosion. The similarity exponents together with their corresponding amplitudes are determined by expanding the flow parameters in powers of time. We also refined the leading similarity exponents near the axis/centre of convergence. We compared our calculated results with the already existing results and found them in good agreements up to two decimal places. Shock position and flow parameters are analysed graphically with respect to the variation of values of different parameters. It is observed that an increase in the density variation index, adiabatic exponent and Van der Waals excluded volume, causes the time of shock collapse to decrease due to which the shock acceleration gets increased and shock reaches the axis/centre much faster. Predictions of the transient loading on box-like objects by arbitrary pressure waves in air https://zbmath.org/1472.76060 2021-11-25T18:46:10.358925Z "Gauch, H. L." https://zbmath.org/authors/?q=ai:gauch.h-l "Bisio, V." https://zbmath.org/authors/?q=ai:bisio.v "Rossin, S." https://zbmath.org/authors/?q=ai:rossin.s "Montomoli, F." https://zbmath.org/authors/?q=ai:montomoli.francesco "Tagarielli, V. L." https://zbmath.org/authors/?q=ai:tagarielli.v-l Summary: This study investigates the transient loading on rigid, isolated, box-like objects by impinging pressure waves of variable intensity and time duration. A numerical solver is used to predict the transient flow around the object and the consequent pressure on the object's surface. An analytical model is developed which is capable of predicting the transient loading history on the faces of a box-like object; it was found in good agreement with the numerical predictions. The numerical and analytical models are then used to construct non-dimensional design maps. Different regimes of loading are identified and explored. The Riemann solutions to the compressible ideal fluid flow https://zbmath.org/1472.76061 2021-11-25T18:46:10.358925Z "Pang, Yicheng" https://zbmath.org/authors/?q=ai:pang.yicheng "Ge, Jianjun" https://zbmath.org/authors/?q=ai:ge.jianjun "Yang, Huawei" https://zbmath.org/authors/?q=ai:yang.huawei "Hu, Min" https://zbmath.org/authors/?q=ai:hu.min Summary: In this paper, we study the exact solutions of Riemann problem for the compressible ideal fluid flow, where the external force is a continuous function of time. The exact expressions for contact discontinuity curve, shock wave curve and rarefaction wave curve are provided. Six types of exact solutions of the Riemann problem are also obtained. In particular, a vacuum arises at $$t > 0$$ although the initial data never involves the vacuum, and these solutions do not possess self-similarity in the $$(t,x)$$-plane. The discontinuous Galerkin method: derivation and properties https://zbmath.org/1472.76062 2021-11-25T18:46:10.358925Z "Kronbichler, Martin" https://zbmath.org/authors/?q=ai:kronbichler.martin Summary: This text introduces to the main ingredients of the discontinuous Galerkin method, combining the framework of high-order finite element methods with Riemann solvers for the information exchange between the elements. The concepts are explained by the example of linear transport and convergence is evaluated in one, two, and three space dimensions. Finally, the construction of schemes for second derivatives is explained and detailed for the symmetric interior penalty method. For the entire collection see [Zbl 1468.76003]. Discrete shallow water equations preserving symmetries and conservation laws https://zbmath.org/1472.76063 2021-11-25T18:46:10.358925Z "Dorodnitsyn, V. A." https://zbmath.org/authors/?q=ai:dorodnitsyn.vladimir-a "Kaptsov, E. I." https://zbmath.org/authors/?q=ai:kaptsov.e-i Summary: The one-dimensional shallow water equations in Eulerian coordinates are considered. Relations between symmetries and conservation laws for the potential form of the equations and symmetries and conservation laws in Eulerian coordinates are shown. An invariant difference scheme for equations in Eulerian coordinates with arbitrary bottom topography is constructed. It possesses all the finite-difference analogs of the conservation laws. Some bottom topographies require moving meshes in Eulerian coordinates, which are stationary meshes in mass Lagrangian coordinates. The developed invariant conservative difference schemes are verified numerically using examples of flow with various bottom topographies. {\copyright 2021 American Institute of Physics} A high order finite difference method to solve the steady state Navier-Stokes equations https://zbmath.org/1472.76064 2021-11-25T18:46:10.358925Z "Siriwardana, Nihal J." https://zbmath.org/authors/?q=ai:siriwardana.nihal-j "Pradhan, Saroj P." https://zbmath.org/authors/?q=ai:pradhan.saroj-p A fourth order finite difference scheme is proposed to solve a system of steady Navier-Stokes equations. The method is applied to the benchmark problem of the square cavity flow. A comparison of the numerical results for velocity components, obtained at the center of the cavity, is presented with the results obtained in an earlier work [\textit{V. Casulli} and \textit{D. Greenspan}, Int. J. Numer. Methods Fluids 4, 1001--1012 (1984; Zbl 0549.76050)], where the time dependent system of Navier-Stokes equations was solved. It is shown that the present method is easy to implement and that it is more efficient and stable than the method with which the comparison is made. The method of the authors is also shown to have some additional convergence properties for a variety of viscosity coefficients. Numerical illustrations are presented. On the accuracy and applicability of a new implicit Taylor method and the high-order spectral method on steady nonlinear waves https://zbmath.org/1472.76065 2021-11-25T18:46:10.358925Z "Klahn, Mathias" https://zbmath.org/authors/?q=ai:klahn.mathias "Madsen, Per A." https://zbmath.org/authors/?q=ai:madsen.per-a "Fuhrman, David R." https://zbmath.org/authors/?q=ai:fuhrman.david-r Summary: This paper presents an investigation and discussion of the accuracy and applicability of an implicit Taylor (IT) method versus the classical higher-order spectral (HOS) method when used to simulate two-dimensional regular waves. This comparison is relevant, because the HOS method is in fact an explicit perturbation solution of the IT formulation. First, we consider the Dirichlet-Neumann problem of determining the vertical velocity at the free surface given the surface elevation and the surface potential. For this problem, we conclude that the IT method is significantly more accurate than the HOS method when using the same truncation order, $$M$$, and spatial resolution, $$N$$, and is capable of dealing with steeper waves than the HOS method. Second, we focus on the problem of integrating the two methods in time. In this connection, it turns out that the IT method is less robust than the HOS method for similar truncation orders. We conclude that the IT method should be restricted to $$M = 4$$, while the HOS method can be used with $$M \leq 8$$. We systematically compare these two options and finally establish the best achievable accuracy of the two methods as a function of the wave steepness and the water depth. Construction of modern robust nodal discontinuous Galerkin spectral element methods for the compressible Navier-Stokes equations https://zbmath.org/1472.76066 2021-11-25T18:46:10.358925Z "Winters, Andrew R." https://zbmath.org/authors/?q=ai:winters.andrew-r "Kopriva, David A." https://zbmath.org/authors/?q=ai:kopriva.david-a "Gassner, Gregor J." https://zbmath.org/authors/?q=ai:gassner.gregor-j "Hindenlang, Florian" https://zbmath.org/authors/?q=ai:hindenlang.florian-j Summary: Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order accuracy and geometric flexibility. However, DG is not perfect and there remain some issues. Concerning robustness, DG has undergone an extensive transformation over the past seven years into its modern form that provides statements on solution boundedness for linear and nonlinear problems. This chapter takes a constructive approach to introduce a modern incarnation of the DG spectral element method for the compressible Navier-Stokes equations in a three-dimensional curvilinear context. The groundwork of the numerical scheme comes from classic principles of spectral methods including polynomial approximations and Gauss-type quadratures. We identify aliasing as one underlying cause of the robustness issues for classical DG spectral methods. Removing said aliasing errors requires a particular differentiation matrix and careful discretization of the advective flux terms in the governing equations. For the entire collection see [Zbl 1468.76003]. A fully coupled hybrid lattice Boltzmann and finite difference method-based study of transient electrokinetic flows https://zbmath.org/1472.76067 2021-11-25T18:46:10.358925Z "Basu, Himadri Sekhar" https://zbmath.org/authors/?q=ai:basu.himadri-sekhar "Bahga, Supreet Singh" https://zbmath.org/authors/?q=ai:singh-bahga.supreet "Kondaraju, Sasidhar" https://zbmath.org/authors/?q=ai:kondaraju.sasidhar Summary: Transient electrokinetic (EK) flows involve the transport of conductivity gradients developed as a result of mixing of ionic species in the fluid, which in turn is affected by the electric field applied across the channel. The presence of three different coupled equations with corresponding different time scales makes it difficult to model the problem using the lattice Boltzmann method (LBM). The present work aims to develop a hybrid LBM and finite difference method (FDM)-based model which can be used to study the electro-osmotic flows (EOFs) and the onset of EK instabilities using an Ohmic model, where fluid and conductivity transport are solved using LBM and the electric field is solved using FDM. The model developed will be used to simulate three different problems: (i) EOF with varying zeta-potential on the wall, (ii) similitude in EOF, and (iii) EK instabilities due to the presence of conductivity gradients. Problems (i) and (ii) will be compared with the analytical results and problem (iii) will be compared with the simulations of a spectral method-based numerical model. The results obtained from the present simulations will show that the developed model is capable of studying transient EK flows and of predicting the onset of instability. Review of smoothed particle hydrodynamics: towards converged Lagrangian flow modelling https://zbmath.org/1472.76068 2021-11-25T18:46:10.358925Z "Lind, Steven J." https://zbmath.org/authors/?q=ai:lind.steven-j "Rogers, Benedict D." https://zbmath.org/authors/?q=ai:rogers.benedict-d "Stansby, Peter K." https://zbmath.org/authors/?q=ai:stansby.peter-k Summary: This paper presents a review of the progress of smoothed particle hydrodynamics (SPH) towards high-order converged simulations. As a mesh-free Lagrangian method suitable for complex flows with interfaces and multiple phases, SPH has developed considerably in the past decade. While original applications were in astrophysics, early engineering applications showed the versatility and robustness of the method without emphasis on accuracy and convergence. The early method was of weakly compressible form resulting in noisy pressures due to spurious pressure waves. This was effectively removed in the incompressible (divergence-free) form which followed; since then the weakly compressible form has been advanced, reducing pressure noise. Now numerical convergence studies are standard. While the method is computationally demanding on conventional processors, it is well suited to parallel processing on massively parallel computing and graphics processing units. Applications are diverse and encompass wave-structure interaction, geophysical flows due to landslides, nuclear sludge flows, welding, gearbox flows and many others. In the state of the art, convergence is typically between the first- and second-order theoretical limits. Recent advances are improving convergence to fourth order (and higher) and these will also be outlined. This can be necessary to resolve multi-scale aspects of turbulent flow. Collective vibrations of a hydrodynamic active lattice https://zbmath.org/1472.76069 2021-11-25T18:46:10.358925Z "Thomson, S. J." https://zbmath.org/authors/?q=ai:thomson.s-j "Durey, M." https://zbmath.org/authors/?q=ai:durey.matthew "Rosales, R. R." https://zbmath.org/authors/?q=ai:rosales.rodolfo-ruben Summary: Recent experiments show that quasi-one-dimensional lattices of self-propelled droplets exhibit collective instabilities in the form of out-of-phase oscillations and solitary-like waves. This hydrodynamic lattice is driven by the external forcing of a vertically vibrating fluid bath, which invokes a field of subcritical Faraday waves on the bath surface, mediating the spatio-temporal droplet coupling. By modelling the droplet lattice as a memory-endowed system with spatially non-local coupling, we herein rationalize the form and onset of instability in this new class of dynamical oscillator. We identify the memory-driven instability of the lattice as a function of the number of droplets, and determine equispaced lattice configurations precluded by geometrical constraints. Each memory-driven instability is then classified as either a super- or subcritical Hopf bifurcation via a systematic weakly nonlinear analysis, rationalizing experimental observations. We further discover a previously unreported symmetry-breaking instability, manifest as an oscillatory-rotary motion of the lattice. Numerical simulations support our findings and prompt further investigations of this nonlinear dynamical system. Homogenization of a micropolar fluid past a porous media with nonzero spin boundary condition https://zbmath.org/1472.76070 2021-11-25T18:46:10.358925Z "Suárez-Grau, Francisco J." https://zbmath.org/authors/?q=ai:suarez-grau.francisco-javier After studying the well-posedness of the microscopic problem -- a micropolar fluid past a perforated domain with non vanishing spin boundary conditions, the author uses the periodic unfolding technique to pass to the periodic homogenization limit. The weak formulation of the upscaled limit is provided. Corrigendum to: The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows'' https://zbmath.org/1472.76071 2021-11-25T18:46:10.358925Z "Carlberg, Kevin" https://zbmath.org/authors/?q=ai:carlberg.kevin-t "Farhat, Charbel" https://zbmath.org/authors/?q=ai:farhat.charbel-h "Cortial, Julien" https://zbmath.org/authors/?q=ai:cortial.julien "Amsallem, David" https://zbmath.org/authors/?q=ai:amsallem.david A typo in the first of equation (13) in [the authors, ibid. 242, 623--647 (2013; Zbl 1299.76180)] is corrected. Application of coupled map lattice as an alternative to classical finite difference method for solving the convection-diffusion boundary value problem https://zbmath.org/1472.76072 2021-11-25T18:46:10.358925Z "Korus, Lukasz" https://zbmath.org/authors/?q=ai:korus.lukasz Summary: This paper presents a mathematical model for a piston flow reactor based on the material balance law using partial differential equations. A more general, nondimensional variant of the model is also derived. The finite difference method and coupled map lattice are used to create numerical algorithms to simulate spatio-temporal behavior in the studied system. The paper also includes a stability analysis of the proposed algorithms and results of numerous numerical simulations, done in order to compare both methods and to visualize the spatio-temporal behavior of the reactor and the effects of different model parameters. Discussion of the obtained results and comparison of both algorithms is also provided. Numerical investigations on bubble-induced jetting and shock wave focusing: application on a needle-free injection https://zbmath.org/1472.76073 2021-11-25T18:46:10.358925Z "Kyriazis, Nikolaos" https://zbmath.org/authors/?q=ai:kyriazis.nikolaos "Koukouvinis, Phoevos" https://zbmath.org/authors/?q=ai:koukouvinis.phoevos-k "Gavaises, Manolis" https://zbmath.org/authors/?q=ai:gavaises.manolis Summary: The formation of a liquid jet into air induced by the growth of a laser-generated bubble inside a needle-free device is numerically investigated by employing the compressible Navier-Stokes equations. The three co-existing phases (liquid, vapour and air) are assumed to be in thermal equilibrium. A transport equation for the gas mass fraction is solved in order to simulate the non-condensable gas. The homogeneous equilibrium model is used in order to account for the phase change process between liquid and vapour. Thermodynamic closure for all three phases is achieved by a barotropic Equation of State. Two-dimensional axisymmetric simulations are performed for a needle-free device for which experimental data are available and used for the validation of the developed model. The influence of the initial bubble pressure and the meniscus geometry on the jet velocity is examined by two different sets of studies. Based on the latter, a new meniscus design similar to shaped-charge jets is proposed, which offers a more focused and higher velocity jet compared to the conventional shape of the hemispherical gas-liquid interface. Preliminary calculations show that the developed jet can penetrate the skin and thus, such configurations can contribute towards a new needle-free design. Time domain simulation of focused waves by high-level irrotational Green-Naghdi equations and harmonic polynomial cell method https://zbmath.org/1472.76074 2021-11-25T18:46:10.358925Z "Zhao, B. B." https://zbmath.org/authors/?q=ai:zhao.binbin "Zheng, K." https://zbmath.org/authors/?q=ai:zheng.kaimin|zheng.kaikai|zheng.kaidi|zheng.keni|zheng.kangcheng|zheng.kuijing|zheng.kan|zheng.kougen|zheng.kaiyue|zheng.kexin|zheng.kaiyan|zheng.kengtao|zheng.kai|zheng.kouquan|zheng.kejie|zheng.ke|zheng.keke|zheng.kehong|zheng.kenneth|zheng.kangfeng|zheng.kang|zheng.kun|zheng.kai.1|zheng.kunming|zheng.kewang|zheng.keli|zheng.kelong|zheng.kaijie "Duan, W. Y." https://zbmath.org/authors/?q=ai:duan.wenyang "Ertekin, R. C." https://zbmath.org/authors/?q=ai:ertekin.r-cengiz "Shao, Y. L." https://zbmath.org/authors/?q=ai:shao.yanling|shao.yinli|shao.yanlin|shao.yingli|shao.yun-long|shao.yulong Summary: Wave focusing is one of the main mechanisms that can generate freak waves in deep water. The strongly nonlinear High-Level Irrotational Green-Naghdi (HLIGN) equations and the Harmonic Polynomial Cell (HPC) method are used here to simulate the focused waves. Numerical simulations are performed in intermediate water depth as well as in deep water. In intermediate water, the HLIGN free surface and wave kinematics are then compared with the well-accepted laboratory data and the results of the HPC method. The effect of water depth on focused waves is also carried out. It is demonstrated that both the HLIGN equations and the HPC method can accurately simulate the surface elevation and particle velocity of focused waves compared with the experiments. The velocity distribution is distinct for the focused waves with the same crest elevations but in different water depths. The HLIGN equations are considered to be an accurate and efficient wave model to investigate focused waves in the intermediate and deep water cases. Development of mathematical model of circular grill of piece-smooth profiles and creation on its basis of gas-sucking fans https://zbmath.org/1472.76075 2021-11-25T18:46:10.358925Z "Makarov, N. V." https://zbmath.org/authors/?q=ai:makarov.n-v "Makarov, V. N." https://zbmath.org/authors/?q=ai:makarov.v-n "Lifanov, A. V." https://zbmath.org/authors/?q=ai:lifanov.a-v "Materov, A. Y." https://zbmath.org/authors/?q=ai:materov.a-y "Kitonsa, H." https://zbmath.org/authors/?q=ai:kitonsa.h Summary: Further intensification of mining operations, application of innovative technologies that ensure efficient extraction and processing of mineral raw materials is limited by the requirements to the air and gas dynamic safety system, one of thesect energy-intensive elements of which are gas-suction fans characterized by insufficient adaptability and aerodynamic loading. Using the Christofel-Schwartz equation, taking into account the theory of attached vortices, the Chaplygin method of singular points and residues, the conformal mappings method was modified and an additive mathematical model of the circular lattice of S''-shaped profiles with circulation control vortexes was developed. The uniqueness of the obtained solution is proved up to a constant for the given parameters of vortex sources. A technique for calculation of aerodynamic schemes of adaptive highly loaded circular gratings with S''-shaped profiles and built-in vortex sources is proposed. A parametric series of patented block-modular gas-sucking ventilators was developed on the basis of the designed aerodynamic scheme of TS145-20, providing for the coverage of ventilation regimes for gas-abundunt coal mines for a perspective up to 2025. The test results of the prototype gas-sucking fan BPVG-7 confirmed the increase in adaptability by more than 50\% and aerodynamic loading by 35\%. For the entire collection see [Zbl 1467.34001]. Thermodynamic and vortic structures of real Schur flows https://zbmath.org/1472.76076 2021-11-25T18:46:10.358925Z "Zhu, Jian-Zhou" https://zbmath.org/authors/?q=ai:zhu.jian-zhou Summary: A two-component-two-dimensional coupled with one-component-three-dimensional (2C2Dcw1C3D) flow may also be called a real Schur flow (RSF), as its velocity gradient is uniformly of real Schur form, the latter being the intrinsic local property of any general flows. The thermodynamic and vortic'' fine structures of RSF are exposed and, in particular, the complete set of equations governing a (viscous and/or driven) 2C2Dcw1C3D flow are derived. The Lie invariances of the decomposed vorticity 2-forms of RSFs in $$d$$-dimensional Euclidean space $$\mathbb{E}^d$$ for any interger $$d \geq 3$$ are also proven, and many Lie-invariant fine results, such as those of the combinations of the entropic and vortic quantities, including the invariances of the decomposed Ertel potential vorticity (and their multiplications by any interger powers of entropy) 3-forms, then follow. {\copyright 2021 American Institute of Physics} Hessian measures in the aerodynamic Newton problem https://zbmath.org/1472.76077 2021-11-25T18:46:10.358925Z "Lokutsievskiy, L. V." https://zbmath.org/authors/?q=ai:lokutsievskiy.lev-viacheslavovich "Zelikin, M. I." https://zbmath.org/authors/?q=ai:zelikin.mikhail-i Summary: Simple natural proofs of all known results regarding the aerodynamic Newton problem are obtained. Additional new theorems and new promising formulas in terms of Hessian measures are found. A BGK model for high temperature rarefied gas flows https://zbmath.org/1472.76078 2021-11-25T18:46:10.358925Z "Baranger, C." https://zbmath.org/authors/?q=ai:baranger.celine "Dauvois, Y." https://zbmath.org/authors/?q=ai:dauvois.y "Marois, G." https://zbmath.org/authors/?q=ai:marois.g "Mathé, J." https://zbmath.org/authors/?q=ai:mathe.jordane|mathe.j-m|mathe.johan "Mathiaud, J." https://zbmath.org/authors/?q=ai:mathiaud.julien "Mieussens, L." https://zbmath.org/authors/?q=ai:mieussens.luc Summary: High temperature gases, for instance in hypersonic reentry flows, show complex phenomena like excitation of rotational and vibrational energy modes, and even chemical reactions. For flows in the continuous regime, simulation codes use analytic or tabulated constitutive laws for pressure and temperature. In this paper, we propose a BGK model which is consistent with any arbitrary constitutive laws, and which is designed to make high temperature gas flow simulations in the rarefied regime. A Chapman-Enskog analysis gives the corresponding transport coefficients. Our approach is illustrated by a numerical comparison with a compressible Navier-Stokes solver with rotational and vibrational non equilibrium. The BGK approach gives a deterministic solver with a computational cost which is close to that of a simple monoatomic gas. Non-reciprocal acoustics in a viscous environment https://zbmath.org/1472.76079 2021-11-25T18:46:10.358925Z "Heo, Hyeonu" https://zbmath.org/authors/?q=ai:heo.hyeonu "Walker, Ezekiel" https://zbmath.org/authors/?q=ai:walker.ezekiel "Zubov, Yurii" https://zbmath.org/authors/?q=ai:zubov.yurii "Shymkiv, Dmitrii" https://zbmath.org/authors/?q=ai:shymkiv.dmitrii "Wages, Dylan" https://zbmath.org/authors/?q=ai:wages.dylan "Krokhin, Arkadii" https://zbmath.org/authors/?q=ai:krokhin.arkadii "Choi, Tae-Youl" https://zbmath.org/authors/?q=ai:choi.tae-youl "Neogi, Arup" https://zbmath.org/authors/?q=ai:neogi.arup Summary: It is demonstrated that acoustic transmission through a phononic crystal with anisotropic solid scatterers becomes non-reciprocal if the background fluid is viscous. In an ideal (inviscid) fluid, the transmission along the direction of broken $$P$$ symmetry is asymmetric. This asymmetry is compatible with reciprocity since time-reversal symmetry $$(T$$ symmetry) holds. Viscous losses break $$T$$ symmetry, adding a non-reciprocal contribution to the transmission coefficient. The non-reciprocal transmission spectra for a phononic crystal of metallic circular cylinders in water are experimentally obtained and analysed. The surfaces of the cylinders were specially processed in order to weakly break $$P$$ symmetry and increase viscous losses through manipulation of surface features. Subsequently, the non-reciprocal part of transmission is separated from its asymmetric reciprocal part in numerically simulated transmission spectra. The level of non-reciprocity is in agreement with the measure of broken $$P$$ symmetry. The reported study contradicts commonly accepted opinion that linear dissipation cannot be a reason leading to non-reciprocity. It also opens a way for engineering passive acoustic diodes exploring the natural viscosity of any fluid as a factor leading to non-reciprocity. Image conditions for elliptical-coordinate separation-of-variables acoustic multiple scattering models with perfectly reflecting flat boundaries: application to \textit{in Situ} tunable noise barriers https://zbmath.org/1472.76080 2021-11-25T18:46:10.358925Z "Shin, Ho-Chul" https://zbmath.org/authors/?q=ai:shin.ho-chul Summary: Two-dimensional time-harmonic multiple scattering problems are addressed for a finite number of elliptical objects placed in wedge-shaped acoustic domains including half-plane and right-angled corners. The method of separation of variables in conjunction with the addition theorems is employed in the elliptical coordinates. The wavefunctions are represented in terms of radial and angular Mathieu functions. The method of images is applied to consider the effect of the infinitely long flat boundaries which are perfectly reflecting: either rigid or pressure release. The wedge angle is $$\pi/n$$ rad with integer $$n$$; image ellipses must be appropriately rotated to realise the mirror reflection. Then, the image conditions' are developed to reduce the number of unknowns by expressing the unknown expansion coefficients of image scattered fields in terms of real counterparts. Use of image conditions, therefore, leads to the $$4n^2$$-fold reduction in the size of a matrix for direct solvers and $$2n$$-times faster computation in building the system of linear equations than the approach without using them. Multiple scattering models using image conditions are formulated for rigid, pressure release and fluid ellipses under either plane- or cylindrical-wave incidence, and are numerically validated by the boundary element method. Furthermore, potential applications are presented: arrays of elliptically shaped scatterers make \textit{in situ} tunable noise barriers by rotating scatterers. Finally, polar-coordinate image conditions (for circular objects) are also discussed when coordinates local to circles are also rotated. In Appendix, analytic formulae are provided, which permits the elliptical-coordinate addition theorems used in this article to be calculated by summation instead of numerical integration. A pressure decomposition framework for aeroacoustic analysis of turbulent jets https://zbmath.org/1472.76081 2021-11-25T18:46:10.358925Z "Unnikrishnan, S." https://zbmath.org/authors/?q=ai:unnikrishnan.sanil "Gaitonde, Datta V." https://zbmath.org/authors/?q=ai:gaitonde.datta-v Summary: Aeroacoustic analyses of jet flows have benefited greatly from a decomposition of turbulent pressure fluctuations into hydrodynamic and acoustic components. This is typically accomplished using signal processing techniques based on phase speeds, coherence properties or spectral analyses. We present an approach, building on the Momentum Potential Theory (MPT) approach of \textit{P. E. Doak} [Momentum potential theory of energy flux carried by momentum fluctuations'', J. Sound Vib. 131, No. 1, 67--90 (1989; \url{doi:10.1016/0022-460X(89)90824-9})], to split pressure fluctuations into their hydrodynamic, acoustic and entropic, collectively designated fluid-thermodynamic (FT), components. Key advantages are that the approach is applicable everywhere in the jet \textit{i.e}, not restricted to the near-acoustic field, and does not need user-defined thresholds. The effectiveness of the technique is demonstrated by analyzing the flowfields of three simulated jets, to encompass moderate-compressible to supersonic conditions. The statistical properties and wavepacket dynamics of each pressure component, and their relationships with the unsplit pressure are elaborated. The acoustic pressure field has the form of a wavepacket that attenuates downstream and whose modal analysis reveals low-rank behavior. At each Mach number examined, the acoustic pressure also identifies the relative prominence of each of three components: i) waves with upstream propagating energy content (negative group velocity), ii) supersonically traveling radiating downstream waves, and iii) subsonically convected evanescent waves, which follow the convection pattern of hydrodynamic eddies in the turbulent region. With increasing Mach number, the radiating and convected bands of energy move closer to each other. The hydrodynamic pressure also displays a wavepacket structure, but its features are different: it displays large-scale subsonically convected structures even past the core collapse region. Thus, in the turbulent region of the jet, the acoustic pressure displays smaller integral time scales of fluctuations than the hydrodynamic component. The acoustic pressure field, which includes a zero-crossing in its radial profiles, displays larger wavelengths than the hydrodynamic pressure field, correlates better with the near-field pressure signal and captures the radiated component of noise, especially at shallow angles. These properties make it a suitable field for informing pressure-based wavepacket models for jet noise. A revisit of the tonal noise of small rotors https://zbmath.org/1472.76082 2021-11-25T18:46:10.358925Z "Zhong, Siyang" https://zbmath.org/authors/?q=ai:zhong.siyang "Zhou, Peng" https://zbmath.org/authors/?q=ai:zhou.peng|zhou.peng.1|zhou.peng.2 "Fattah, Ryu" https://zbmath.org/authors/?q=ai:fattah.ryu "Zhang, Xin" https://zbmath.org/authors/?q=ai:zhang.xin.3|zhang.xin.4|zhang.xin|zhang.xin.1 Summary: In this study, asymptotic analysis of the frequency-domain formulation to compute the tonal noise of the small rotors in the now ubiquitously multi-rotor powered drones is conducted. Simple scaling laws are proposed to evaluate the impacts of the influential parameters such as blade number, flow speed, rotation speed, unsteady motion, thrust and observer angle on the tonal noise. The rate of noise increment with thrust (or rotational speed) is determined by orders of blade passing frequency harmonics and the unsteady motion. The axial mean flow influence can be approximated by quadratic functions. At given thrust, the sound decreases rapidly with the radius and blade number as the surface pressure becomes less intensive. The higher tonal harmonics are significantly increased if unsteady motions, although of small-amplitude, are existed, as indicated by the defined sensitivity function, emphasizing that the unsteady motions should be avoided for quiet rotor designs. The scaling laws are examined by comparing with the full computations of the rotor noise using the frequency-domain method, the implementation of which has been validated by comparing with experiments. Good data collapse is obtained when the proposed scaling laws, which highlights the dominant influence of the design parameters, are incorporated. Marangoni convection of a viscous fluid over a vibrating plate https://zbmath.org/1472.76083 2021-11-25T18:46:10.358925Z "Celli, M." https://zbmath.org/authors/?q=ai:celli.michele|celli.martin "Kuznetsov, A. V." https://zbmath.org/authors/?q=ai:kuznetsov.aleksandr-vladimirovich|kuznetsov.andrey-v|kuznetsov.alex-v Summary: This research presents a new insight into Marangoni convection through investigating, both numerically and analytically, the surface tension driven instability activated by a coupled effect of a vibrating plate and viscous dissipation. A horizontal, thin fluid layer is bounded from below by an impermeable, adiabatic plate that vibrates in the horizontal direction. The upper boundary is modelled by a free surface subject to a thermal boundary condition of the third kind (Robin). The internal heat generation due to viscous dissipation yields a vertical, potentially unstable temperature gradient. The linear stability analysis of the stationary terms of the basic state is performed. The perturbed flow, in the form of plane waves, is superimposed onto the basic state. The obtained system of ordinary differential equations is solved numerically by means of the Runge-Kutta method coupled with the shooting method. For the two limiting cases, the isothermal upper boundary and adiabatic upper boundary, the analytical solutions of the eigenvalue problem are obtained. The values of the critical parameter, which identifies the threshold for the onset of Marangoni convection, are presented. Nanofluid buoyancy-driven heat transfer in three-dimensional horizontal annuli https://zbmath.org/1472.76084 2021-11-25T18:46:10.358925Z "Huang, Xiao-Jie" https://zbmath.org/authors/?q=ai:huang.xiaojie "Vafai, Kambiz" https://zbmath.org/authors/?q=ai:vafai.kambiz "Li, You-Rong" https://zbmath.org/authors/?q=ai:li.you-rong Summary: The effect of Rayleigh number and nanoparticle concentration on the flow dynamics and natural convection in three-dimensional large- and moderate-gap annuli is analyzed in detail in this work. A nanofluid is applied as the working fluid, with typical nanoparticle concentration ranging from zero to nine percent. The results indicate that the flow strength and deformation of isotherms becomes less intensive with an increase in the nanoparticle concentration for both large- and moderate-gap annuli. There exists a core region in the large-gap annulus, where the flow is two-dimensional and the value of the local Nusselt number is almost uniform in the axial direction. The core region exists between two secondary rolls, which are adjacent to the primary end rolls. The secondary flow decreases in size and finally disappears with an increase in the nanoparticle concentration. For the moderate-gap annulus, the space between the two end walls near the top portion is filled by multiple rolls, and an increase in the nanoparticle concentration gradually reduces the number of the rolls. The locations of the descending and ascending rolls relate to the maximum peaks of the Nusselt number on the inner and outer cylinders, respectively. The heat transfer enhancement only occurs at low nanoparticle concentrations ($$\varphi < 3\%$$) and higher Rayleigh numbers ($$\mathrm{Ra} > 10^5$$) for a large-gap annulus. Otherwise, in general, a deterioration in heat transfer is observed when the nanoparticle concentration increases from 1 to 9\% for both large- and moderate-gap annuli. Anisotropic bidispersive convection https://zbmath.org/1472.76085 2021-11-25T18:46:10.358925Z "Straughan, B." https://zbmath.org/authors/?q=ai:straughan.brian Summary: This paper investigates thermal convection in an anisotropic bidisperse porous medium. A bidisperse porous medium is one which possesses the usual pores, but in addition, there are cracks or fissures in the solid skeleton and these give rise to a second porosity known as micro porosity. The novelty of this paper is that the macro permeability and the micro permeability are each diagonal tensors but the three components in the vertical and in the horizontal directions may be distinct in both the macro and micro phases. Thus, there are six independent permeability coefficients. A linear instability analysis is presented and a fully nonlinear stability analysis is inferred. Several Rayleigh number and wavenumber calculations are presented and it is found that novel cell structures are predicted which are not present in the single porosity case. Diffusion in arrays of obstacles: beyond homogenization https://zbmath.org/1472.76086 2021-11-25T18:46:10.358925Z "Farah, Yahya" https://zbmath.org/authors/?q=ai:farah.yahya "Loghin, Daniel" https://zbmath.org/authors/?q=ai:loghin.daniel "Tzella, Alexandra" https://zbmath.org/authors/?q=ai:tzella.alexandra "Vanneste, Jacques" https://zbmath.org/authors/?q=ai:vanneste.jacques Summary: We revisit the classical problem of diffusion of a scalar (or heat) released in a two-dimensional medium with an embedded periodic array of impermeable obstacles such as perforations. Homogenization theory provides a coarse-grained description of the scalar at large times and predicts that it diffuses with a certain effective diffusivity, so the concentration is approximately Gaussian. We improve on this by developing a large-deviation approximation which also captures the non-Gaussian tails of the concentration through a rate function obtained by solving a family of eigenvalue problems. We focus on cylindrical obstacles and on the dense limit, when the obstacles occupy a large area fraction and non-Gaussianity is most marked. We derive an asymptotic approximation for the rate function in this limit, valid uniformly over a wide range of distances. We use finite-element implementations to solve the eigenvalue problems yielding the rate function for arbitrary obstacle area fractions and an elliptic boundary-value problem arising in the asymptotics calculation. Comparison between numerical results and asymptotic predictions confirms the validity of the latter. Modelling of withdrawal of a stratified fluid from a porous medium (Abstract of thesis) https://zbmath.org/1472.76087 2021-11-25T18:46:10.358925Z "Al-Ali, Suha Ibrahim Salih" https://zbmath.org/authors/?q=ai:al-ali.suha-ibrahim-salih (no abstract) Corrigendum to: The Horton-Rogers-Lapwood problem for an inclined porous layer with permeable boundaries'' https://zbmath.org/1472.76088 2021-11-25T18:46:10.358925Z "Barletta, Antonio" https://zbmath.org/authors/?q=ai:barletta.antonio "Celli, Michele" https://zbmath.org/authors/?q=ai:celli.michele Corrects several misprints in the authors' paper [ibid. 474, No. 2217, Article ID 20180021, 11 p. (2018; Zbl 1407.76147)]. Methodology for calculating the parameters of the $$\mathrm{CO}_2$$-$$\mathrm{CH}_4$$ replacement process in methane hydrate during the gas hydrate deposits development https://zbmath.org/1472.76089 2021-11-25T18:46:10.358925Z "Borodin, S. L." https://zbmath.org/authors/?q=ai:borodin.stansilav-leonidovich|borodin.stanislav-leonidovich "Khasanov, M. K." https://zbmath.org/authors/?q=ai:khasanov.marat-kamilovich Summary: A method for solving numerically the mathematical model system of equations describing the process of replacing methane with carbon dioxide in $$\mathrm{CH}_4$$ hydrate during the development of a gas hydrate deposit is presented. This model is considered in a one-dimensional linear approximation for the case of negative temperatures and injection of carbon dioxide in gaseous state. The process of $$\mathrm{CO}_2$$-$$\mathrm{CH}_4$$ replacement is assumed to be equilibrium. Partial differential equations are solved using an implicit scheme and tridiagonal matrix algorithm. To solve the system of equations, the method of simple iterations is used. The phase transitions methane+ice -- methane hydrate'' and carbon dioxide+ice -- carbon dioxide hydrate'' are calculated using an original algorithm suggested by the authors. Coriolis effect on thermal convection in a rotating bidispersive porous layer https://zbmath.org/1472.76090 2021-11-25T18:46:10.358925Z "Capone, F." https://zbmath.org/authors/?q=ai:capone.florinda "De Luca, R." https://zbmath.org/authors/?q=ai:de-luca.roberta "Gentile, M." https://zbmath.org/authors/?q=ai:gentile.maurizio Summary: We obtain the linear instability and nonlinear stability thresholds for a problem of thermal convection in a rotating bidispersive porous medium with a single temperature. We show that the linear instability threshold is the same as the nonlinear stability one. This means that the linear theory is capturing completely the physics of the onset of thermal convection. Pressure drop in fibrous filters https://zbmath.org/1472.76091 2021-11-25T18:46:10.358925Z "Chaudhuri, Jayotpaul" https://zbmath.org/authors/?q=ai:chaudhuri.jayotpaul "Baukelmann, Alexander" https://zbmath.org/authors/?q=ai:baukelmann.alexander "Boettcher, Konrad" https://zbmath.org/authors/?q=ai:boettcher.konrad-e-r "Ehrhard, Peter" https://zbmath.org/authors/?q=ai:ehrhard.peter Summary: Coalescing filtration is a mechanical process, which is employed to remove dispersed aerosol particles from a gas stream. This kind of filtration is a depth filtration process and it is widely used in process industries to remove particulate matter from exhaust gases, or in compressed air applications to filter oil particles introduced during compression. Fibrous filters are often used due to low cost, high capture efficiency and low pressure-drop, where droplets are first captured on fibres, then coalesce, and eventually drain out. The performance of a filter medium is judged based on its capture efficiency and its pressure drop characteristics. Estimating these parameters without setting up experimental investigations of each filter medium would be beneficial for choosing and developing optimal filters. In the present study, numerical simulations using ANSYS CFX$$^\copyright$$ are used to predict the pressure drop caused due to the air flow through the randomly oriented fibrous filter medium. A fictitious domain approach is used to simulate solid fibres without the need to create a case-specific mesh for each different fibre alignment. The method is compared to a benchmark simulation and a mesh analysis is carried out to find a balance between mesh refinement and computational effort required. This method is extended to model 3D fibres with random orientations. Multiple simulations, each with a different randomized fibre alignment, is carried out, varying both Reynolds number and solidity, and the results are compared with theoretical and 2D simulation results. It is seen that both available theoretical models and 2D simulation results overestimate the pressure drop caused by a real fibrous filter which is attributed to the inherent random orientation of the fibres. Modelling foam improved oil recovery: towards a formulation of pressure-driven growth with flow reversal https://zbmath.org/1472.76092 2021-11-25T18:46:10.358925Z "Eneotu, M." https://zbmath.org/authors/?q=ai:eneotu.m "Grassia, P." https://zbmath.org/authors/?q=ai:grassia.paul|grassia.p-s Summary: The pressure-driven growth model that describes the two-dimensional (2-D) propagation of a foam through an oil reservoir is considered as a model for surfactant-alternating-gas improved oil recovery. The model assumes a region of low mobility, finely textured foam at the foam front where injected gas meets liquid. The net pressure driving the foam is assumed to reduce suddenly at a specific time. Parts of the foam front, deep down near the bottom of the front, must then backtrack, reversing their flow direction. Equations for one-dimensional fractional flow, underlying 2-D pressure-driven growth, are solved via the method of characteristics. In a diagram of position versus time, the backtracking front has a complex double fan structure, with two distinct characteristic fans interacting. One of these characteristic fans is a reflection of a fan already present in forward flow mode. The second fan however only appears upon flow reversal. Both fans contribute to the flow's Darcy pressure drop, the balance of the pressure drop shifting over time from the first fan to the second. The implications for 2-D pressure-driven growth are that the foam front has even lower mobility in reverse flow mode than it had in the original forward flow case. On the stability of carbon sequestration in an anisotropic horizontal porous layer with a first-order chemical reaction https://zbmath.org/1472.76093 2021-11-25T18:46:10.358925Z "Gautam, K." https://zbmath.org/authors/?q=ai:gautam.k-k|gautam.kumar "Narayana, P. A. L." https://zbmath.org/authors/?q=ai:narayana.puranam-anantha-lakshmi|narayana.p-a-lakshmi Summary: Carbon dioxide $$(CO_2)$$ sequestration in deep saline aquifers is considered to be one of the most promising solutions to reduce the amount of greenhouse gases in the atmosphere. As the concentration of dissolved $$CO_2$$ increases in unsaturated brine, the density increases and the system may ultimately become unstable, and it may initiate convection. In this article, we study the stability of convection in an anisotropic horizontal porous layer, where the solute is assumed to decay via a first-order chemical reaction. We perform linear and nonlinear stability analyses based on the steady-state concentration field to assess neutral stability curves as a function of the anisotropy ratio, Damköhler number and Rayleigh number. We show that anisotropy in permeability and solutal diffusivity play an important role in convective instability. It is shown that when solutal horizontal diffusivity is larger than the vertical diffusivity, varying the ratio of vertical to horizontal permeabilities does not significantly affect the behaviour of instability. It is also noted that, when horizontal permeability is higher than the vertical permeability, varying the ratio of vertical to horizontal solutal diffusivity does have a substantial effect on the instability of the system when the reaction rate is dominated by the diffusion rate. We used the Chebyshev-tau method coupled with the QZ algorithm to solve the eigenvalue problem obtained from both the linear and nonlinear stability theories. Vigorous convection in porous media https://zbmath.org/1472.76094 2021-11-25T18:46:10.358925Z "Hewitt, D. R." https://zbmath.org/authors/?q=ai:hewitt.duncan-r Summary: The problem of convection in a fluid-saturated porous medium is reviewed with a focus on vigorous' convective flow, when the driving buoyancy forces are large relative to any dissipative forces in the system. This limit of strong convection is applicable in numerous settings in geophysics and beyond, including geothermal circulation, thermohaline mixing in the subsurface and heat transport through the lithosphere. Its manifestations range from black smoker' chimneys at mid-ocean ridges to salt-desert patterns to astrological plumes, and it has received a great deal of recent attention because of its important role in the long-term stability of geologically sequestered $$CO_2$$. In this review, the basic mathematical framework for convection in porous media governed by Darcy's Law is outlined, and its validity and limitations discussed. The main focus of the review is split between two-sided' and one-sided' systems: the former mimics the classical Rayleigh-Bénard set-up of a cell heated from below and cooled from above, allowing for detailed examination of convective dynamics and fluxes; the latter involves convection from one boundary only, which evolves in time through a series of regimes. Both set-ups are reviewed, accounting for theoretical, numerical and experimental studies in each case, and studies that incorporate additional physical effects are discussed. Future research in this area and various associated modelling challenges are also discussed. Linear and nonlinear thermosolutal instabilities in an inclined porous layer https://zbmath.org/1472.76095 2021-11-25T18:46:10.358925Z "Kumar, Gautam" https://zbmath.org/authors/?q=ai:kumar.gautam "Narayana, Puranam Anantha Lakshmi" https://zbmath.org/authors/?q=ai:narayana.puranam-anantha-lakshmi "Sahu, Kirti Chandra" https://zbmath.org/authors/?q=ai:sahu.kirti-chandra Summary: We investigate the double-diffusive instability in an inclined porous layer with a concentration-based internal heat source by conducting linear instability and nonlinear energy analyses. The effects of different dimensionless parameters, such as the thermal $$\mathrm{Ra}_T)$$ and solutal $$\mathrm{Ra}_S)$$ Rayleigh numbers, the angle of inclination $$( \varphi )$$, the Lewis number (Le) and the concentration-based internal heat source $$(Q)$$ are examined. A comparison between the linear and nonlinear thresholds for the longitudinal and transverse rolls provides the region of subcritical instability. We found that the system becomes more unstable when the thermal diffusivity is greater than the solute and the internal heat source strength increases. It is observed that the system is stabilized by increasing the angle of inclination. While the longitudinal roll remains stationary without the region of subcritical instability, as the angle of inclination increases, the transverse roll switches from stationary-oscillatory-stationary mode. Our numerical results show that for $$\mathrm{Ra}_S < 0$$, for all $$Q$$ values, the subcritical instability only exists for transverse rolls. For $$\mathrm{Ra}_S \geq 0$$, however, the subcritical instability appears only for $$Q = 0$$ and $$Q \geq 0$$, respectively, for longitudinal and transverse rolls. Exact solutions to the deep bed filtration problem for low-concentration suspension https://zbmath.org/1472.76096 2021-11-25T18:46:10.358925Z "Leontiev, N. E." https://zbmath.org/authors/?q=ai:leontev.n-e "Roshchin, E. I." https://zbmath.org/authors/?q=ai:roshchin.e-i Summary: For deep bed filtration equations, exact solutions are constructed that describe typical laboratory experiments: injection of a suspension into a porous sample. In the case of kinetic equation with an arbitrary dependence of the clogging rate on the retention (the volume of deposited particles per unit filter volume), the solution is obtained in quadratures. In the special case of linear dependence of the clogging rate on the retained particles volume, an analytical solution is given. For the axisymmetric flows of suspensions (injection into a porous bed through a well), the solution is provided in terms of the solution to a system of ordinary differential equations. Capillary transport in paper porous materials at low saturation levels: normal, fast or superfast? https://zbmath.org/1472.76097 2021-11-25T18:46:10.358925Z "Lukyanov, Alex V." https://zbmath.org/authors/?q=ai:lukyanov.alex-v "Mitkin, Vladimir V." https://zbmath.org/authors/?q=ai:mitkin.vladimir-v "Pryer, Tristan" https://zbmath.org/authors/?q=ai:pryer.tristan "Sirimark, Penpark" https://zbmath.org/authors/?q=ai:sirimark.penpark "Theofanous, Theo G." https://zbmath.org/authors/?q=ai:theofanous.theo-g Summary: The problem of capillary transport in fibrous porous materials at low levels of liquid saturation has been addressed. It has been demonstrated that the process of liquid spreading in this type of porous material at low saturation can be described macroscopically by a similar super-fast, nonlinear diffusion model to that which had been previously identified in experiments and simulations in particulate porous media. The macroscopic diffusion model has been underpinned by simulations using a microscopic network model. The theoretical results have been qualitatively compared with available experimental observations within the witness card technique using persistent liquids. The long-term evolution of the wetting spots was found to be truly universal and fully in line with the mathematical model developed. The result has important repercussions for the witness card technique used in field measurements of the dissemination of various low-volatility agents in imposing severe restrictions on collection and measurement times. Macroscopic permeability of doubly porous solids with spheroidal macropores: closed-form approximate solutions of the longitudinal permeability https://zbmath.org/1472.76098 2021-11-25T18:46:10.358925Z "Monchiet, Vincent" https://zbmath.org/authors/?q=ai:monchiet.vincent Summary: The presence of macropores and fractures significantly affects the effective transport properties of porous solids such as concrete and rocks. The dimensions of the fractures are generally large behind that of the initial porosity, so that the problem contains two porosities. The influence of the macroporosity is studied in the homogenization framework by solving at the intermediate scale, that of the macropores, a coupled Darcy/Stokes problem with the Beavers-Joseph-Saffman (BJS) interface condition. We derive analytic expressions of the macroscopic permeability in the case of an isotropic permeable matrix containing spheroidal-shaped macropores. To this aim, we consider a representative volume element (RVE) on which uniform boundary conditions are considered for the velocity and pressure fields. The local problem is written as minimum principles; kinematic and static approaches are developed to derive rigorous bounds for the macroscopic permeability. Closed-form expressions of the longitudinal permeability (along the revolution axe of the spheroid) are determined by considering a simplified RVE constituted of two confocal spheroids. They depend on the volume fraction and the eccentricity of the spheroidal macropores, the scale factor between the two porosities and the slip coefficient of the BJS model. Illustrations show the influence of these parameters. Mathematical modeling of oil reservoir waterflooding using fixed streamtube at various values of viscosity ratio https://zbmath.org/1472.76099 2021-11-25T18:46:10.358925Z "Potashev, K. A." https://zbmath.org/authors/?q=ai:potashev.konstantin-andreevich "Mazo, A. B." https://zbmath.org/authors/?q=ai:mazo.a-b Summary: The speed up of numerical modeling of the oil reservoir waterflooding on high-resolution grids is possible by reducing the dimension of the two-phase flow problem. This problem is posed in fixed streamtubes connecting injection and production wells. The article describes an algorithm for constructing an effective streamtube between a pair of wells in a homogeneous oil reservoir, which guarantees the best approximation of the functions of the total flow rate and water cut of a production well. The obtained functions of the relative width of the streamtube for the periodicity cells of typical well patterns are approximated by piecewise linear functions. An assessment is made of the applicability of the constructed streamtubes for the numerical simulation of two-phase flow with a change in the viscosity ratio of the displacing and displaced phases, which is characteristic of measures to increase oil recovery. Network-inspired versus Kozeny-Carman based permeability-porosity relations applied to Biot's poroelasticity model https://zbmath.org/1472.76100 2021-11-25T18:46:10.358925Z "Rahrah, Menel" https://zbmath.org/authors/?q=ai:rahrah.menel "Lopez-Peña, Luis A." https://zbmath.org/authors/?q=ai:lopez-pena.luis-a "Vermolen, Fred" https://zbmath.org/authors/?q=ai:vermolen.fred-j "Meulenbroek, Bernard" https://zbmath.org/authors/?q=ai:meulenbroek.bernard-j Summary: Water injection in the aquifer induces deformations in the soil. These mechanical deformations give rise to a change in porosity and permeability, which results in non-linearity of the mathematical problem. Assuming that the deformations are very small, the model provided by Biot's theory of linear poroelasticity is used to determine the local displacement of the skeleton of a porous medium, as well as the fluid flow through the pores. In this continuum scale model, the Kozeny-Carman equation is commonly used to determine the permeability of the porous medium from the porosity. The Kozeny-Carman relation states that flow through the pores is possible at a certain location as long as the porosity is larger than zero at this location in the aquifer. However, from network models it is known that percolation thresholds exist, indicating that the permeability will be equal to zero if the porosity becomes smaller than these thresholds. In this paper, the relationship between permeability and porosity is investigated. A new permeability-porosity relation, based on the percolation theory, is derived and compared with the Kozeny-Carman relation. The strongest feature of the new approach is related to its capability to give a good description of the permeability in case of low porosities. However, with this network-inspired approach small values of the permeability are more likely to occur. Since we show that the solution of Biot's model converges to the solution of a saddle point problem for small time steps and low permeability, we need stabilisation in the finite element approximation. Heat transfer in laminar viscous flow in a channel with one porous wall https://zbmath.org/1472.76101 2021-11-25T18:46:10.358925Z "Rashevski, M." https://zbmath.org/authors/?q=ai:rashevsky.m-o "Slavtchev, S." https://zbmath.org/authors/?q=ai:slavtchev.slavtcho|slavtchev.s-g Summary: Similarity solutions to the two-dimensional steady Navier-Stokes and energy equations for viscous flow in a semi-infinite horizontal channel with upper porous and lower impermeable walls are presented. The finite end of the channel is closed. Both fluid suction and injection through the porous boundary are considered. Two cases of thermal conditions at the walls are studied. In one case the temperature of both channel boundaries decreases linearly along the channel. In the second one, the upper wall has the same decreasing temperature, while the lower boundary is thermally insulated. By means of similarity transformations the dynamic and heat transfer equations are reduced to three ordinary differential equations for the velocity, pressure and temperature functions. The velocity equation is solved numerically for different values of the suction/injection Reynolds number. Analytical solution of the dynamic problem in a series of small Reynolds number is also found. The thermal problem is solved numerically for arbitrary Peclet number and two values of the Prandtl number. Analytical solution for small Peclet and Reynolds numbers is also obtained. The dependence of the Nusselt number on the Peclet number at both walls is studied. The stream lines and isotherms are presented graphically for some values of the Reynolds number at the Prandtl number equal one. It is shown the strong influence of the flow behavior on the heat transfer inside the channel. Effect of porous layer on the Faraday instability in viscous liquid https://zbmath.org/1472.76102 2021-11-25T18:46:10.358925Z "Samanta, Arghya" https://zbmath.org/authors/?q=ai:samanta.arghya Summary: A linear stability analysis of a viscous liquid on a vertically oscillating porous plane is performed for infinitesimal disturbances of arbitrary wavenumbers. A time-dependent boundary value problem is derived and solved based on the Floquet theory along with the complex Fourier series expansion. Numerical results show that the Faraday instability is dominated by the subharmonic solution at high forcing frequency, but it responds harmonically at low forcing frequency. The unstable regions corresponding to both subharmonic and harmonic solutions enhance with the increasing value of permeability and yields a destabilizing effect on the Faraday instability. Further, the presence of porous layer makes faster the transition process from subharmonic instability to harmonic instability in the wavenumber regime. In addition, the first harmonic solution shrinks gradually and becomes an unstable island, and ultimately disappears from the neutral curve if the porous layer thickness is increased. In contrast, the first and second subharmonic solutions coalesce, and the onset of Faraday instability is dominated by the subharmonic solution. In a special case, the study of Faraday instability of a viscous liquid on a porous substrate can be replaced by a study of Faraday instability of a viscous liquid on a slippery substrate when the permeability of the porous substrate is very low. Further, the Faraday instability can be destabilized by introducing a slip effect at the bottom plane. Dynamics of fluid displacement in mixed-wet porous media https://zbmath.org/1472.76103 2021-11-25T18:46:10.358925Z "Scanziani, Alessio" https://zbmath.org/authors/?q=ai:scanziani.alessio "Lin, Qingyang" https://zbmath.org/authors/?q=ai:lin.qingyang "Alhosani, Abdulla" https://zbmath.org/authors/?q=ai:alhosani.abdulla "Blunt, Martin J." https://zbmath.org/authors/?q=ai:blunt.martin-j "Bijeljic, Branko" https://zbmath.org/authors/?q=ai:bijeljic.branko Summary: We identify a distinct two-phase flow invasion pattern in a mixed-wet porous medium. Time-resolved high-resolution synchrotron X-ray imaging is used to study the invasion of water through a small rock sample filled with oil, characterized by a wide non-uniform distribution of local contact angles both above and below $$90^\degree$$. The water advances in a connected front, but throats are not invaded in decreasing order of size, as predicted by invasion percolation theory for uniformly hydrophobic systems. Instead, we observe pinning of the three-phase contact between the fluids and the solid, manifested as contact angle hysteresis, which prevents snap-off and interface retraction. In the absence of viscous dissipation, we use an energy balance to find an effective, thermodynamic, contact angle for displacement and show that this angle increases during the displacement. Displacement occurs when the local contact angles overcome the advancing contact angles at a pinned interface: it is wettability which controls the filling sequence. The product of the principal interfacial curvatures, the Gaussian curvature, is negative, implying well-connected phases which is consistent with pinning at the contact line while providing a topological explanation for the high displacement efficiencies in mixed-wet media. On the study of fluid flow in a soft porous media using a scaled-up indenter https://zbmath.org/1472.76104 2021-11-25T18:46:10.358925Z "Wang, Qiuyun" https://zbmath.org/authors/?q=ai:wang.qiuyun "Zhu, Zenghao" https://zbmath.org/authors/?q=ai:zhu.zenghao "Nathan, Rungun" https://zbmath.org/authors/?q=ai:nathan.rungun "Wu, Qianhong" https://zbmath.org/authors/?q=ai:wu.qianhong Summary: Soft porous materials are ubiquitous in the nature. Issues inherent in the response of these materials to external impacts raise problems that are broadly important in diverse areas of science and increasingly attract attentions in technology. In this paper, we report a comprehensive, experimental and theoretical approach to examine the transient fluid pressure distribution inside soft porous media when a spherical loading surface impacts on it. A novel experimental setup was developed that includes a fully instrumented hemi-spherical piston with supporting structures, and a soft porous layer underneath. Extensive experimental studies are performed in which the motion of the loading surface and the resulting transient pressure distribution are recorded. The results are compared with a novel theoretical model, leading to excellent agreements. The study significantly improves our understanding of the dynamic response of soft porous material to external compression. Especially it provides a scaled-up model to simulate the process of probe indentation, which, however, does not provide any information about the transient pore pressure distribution under the loading surface. Improved phase-field models of melting and dissolution in multi-component flows https://zbmath.org/1472.76105 2021-11-25T18:46:10.358925Z "Hester, Eric W." https://zbmath.org/authors/?q=ai:hester.eric-w "Couston, Louis-Alexandre" https://zbmath.org/authors/?q=ai:couston.louis-alexandre "Favier, Benjamin" https://zbmath.org/authors/?q=ai:favier.benjamin "Burns, Keaton J." https://zbmath.org/authors/?q=ai:burns.keaton-j "Vasil, Geoffrey M." https://zbmath.org/authors/?q=ai:vasil.geoffrey-m Summary: We develop and analyse the first second-order phase-field model to combine melting and dissolution in multi-component flows. This provides a simple and accurate way to simulate challenging phase-change problems in existing codes. Phase-field models simplify computation by describing separate regions using a smoothed phase field. The phase field eliminates the need for complicated discretizations that track the moving phase boundary. However, standard phase-field models are only first-order accurate. They often incur an error proportional to the thickness of the diffuse interface. We eliminate this dominant error by developing a general framework for asymptotic analysis of diffuse-interface methods in arbitrary geometries. With this framework, we can consistently unify previous second-order phase-field models of melting and dissolution and the volume-penalty method for fluid-solid interaction. We finally validate second-order convergence of our model in two comprehensive benchmark problems using the open-source spectral code Dedalus. The influence of invariant solutions on the transient behaviour of an air bubble in a Hele-Shaw channel https://zbmath.org/1472.76106 2021-11-25T18:46:10.358925Z "Keeler, Jack S." https://zbmath.org/authors/?q=ai:keeler.jack-s "Thompson, Alice B." https://zbmath.org/authors/?q=ai:thompson.alice-b "Lemoult, Grégoire" https://zbmath.org/authors/?q=ai:lemoult.gregoire "Juel, Anne" https://zbmath.org/authors/?q=ai:juel.anne "Hazel, Andrew L." https://zbmath.org/authors/?q=ai:hazel.andrew-l Summary: We hypothesize that dynamical systems concepts used to study the transition to turbulence in shear flows are applicable to other transition phenomena in fluid mechanics. In this paper, we consider a finite air bubble that propagates within a Hele-Shaw channel containing a depth-perturbation. Recent experiments revealed that the bubble shape becomes more complex, quantified by an increasing number of transient bubble tips, with increasing flow rate. Eventually, the bubble changes topology, breaking into multiple distinct entities with non-trivial dynamics. We demonstrate that qualitatively similar behaviour to the experiments is exhibited by a previously established, depth-averaged mathematical model and arises from the model's intricate solution structure. For the bubble volumes studied, a stable asymmetric bubble exists for all flow rates of interest, while a second stable solution branch develops above a critical flow rate and transitions between symmetric and asymmetric shapes. The region of bistability is bounded by two Hopf bifurcations on the second branch. By developing a method for a numerical weakly nonlinear stability analysis we show that unstable periodic orbits (UPOs) emanate from the first Hopf bifurcation. Moreover, as has been found in shear flows, the UPOs are edge states that influence the transient behaviour of the system. Gas-babble oscillations: resonance effects in nonviscous and Newton media https://zbmath.org/1472.76107 2021-11-25T18:46:10.358925Z "Sadrislamov, A. U." https://zbmath.org/authors/?q=ai:sadrislamov.a-u Summary: A linear mathematical model of forced oscillations of a gas bubble in viscous Newtonian fluid is developed in this paper. The natural frequency of oscillations of the gas bubble is found. A numerical analysis of the resonant effects of gas bubble oscillations within the media is carried out and a comparison of the obtained results with the existing classical ones for non-viscous media is discussed. Thermophoretic motion of an aerosol sphere in a spherical cavity https://zbmath.org/1472.76108 2021-11-25T18:46:10.358925Z "Tseng, Yu M." https://zbmath.org/authors/?q=ai:tseng.yu-m "Keh, Huan J." https://zbmath.org/authors/?q=ai:keh.huan-j Summary: A theoretical investigation of the quasi-steady thermophoresis of an aerosol sphere located arbitrarily in a spherical cavity normal to the line of their centers is presented. In the slip-flow regime for the gas motion, the thermal creep, thermal stress slip, frictional slip, and temperature jump are permitted at the solid surfaces. The general solutions to the conservative equations governing the temperature and fluid velocity distributions in the two spherical coordinate systems with respect to the particle and cavity centers are superimposed, and the boundary conditions are satisfied by a collocation technique. The translational and angular velocities of the particle are determined as functions of the scaled center-to-center distance between the particle and cavity (eccentricity of the particle position), their radius ratio, and their relative thermal and surface properties. The results indicate that the boundary effect on the thermophoretic motion is significant, interesting, and complicated. When the particle is located at the cavity center, its migration velocity agrees well with the available analytical solution. In general, the thermophoretic mobility decreases with increases in the particle-to-cavity size ratio and in the normalized distance between the particle and cavity centers, but there exist some exceptions. The circulating cavity-induced thermoosmotic flow can increase or decrease the thermophoretic migration and retard the particle rotation, even reverse their directions, depending on the geometric and characteristic parameters. The boundary effect on the thermophoretic migration normal to the line through the particle and cavity centers is slightly weaker than that along the line. Oriented suspension mechanics with application to improving flow linear dichroism spectroscopy https://zbmath.org/1472.76109 2021-11-25T18:46:10.358925Z "Cupples, G." https://zbmath.org/authors/?q=ai:cupples.g "Smith, D. J." https://zbmath.org/authors/?q=ai:smith.dealton-j|smith.david-j|smith.douglas-j|smith.derek-j "Hicks, M. R." https://zbmath.org/authors/?q=ai:hicks.m-r "Dyson, R. J." https://zbmath.org/authors/?q=ai:dyson.rosemary-j Summary: Flow linear dichroism is a biophysical spectroscopic technique that exploits the shear-induced alignment of elongated particles in suspension. Motivated by the broad aim of optimizing the sensitivity of this technique, and more specifically by a hand-held synthetic biotechnology prototype for waterborne-pathogen detection, a model of steady and oscillating pressure-driven channel flow and orientation dynamics of a suspension of slender microscopic fibres is developed. The model couples the Fokker-Planck equation for Brownian suspensions with the narrow channel flow equations, the latter modified to incorporate mechanical anisotropy induced by the particles. The linear dichroism signal is estimated through integrating the perpendicular components of the distribution function via an appropriate formula which takes the biaxial nature of the orientation into account. For the specific application of pathogen detection via binding of M13 bacteriophage, it is found that increases in the channel depth are more significant in improving the linear dichroism signal than increases in the channel width. Increasing the channel depth to 2 mm and pressure gradient to $$5 \times 10^4 Pa m^{-1}$$ essentially maximizes the alignment. Oscillating flow can produce nearly equal alignment to steady flow at appropriate frequencies, which has significant potential practical value in the analysis of small sample volumes. Lubrication model of suspension flow in a hydraulic fracture with frictional rheology for shear-induced migration and jamming https://zbmath.org/1472.76110 2021-11-25T18:46:10.358925Z "Dontsov, E. V." https://zbmath.org/authors/?q=ai:dontsov.egor-v "Boronin, S. A." https://zbmath.org/authors/?q=ai:boronin.s-a "Osiptsov, A. A." https://zbmath.org/authors/?q=ai:osiptsov.andrei-a "Derbyshev, D. Yu." https://zbmath.org/authors/?q=ai:derbyshev.d-yu Summary: We developed a model for suspension flow in a hydraulic fracture, taking into account frictional rheology to capture the effects of shear-induced particle migration, jamming and transition to close packing. One of the key issues with the existing slurry rheology models is that each of them diverges near the close packing limit, which is typically resolved in numerical simulations via a pragmatic (and mostly unjustified) regularization. Another drawback of the family of existing models for proppant transport in fractures is the assumption of a uniform cross-flow concentration profile, which neglects the effects of shear-induced migration. We developed a self-consistent model for slurry flow with a constitutive relation for suspension rheology, which is applicable in the entire range of particle volume concentration, from dilute suspension through dense suspension to the close packing limit. In addition, we investigated the influence of various constitutive relations for the suspension rheology on the final model for the slurry flow. The selected model for slurry flow was implemented into a two-dimensional lubrication model of proppant transport in a fracture (based on the two-continua approach), and illustrative simulations were conducted in comparison with the family of existing suspension rheology models (having a singularity). Validation against laboratory experiments is discussed. Electrohydrodynamic assembly of colloidal particles on a drop interface https://zbmath.org/1472.76111 2021-11-25T18:46:10.358925Z "Hu, Yi" https://zbmath.org/authors/?q=ai:hu.yi|hu.yi.1 "Vlahovska, Petia M." https://zbmath.org/authors/?q=ai:vlahovska.petia-m "Miksis, Michael J." https://zbmath.org/authors/?q=ai:miksis.michael-j Summary: A mathematical model to simulate the dynamics of colloidal particles on a drop interface in an applied electric field is presented. The model accounts for the electric field driven flow within the drop and suspending fluid, particle-particle electrostatic interaction, and the particle motion and rotation due to the induced flow and the applied electric field. The model predicts the formation of chains in the case of conducting particles or an undulating band around the equator in the case of dielectric particles. The model results are in agreement with recent experimental work. A study is presented on the impact of particle concentration and electric field strength on the collective motions of the particles. In the case of non-conducting particles, we find that in the presence of Quincke rotation, the amplitude of the undulations of the observed equatorial particle belt increases with particle concentration but decreases with electric field strength. We also show that the wavelength of the undulations appears independent of the applied field strength. New regimes of dispersion in microfluidics as mediated by travelling temperature waves https://zbmath.org/1472.76112 2021-11-25T18:46:10.358925Z "Pal, Debashis" https://zbmath.org/authors/?q=ai:pal.debashis "Chakraborty, Suman" https://zbmath.org/authors/?q=ai:chakraborty.suman Summary: We unveil new regimes of dispersion in miniaturized fluidic devices, by considering fluid flow triggered by a travelling temperature wave. When a temperature wave travels along a channel wall, it alters the density and viscosity of the adjacent fluid periodically. Successive expansion-contraction of the fluid volume through a spatio-temporally evolving viscosity field generates a net fluidic current. Based on the temporal evolution of the axial dispersion coefficient, new regimes of dispersion---such as a short-time oscillating regime' and a large-time stable regime' -- have been identified, which are absent in traditionally addressed flows through miniaturized fluidic devices. Our analysis reveals that the oscillation of axial dispersion persists until the variance of species concentration becomes equal to half of the square of the wavelength of the thermal wave. The time period of oscillation in the dispersion coefficient turns out to be a unique function of the thermal wavelength and net flow velocity induced by thermoviscous pumping. The results of this study are likely to contribute towards the improvement of microscale systems that are subjected to periodic temperature variations, including microreactors and DNA amplification devices. Free and circular jets cooled by single phase nanofluids https://zbmath.org/1472.76113 2021-11-25T18:46:10.358925Z "Turkyilmazoglu, Mustafa" https://zbmath.org/authors/?q=ai:turkyilmazoglu.mustafa Summary: Nanofluids are widely known to enhance the heat transfer rate resulting in a cooled system. In the present paper, we show mathematically that the nanofluids indeed cool the system as the nanoparticles volume fraction is increased. The key role is explained for a two-dimensional laminar free nanofluid jet and for a circular axisymmetric free nanofluid jet issuing into the same nanofluid medium. Exact nanofluid flow results are obtained and, integral flux relations of momentum and thermal layers concerning five most studied nanofluids, respectively Ag, Cu, CuO, Al$$_{2}$$O$$_{3}$$ and TiO$$_{2}$$, are derived. A shape factor is defined controlling the momentum layer thickness. By means of another shape factor representing the thermal layer thickness, the relevant energy equation enables one to identify the regimes of nanoparticle size leading to a coolant jet, without a need to solve the energy equation fully. Two recently popular nanofluid models, resulting in the same conclusion, are examined on the considered free nanofluid jets. Additionally, an exact temperature field associated with the laminar two-dimensional free jet of nanoparticles is obtained offering explicit support to the current approach. The many behaviors of deformable active droplets https://zbmath.org/1472.76114 2021-11-25T18:46:10.358925Z "Young, Y. -N." https://zbmath.org/authors/?q=ai:young.yuan-na|young.yuan-nan "Shelley, Michael J." https://zbmath.org/authors/?q=ai:shelley.michael-j "Stein, David B." https://zbmath.org/authors/?q=ai:stein.david-b Summary: Active fluids consume fuel at the microscopic scale, converting this energy into forces that can drive macroscopic motions over scales far larger than their microscopic constituents. In some cases, the mechanisms that give rise to this phenomenon have been well characterized, and can explain experimentally observed behaviors in both bulk fluids and those confined in simple stationary geometries. More recently, active fluids have been encapsulated in viscous drops or elastic shells so as to interact with an outer environment or a deformable boundary. Such systems are not as well understood. In this work, we examine the behavior of droplets of an active nematic fluid. We study their linear stability about the isotropic equilibrium over a wide range of parameters, identifying regions in which different modes of instability dominate. Simulations of their full dynamics are used to identify their nonlinear behavior within each region. When a single mode dominates, the droplets behave simply: as rotors, swimmers, or extensors. When parameters are tuned so that multiple modes have nearly the same growth rate, a pantheon of modes appears, including zigzaggers, washing machines, wanderers, and pulsators. Three-phase flow displacement dynamics and Haines jumps in a hydrophobic porous medium https://zbmath.org/1472.76115 2021-11-25T18:46:10.358925Z "Alhosani, Abdulla" https://zbmath.org/authors/?q=ai:alhosani.abdulla "Scanziani, Alessio" https://zbmath.org/authors/?q=ai:scanziani.alessio "Lin, Qingyang" https://zbmath.org/authors/?q=ai:lin.qingyang "Selem, Ahmed" https://zbmath.org/authors/?q=ai:selem.ahmed "Pan, Ziqing" https://zbmath.org/authors/?q=ai:pan.ziqing "Blunt, Martin J." https://zbmath.org/authors/?q=ai:blunt.martin-j "Bijeljic, Branko" https://zbmath.org/authors/?q=ai:bijeljic.branko Summary: We use synchrotron X-ray micro-tomography to investigate the displacement dynamics during three-phase -- oil, water and gas -- flow in a hydrophobic porous medium. We observe a distinct gas invasion pattern, where gas progresses through the pore space in the form of disconnected clusters mediated by double and multiple displacement events. Gas advances in a process we name three-phase Haines jumps, during which gas re-arranges its configuration in the pore space, retracting from some regions to enable the rapid filling of multiple pores. The gas retraction leads to a permanent disconnection of gas ganglia, which do not reconnect as gas injection proceeds. We observe, \textit{in situ}, the direct displacement of oil and water by gas as well as gas-oil-water double displacement. The use of local \textit{in situ} measurements and an energy balance approach to determine fluid-fluid contact angles alongside the quantification of capillary pressures and pore occupancy indicate that the wettability order is oil-gas-water from most to least wetting. Furthermore, quantifying the evolution of Minkowski functionals implied well-connected oil and water, while the gas connectivity decreased as gas was broken up into discrete clusters during injection. This work can be used to design $$CO_2$$ storage, improved oil recovery and microfluidic devices. A four-field three-phase flow model with both miscible and immiscible components https://zbmath.org/1472.76116 2021-11-25T18:46:10.358925Z "Hérard, Jean-Marc" https://zbmath.org/authors/?q=ai:herard.jean-marc "Hurisse, Olivier" https://zbmath.org/authors/?q=ai:hurisse.olivier "Quibel, Lucie" https://zbmath.org/authors/?q=ai:quibel.lucie Summary: A three-phase flow model with hybrid miscibility constraints is proposed: three immiscible phases are considered (liquid water, liquid metal and gas) but the gaseous phase is composed with two miscible components (steam water and non-condensable gas). The modelling approach is based on the building of an entropy inequality for the system of partial differential equations: once an interfacial velocity is given by the user, the model is uniquely defined, up to some relaxation time scales, and source terms complying with the second principle of thermodynamics can then be provided. The convective part of the system is hyperbolic when fulfilling a non-resonance condition and classical properties are studied (Riemann invariants, symmetrization). A key property is that the system possesses uniquely defined jump conditions. Last, preservation of thermodynamically admissible states and pressure relaxation are investigated. Industrial dry spinning processes: algorithmic for a two-phase fiber model in airflows https://zbmath.org/1472.76117 2021-11-25T18:46:10.358925Z "Wieland, Manuel" https://zbmath.org/authors/?q=ai:wieland.manuel "Arne, Walter" https://zbmath.org/authors/?q=ai:arne.walter "Marheineke, Nicole" https://zbmath.org/authors/?q=ai:marheineke.nicole "Wegener, Raimund" https://zbmath.org/authors/?q=ai:wegener.raimund Summary: The dry spinning of fibers can be described by three-dimensional multi-phase flow models that contain key effects like solvent evaporation and fiber-air interaction. Since the direct numerical simulation of the three-dimensional models is in general not possible, dimensionally reduced models are deduced. We recently developed a one-two-dimensional fiber model and presented a problem-tailored numerical solution strategy in [the first author et al., J. Comput. Phys. 384, 326--348 (2019; Zbl 1451.74082)]. However, in view of industrial setups with multiple fibers spun simultaneously the numerical schemes must be accelerated to achieve feasible simulation times. The bottleneck builds the computation of the radial concentration and temperature profiles as well as their cross-sectionally averaged values. In this paper we address this issue and develop efficient numerical algorithms. Mathematical model of hydrovortex hetero-coagulation https://zbmath.org/1472.76118 2021-11-25T18:46:10.358925Z "Nosyrev, M. B." https://zbmath.org/authors/?q=ai:nosyrev.m-b "Makarov, N. V." https://zbmath.org/authors/?q=ai:makarov.n-v "Makarov, V. N." https://zbmath.org/authors/?q=ai:makarov.v-n "Ugolnikov, A. V." https://zbmath.org/authors/?q=ai:ugolnikov.a-v "Kitonsa, H." https://zbmath.org/authors/?q=ai:kitonsa.h Summary: The dynamics of improvement of equipment and technology of dust suppression in the mining and metallurgical complex of Russia shows their insufficient efficiency of providing sanitary conditions, and most importantly the localization of explosions of dust mixtures. Further increase of efficiency of coal mining and mineral processing is significantly limited by the imperfection of technology of localization and elimination of coal dust explosions. On the basis of the theory of attached vortices the method of high-pressure hydro-vortex dust separation is developed. The mathematical model of the hydro-vortex inertial, kinematic heterocoagulation, significantly increasing the energy efficiency of dust suppression, is proposed. The graphical model of interaction in the contact zone at the moment of collision in the system liquid-solid'' is refined; the equations of the Stokes and Reynolds criteria for hydro-vortex inertial orthokinetic heterocoagulation are obtained. An equation for calculating the value of the reduction of the required energy of the total absorption of dust particles in the function of the liquid droplets circulation is obtained. The equations for the calculation of the effective contact angle and the minimum diameter of the absorbed dust particles in the function of the liquid droplets spin rate are obtained. It is shown that the hydro-vortex coagulation significantly reduces the size of the dispersed dust composition, water consumption, increasing the efficiency of dust suppression. A significant reduction in the size of the dispersed dust composition increases the efficiency of the system of localization of coal dust explosions, reduces the morbidity of silicosis. The use of patent-protected swirl injectors has confirmed the reduction of the minimum size of the absorbed dust by four times, increasing the efficiency of dust collection up to 99\% while reducing the water consumption at 20\%. For the entire collection see [Zbl 1467.34001]. On the formation of centreline shrinkage porosity in the continuous casting of steel https://zbmath.org/1472.76119 2021-11-25T18:46:10.358925Z "Vynnycky, Michael" https://zbmath.org/authors/?q=ai:vynnycky.michael Summary: A recent asymptotic model for solidification shrinkage-induced macrosegregation in the continuous casting of binary alloys is extended for the purposes of understanding the link between solute segregation and centreline shrinkage porosity, a defect that commonly occurs in the continuous casting of steel. In particular, the analysis elucidates the relationship between microsegregation, mushy-zone permeability, heat transfer and centreline pressure, yielding an inequality that constitutes a criterion for whether or not centreline porosity will form. The possibilities for developing this approach to take account of gas porosity and the implementation of mechanical soft reduction to reduce macrosegregation and shrinkage porosity are also discussed. On the plane-parallel motion of self-gravitating and rotating incompressible fluid with a free boundary https://zbmath.org/1472.76120 2021-11-25T18:46:10.358925Z "Baykov, N. D." https://zbmath.org/authors/?q=ai:baykov.n-d "Petrov, A. G." https://zbmath.org/authors/?q=ai:petrov.aleksandr-georgiev|petrov.alexander-g.1 Summary: In this paper, we study a plane-parallel flow of the homogeneous inviscid incompressible fluid. The close attention is paid to the free boundary deformation under the forces of self-gravitation and fluid rotation. The problem is studied numerically, i.e., we propose the numerical algorithm for the free boundary calculation. The algorithm is based on the boundary element method. Algorithm applications include calculation of thin cumulative jets. The second point of interest is numerical results validation. The computational accuracy is controlled through the conservation laws. In this paper, we provide the derivation of conservation laws of energy and angular momentum for the case of rotating flows. In addition, we analytically investigate dynamics of two-dimensional near-equilibrium shapes and check the consistency of the analytical and numerical results. Non-normal origin of modal instabilities in rotating plane shear flows https://zbmath.org/1472.76121 2021-11-25T18:46:10.358925Z "Jose, Sharath" https://zbmath.org/authors/?q=ai:jose.sharath "Govindarajan, Rama" https://zbmath.org/authors/?q=ai:govindarajan.rama Summary: Small variations introduced in shear flows are known to affect stability dramatically. Rotation of the flow system is one example, where the critical Reynolds number for exponential instabilities falls steeply with a small increase in rotation rate. We ask whether there is a fundamental reason for this sensitivity to rotation. We answer in the affirmative, showing that it is the non-normality of the stability operator in the absence of rotation which triggers this sensitivity. We treat the flow in the presence of rotation as a perturbation on the non-rotating case, and show that the rotating case is a special element of the pseudospectrum of the non-rotating case. Thus, while the non-rotating flow is always modally stable to streamwise-independent perturbations, rotating flows with the smallest rotation are unstable at zero streamwise wavenumber, with the spanwise wavenumbers close to that of disturbances with the highest transient growth in the non-rotating case. The instability critical rotation number scales inversely as the square of the Reynolds number, which we demonstrate is the same as the scaling obeyed by the minimum perturbation amplitude in non-rotating shear flow needed for the pseudospectrum to cross the neutral line. Plane Poiseuille flow and plane Couette flow are shown to behave similarly in this context. Equilibrium of liquid drop on rotating disc https://zbmath.org/1472.76122 2021-11-25T18:46:10.358925Z "Konon, P. N." https://zbmath.org/authors/?q=ai:konon.p-n "Mogilevskiy, E. I." https://zbmath.org/authors/?q=ai:mogilevskii.e-i "Sitsko, G. N." https://zbmath.org/authors/?q=ai:sitsko.g-n "Shkadov, V. Ya." https://zbmath.org/authors/?q=ai:shkadov.victor-ya Summary: In this paper, we consider the equilibrium shapes of a finite volume of liquid on a horizontal rotation surface due to gravity and centrifugal forces under the action of surface tension. It is shown that a solution exits only if the angular velocity is less than the critical value. For large droplets, the angular velocity was obtained analytically. Mathematical model of conformal mappings in the theory of radial grids of mine turbomachines https://zbmath.org/1472.76123 2021-11-25T18:46:10.358925Z "Makarov, V. N." https://zbmath.org/authors/?q=ai:makarov.v-n "Makarov, N. V." https://zbmath.org/authors/?q=ai:makarov.n-v "Lifanov, A. V." https://zbmath.org/authors/?q=ai:lifanov.a-v "Materov, A. Y." https://zbmath.org/authors/?q=ai:materov.a-y "Kitonsa, H." https://zbmath.org/authors/?q=ai:kitonsa.h Summary: Further intensification sof mining operations, the use of innovative technologies to ensure efficient production and processing of mineral raw materials, is limited by the requirements for the system of aerogasodynamic safety, one of the energy-intensive elements of which are mine turbomachines, characterized by insufficient adaptability and aerodynamic loading. On the basis of the theory of attached vortices, as well as the methods of conformal mapping and singular points by S. A. Chaplygin, a mathematical model of a rotating circular grid of aerogasdynamic profiles with jet circulation control is proposed, the problem of its aerodynamic calculation is formulated and solved, the uniqueness of the solution is proved to within a constant. It is shown that the terms of the Zhukovsky-Chaplygin-Kutta method applicable to calculate aerogasdynamic profiles in the absence of the attached vortex at the rear corner point of the profile. The equation is obtained to calculate the circulation of the circular grid of aerogasdynamic profiles as a function of the energy parameters of the sources and sinks of the vortex chamber. It is established that the aerodynamic connection of the turbomachine cavity with vortex chambers, causing the dependence of the energy parameters of the source and the jet control flows on the characteristics of the external network, provides a significant increase in the adaptability of mine turbomachines. Modification of the theory of aerodynamic calculation of circular grids of aerogasdynamic profiles and construction of radial aerodynamic designs with high adaptability allowed us to formulate a qualitatively new direction of improvement of shaft radial turbomachines, the operation principle of which corresponds to nature-like technology of transformation and energy transmission. The possibility of a significant increase in aerodynamic loading, adaptability and efficiency of mine turbomachines, made by radial aerodynamic schemes with built-in impeller blades vortex chambers, performing the functions of adaptive jet circulation control devices, is confirmed. Using the proposed methodology, a straight-through radial vortex fan (VRVP-12A) to ventilate blind drift 3,500 m long is developed. For the entire collection see [Zbl 1467.34001]. On the role of bulk viscosity in compressible reactive shear layer developments https://zbmath.org/1472.76124 2021-11-25T18:46:10.358925Z "Boukharfane, Radouan" https://zbmath.org/authors/?q=ai:boukharfane.radouan "Martínez Ferrer, Pedro José" https://zbmath.org/authors/?q=ai:martinez-ferrer.pedro-jose "Mura, Arnaud" https://zbmath.org/authors/?q=ai:mura.arnaud "Giovangigli, Vincent" https://zbmath.org/authors/?q=ai:giovangigli.vincent Summary: Despite 150 years of research after the reference work of Stokes, it should be acknowledged that some confusion still remains in the literature regarding the importance of bulk viscosity effects in flows of both academic and practical interests. On the one hand, it can be readily shown that the neglection of bulk viscosity (i.e., $$\kappa = 0$$) is strictly exact for mono-atomic gases. The corresponding bulk viscosity effects are also unlikely to alter the flowfield dynamics provided that the ratio of the shear viscosity $$\mu$$ to the bulk viscosity $$\kappa$$ remains sufficiently large. On the other hand, for polyatomic gases, the scattered available experimental and numerical data show that it is certainly not zero and actually often far from negligible. Therefore, since the ratio $$\kappa / \mu$$ can display significant variations and may reach very large values (it can exceed thirty for dihydrogen), it remains unclear to what extent the neglection of $$\kappa$$ holds. The purpose of the present study is thus to analyze the mechanisms through which bulk viscosity and associated processes may alter a canonical turbulent flow. In this context, we perform direct numerical simulations (DNS) of spatially-developing compressible non-reactive and reactive hydrogen-air shear layers interacting with an oblique shock wave. The corresponding flowfield is of special interest for various reactive high-speed flow applications, e.g., scramjets. The corresponding computations either neglect the influence of bulk viscosity ($$\kappa = 0$$) or take it into consideration by evaluating its value using the library. The qualitative inspection of the results obtained for two-dimensional cases in either the presence or the absence of bulk viscosity effects shows that the local and instantaneous structure of the mixing layer may be deeply altered when taking bulk viscosity into account. This contrasts with some mean statistical quantities, e.g., the vorticity thickness growth rate, which do not exhibit any significant sensitivity to the bulk viscosity. Enstrophy, Reynolds stress components, and turbulent kinetic energy (TKE) budgets are then evaluated from three-dimensional reactive simulations. Slight modifications are put into evidence on the energy transfer and dissipation contributions. From the obtained results, one may expect that refined large-eddy simulations (LES) may be rather sensitive to the consideration of bulk viscosity, while Reynolds-averaged Navier-Stokes (RANS) simulations, which are based on statistical averages, are not. The convective instability of a Maxwell-Cattaneo fluid in the presence of a vertical magnetic field https://zbmath.org/1472.76125 2021-11-25T18:46:10.358925Z "Eltayeb, I. A." https://zbmath.org/authors/?q=ai:eltayeb.ibrahim-a "Hughes, D. W." https://zbmath.org/authors/?q=ai:hughes.david-wynne "Proctor, M. R. E." https://zbmath.org/authors/?q=ai:proctor.michael-r-e Summary: We study the instability of a Bénard layer subject to a vertical uniform magnetic field, in which the fluid obeys the Maxwell-Cattaneo (MC) heat flux-temperature relation. We extend the work of \textit{J. J. Bissell} [Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 472, No. 2195, Article ID 20160649, 20 p. (2016; Zbl 1371.76159)] to non-zero values of the magnetic Prandtl number $$p_m$$. With non-zero $$p_m$$, the order of the dispersion relation is increased, leading to considerably richer behaviour. An asymptotic analysis at large values of the Chandrasekhar number $$Q$$ confirms that the MC effect becomes important when $$C Q^{1/2}$$ is $$O(1)$$, where $$C$$ is the MC number. In this regime, we derive a scaled system that is independent of $$Q$$. When $$CQ^{1/2}$$ is large, the results are consistent with those derived from the governing equations in the limit of Prandtl number $$p \rightarrow \infty$$ with $$p_m$$ finite; here we identify a new mode of instability, which is due neither to inertial nor induction effects. In the large $$p_m$$ regime, we show how a transition can occur between oscillatory modes of different horizontal scale. For $$Q \gg 1$$ and small values of $$p$$, we show that the critical Rayleigh number is non-monotonic in $$p$$ provided that $$C > 1/6$$. While the analysis of this paper is performed for stress-free boundaries, it can be shown that other types of mechanical boundary conditions give the same leading-order results. Rayleigh-Bénard magnetoconvection with temperature modulation https://zbmath.org/1472.76126 2021-11-25T18:46:10.358925Z "Hazra, Suparna" https://zbmath.org/authors/?q=ai:hazra.suparna "Kumar, Krishna" https://zbmath.org/authors/?q=ai:kumar.krishna-b|kumar.krishna-dev "Mitra, Saheli" https://zbmath.org/authors/?q=ai:mitra.saheli Summary: Floquet analysis of modulated magnetoconvection in Rayleigh-Bénard geometry is performed. A sinusoidally varying temperature is imposed on the lower plate. As Rayleigh number Ra is increased above a critical value $$Ra_o$$, the oscillatory magnetoconvection begins. The flow at the onset of magnetoconvection may oscillate either subhar- monically or harmonically with the external modulation. The critical Rayleigh number $$Ra_o$$ varies non-monotonically with the modulation frequency $$\omega$$ for appreciable value of the modulation amplitude $$a$$. The temperature modulation may either postpone or prepone the appearance of magnetoconvection. The magnetoconvective flow always oscillates harmonically at larger values of $$\omega$$. The threshold $$Ra_o$$ and the corresponding wavenumber $$k_o$$ approach to their values for the stationary magnetoconvection in the absence of modulation $$(a = 0)$$, as $$\omega \rightarrow \infty$$. Two different zones of harmonic instability merge to form a single instability zone with two local minima for higher values of Chandrasekhar's number $$Q$$, which is qualitatively new. We have also observed a new type of bicritical point, which involves two different sets of harmonic oscillations. The effects of variation of $$Q$$ and Pr on the threshold $$Ra_o$$ and critical wavenumber $$k_o$$ are also investigated. Entropy analysis on unsteady MHD flow of Casson nanofluid over a stretching vertical plate with thermal radiation effect https://zbmath.org/1472.76127 2021-11-25T18:46:10.358925Z "Shit, G. C." https://zbmath.org/authors/?q=ai:shit.g-c "Mandal, S." https://zbmath.org/authors/?q=ai:mandal.samir-ch|mandal.soham|mandal.susobhan|mandal.sayanta|mandal.swarnendu|mandal.sudin|mandal.subhendu-bikash|mandal.subhrangsu|mandal.subhayan|mandal.sikta|mandal.sonia|mandal.sanjoy|mandal.swapan|mandal.satyanarayan|mandal.s-p|mandal.satya|mandal.sayan|mandal.shubhadeep|mandal.santosh-kumar|mandal.sudhindu-bikash|mandal.subhro-jyoti|mandal.siddhartha|mandal.sudhansu-s|mandal.sandip|mandal.sayantan|mandal.soumyajit|mandal.samiran|mandal.seikh-hannan|mandal.swagata|mandal.shyamapada|mandal.sekhar|mandal.soma|mandal.sujit|mandal.supriya|mandal.sanjib-kumar|mandal.shyamal-kumar-das|mandal.saumendranath|mandal.somnath|mandal.soumik|mandal.saptarshi|mandal.sanjay-kumar|mandal.sajib|mandal.saumen|mandal.saroj|mandal.swarup|mandal.shobhan|mandal.sudipto|mandal.sourav-k The authors aim at entropy analysis of unsteady MHD flow of Casson nanofluid over a stretching vertical plate with thermal radiation effect using a fourth-order Runge-Kutta-Fehlberg method along with the shooting method. The flow behavior of non-Newtonian Casson nanofluid, heat transfer characteristics and nanoparticle concentration profiles are obtained to understand the impact of the different dimensionless parameters. Furthermore, the expressions for the dimensionless wall shear stress, heat and mass transfer rate over a heated vertical plate are derived. The results are in good agreement with existing results. Magnetohydrodynamics boundary layer flow of micropolar fluid over an exponentially shrinking sheet with thermal radiation: triple solutions and stability analysis https://zbmath.org/1472.76128 2021-11-25T18:46:10.358925Z "Yahaya, Rusya Iryanti" https://zbmath.org/authors/?q=ai:yahaya.rusya-iryanti "Arifin, Norihan Md" https://zbmath.org/authors/?q=ai:arifin.norihan-md "Isa, Siti Suzilliana Putri Mohamed" https://zbmath.org/authors/?q=ai:isa.siti-suzilliana-putri-mohamed "Rashidi, Mohammad Mehdi" https://zbmath.org/authors/?q=ai:rashidi.mohammad-mehdi Summary: The flow of electrically conducting micropolar fluid past an exponentially permeable shrinking sheet in the presence of a magnetic field and thermal radiation is studied. Similarity transformations are applied to the governing partial differential equations to form ordinary differential equations. The solution for the resultant equations, subject to boundary conditions, is then computed numerically using the bvp4c solver in MATLAB. The effects of several parameters on the local skin friction coefficient, couple stress, Nusselt number, velocity, microrotation and temperature of the fluid are analysed. Because the numerical computations for this problem result in triple solutions, stability analysis is carried out to ascertain the stability and significance of these solutions. The first solution is revealed to be stable, hence more physically meaningful than the other solutions. Meanwhile, it is found that the increase in magnetic and thermal radiation parameters reduces the fluid temperature. A control mechanism of a typical fluid-structure interaction problem based on dielectric barrier discharge plasma actuation model https://zbmath.org/1472.76129 2021-11-25T18:46:10.358925Z "Russo, Nicola" https://zbmath.org/authors/?q=ai:russo.nicola "Gonzalez, Leo M." https://zbmath.org/authors/?q=ai:gonzalez.leo-m "Viccione, Giacomo" https://zbmath.org/authors/?q=ai:viccione.giacomo "Pisacreta, Chiara" https://zbmath.org/authors/?q=ai:pisacreta.chiara Summary: This work numerically investigates the effects of using dielectric barrier discharge (DBD) plasma actuators to control the deformation and the hydrodynamic properties of the well-known fluid-structure interaction (FSI) benchmark presented by \textit{S. Turek} and \textit{J. Hron} [Lect. Notes Comput. Sci. Eng. 53, 371--385 (2006; Zbl 1323.76049)]. A slip boundary condition models the plasma actuation in order to control the interaction between the fluid flow and a deformable bar. The plasma model depends on two parameters, which are the control intensity and the actuation frequency. The effectiveness of the plasma control is examined by evaluating the amplitude and frequency of the vertical displacement of the oscillating bar free tip. First, for non-oscillatory actuation, the critical value for the intensity of the plasma actuation for which the vertical displacement disappears is detected and the physical mechanisms that provoke this behavior are studied. In a second step, the plasma actuator is also modulated with a control frequency, and the combined effect of both control parameters on the oscillation amplitude and frequency of the bar is examined. Depending on the specific values of the control parameters, a lock-in condition might appear. The behavior of the system in terms of drag, amplitude and frequency of the tip oscillation for different combinations of the actuation parameters is quantified. The possibilities of observing resonant phenomena or forcing the tip frequency to match the external plasma frequency are discussed, making it possible to predict the behavior of the system under examination. On relativistic gasdynamics: invariance under a class of reciprocal-type transformations and integrable Heisenberg spin connections https://zbmath.org/1472.76130 2021-11-25T18:46:10.358925Z "Rogers, C." https://zbmath.org/authors/?q=ai:rogers.colin "Ruggeri, T." https://zbmath.org/authors/?q=ai:ruggeri.tommaso "Schief, W. K." https://zbmath.org/authors/?q=ai:schief.wolfgang-karl Summary: A classical system of conservation laws descriptive of relativistic gasdynamics is examined. In the two-dimensional stationary case, the system is shown to be invariant under a novel multi-parameter class of reciprocal transformations. The class of invariant transformations originally obtained by Bateman in non-relativistic gasdynamics in connection with lift and drag phenomena is retrieved as a reduction in the classical limit. In the general 3+1-dimensional case, it is demonstrated that Synge's geometric characterization of the pressure being constant along streamlines encapsulates a three-dimensional extension of an integrable Heisenberg spin equation. Particle-fluid two phase modeling of electro-magneto hydrodynamic pulsatile flow of Jeffrey fluid in a constricted tube under periodic body acceleration https://zbmath.org/1472.76131 2021-11-25T18:46:10.358925Z "Ponalagusamy, R." https://zbmath.org/authors/?q=ai:ponalagusamy.r "Manchi, Ramakrishna" https://zbmath.org/authors/?q=ai:manchi.ramakrishna Summary: The present article investigates the combined role of electric and magnetic fields on the pulsatile flow of Jeffrey fluid (blood) with the suspension of particles (blood cells) in a stenosed artery under the influence of external periodic body acceleration. The Debye-Hückel linearization principle is invoked by assuming the zeta potential on the vessel wall is very small, and the coupled non-linear governing equations which comprise the continuity and momentum conservation equations for the fluid phase and particle phase are simplified by using dimensional analysis under the mild stenosis approximation. The closed-form solutions for electric potential, velocity profiles of both fluid and particle, volumetric flux, skin friction, and the flow resistance are derived in terms of Bessel functions by employing Laplace and Hankel transforms under the appropriate initial and boundary conditions. The influence of some evolving physical parameters like pulsatile Reynolds number, the amplitude of blood flow, Jeffrey parameter, hematocrit, body acceleration amplitude, phase angle, Hartmann number, and electro-osmotic parameter on velocity profiles, skin friction, and resistance to flow were shown graphically and debated concisely. The analysis reveals that the flow of blood in a stenosed duct is substantially influenced by the appropriate strength of externally applied electric and magnetic fields. The study further demonstrates that wall shear stress attenuates as the Jeffrey parameter increases, whereas the reverse trend is noticed with the concentration of blood cells. Moreover, it is worth mentioning that the increment in electric field intensity (i.e., decreasing Debye length) causes a reduction in the skin friction and impedance to flow, which, in turn, aids in improving the flow of blood under diseased conditions. Representative subsampling of sedimenting blood https://zbmath.org/1472.76132 2021-11-25T18:46:10.358925Z "Rallabandi, Bhargav" https://zbmath.org/authors/?q=ai:rallabandi.bhargav "Nunes, Janine K." https://zbmath.org/authors/?q=ai:nunes.janine-k "Perazzo, Antonio" https://zbmath.org/authors/?q=ai:perazzo.antonio "Gershtein, Sergey" https://zbmath.org/authors/?q=ai:gershtein.sergey "Stone, Howard A." https://zbmath.org/authors/?q=ai:stone.howard-a Summary: It is often necessary to extract a small amount of a suspension, such as blood, from a larger sample of the same material for the purposes of diagnostics, testing or imaging. A practical challenge is that the cells in blood sediment noticeably on the time scale of a few minutes, making a representative subsampling of the original sample challenging. Guided by experimental data, we develop a Kynch sedimentation model to discuss design considerations that ensure a representative subsampling of blood, from a container of constant cross-sectional area, for the entire range of physiologically relevant hematocrit over a specified time of interest. Additionally, we show that this design may be modified to exploit the sedimentation and perform subsampling to achieve either higher or lower hematocrit relative to that of the original sample. Thus, our method provides a simple tool to either concentrate or dilute small quantities of blood or other sedimenting suspensions. A mathematical analysis for constructal design of tree flow networks under unsteady flow https://zbmath.org/1472.76133 2021-11-25T18:46:10.358925Z "Soni, Bharat" https://zbmath.org/authors/?q=ai:soni.bharat-k "Miguel, Antonio F." https://zbmath.org/authors/?q=ai:miguel.antonio-f "Nayak, Ameeya Kumar" https://zbmath.org/authors/?q=ai:nayak.ameeya-kumar Summary: Tree flow networks play an important role in both natural and man-made systems. In an effort to develop a deeper understanding of the optimal design of these networks, we have developed a simple analytical approach to deal with steady and unsteady flows. As a result, optimal relations for the homothetic ratio of tube sizes and optimal angles between daughter tubes are obtained. The obtained optimum homothetic ratios satisfy the criterion of the minimization procedure of flow impedance based on geometry and the svelteness ratio. The robustness, accuracy and convergence of model are also proved mathematically in order to validate the results. Fibrous gels modelled as fluid-filled continua with double-well energy landscape https://zbmath.org/1472.76134 2021-11-25T18:46:10.358925Z "Sun, Chuanpeng" https://zbmath.org/authors/?q=ai:sun.chuanpeng "Chernysh, Irina N." https://zbmath.org/authors/?q=ai:chernysh.irina-n "Weisel, John W." https://zbmath.org/authors/?q=ai:weisel.john-w "Purohit, Prashant K." https://zbmath.org/authors/?q=ai:purohit.prashant-k Summary: Several biological materials are fibre networks infused with fluid, often referred to as fibrous gels. An important feature of these gels is that the fibres buckle under compression, causing a densification of the network that is accompanied by a reduction in volume and release of fluid. Displacement-controlled compression of fibrous gels has shown that the network can exist in a rarefied and a densified state over a range of stresses. Continuum chemo-elastic theories can be used to model the mechanical behaviour of these gels, but they suffer from the drawback that the stored energy function of the underlying network is based on neo-Hookean elasticity, which cannot account for the existence of multiple phases. Here we use a double-well stored energy function in a chemo-elastic model of gels to capture the existence of two phases of the network. We model cyclic compression/decompression experiments on fibrous gels and show that they exhibit propagating interfaces and hysteretic stress-strain curves that have been observed in experiments. We can capture features in the rate-dependent response of these fibrous gels without recourse to finite-element calculations. We also perform experiments to show that certain features in the stress-strain curves of fibrous gels predicted by our model can be found in the compression response of blood clots. Our methods may be extended to other tissues and synthetic gels that have a fibrous structure. A thin-film extensional flow model for biofilm expansion by sliding motility https://zbmath.org/1472.76135 2021-11-25T18:46:10.358925Z "Tam, Alexander" https://zbmath.org/authors/?q=ai:tam.alexander "Green, J. Edward F." https://zbmath.org/authors/?q=ai:green.j-edward-f "Balasuriya, Sanjeeva" https://zbmath.org/authors/?q=ai:balasuriya.sanjeeva "Tek, Ee Lin" https://zbmath.org/authors/?q=ai:tek.ee-lin "Gardner, Jennifer M." https://zbmath.org/authors/?q=ai:gardner.jennifer-m "Sundstrom, Joanna F." https://zbmath.org/authors/?q=ai:sundstrom.joanna-f "Jiranek, Vladimir" https://zbmath.org/authors/?q=ai:jiranek.vladimir "Binder, Benjamin J." https://zbmath.org/authors/?q=ai:binder.benjamin-james Summary: In the presence of glycoproteins, bacterial and yeast biofilms are hypothesized to expand by sliding motility. This involves a sheet of cells spreading as a unit, facilitated by cell proliferation and weak adhesion to the substratum. In this paper, we derive an extensional flow model for biofilm expansion by sliding motility to test this hypothesis. We model the biofilm as a two-phase (living cells and an extracellular matrix) viscous fluid mixture, and model nutrient depletion and uptake from the substratum. Applying the thin-film approximation simplifies the model, and reduces it to one-dimensional axisymmetric form. Comparison with \textit{Saccharomyces cerevisiae} mat formation experiments reveals good agreement between experimental expansion speed and numerical solutions to the model with $$\mathcal{O}(1)$$ parameters estimated from experiments. This confirms that sliding motility is a possible mechanism for yeast biofilm expansion. Having established the biological relevance of the model, we then demonstrate how the model parameters affect expansion speed, enabling us to predict biofilm expansion for different experimental conditions. Finally, we show that our model can explain the ridge formation observed in some biofilms. This is especially true if surface tension is low, as hypothesized for sliding motility. Correction to: Optimization and small-amplitude analysis of Purcell's three-link microswimmer model'' https://zbmath.org/1472.76136 2021-11-25T18:46:10.358925Z "Wiezel, O." https://zbmath.org/authors/?q=ai:wiezel.o "Or, Y." https://zbmath.org/authors/?q=ai:or.yizhar Corrects figures and equations in the authors' paper [ibid. 472, No. 2192, Article ID 20160425, 20 p. (2016; Zbl 1371.76181)] Analytical model for electrohydrodynamic thrust https://zbmath.org/1472.78012 2021-11-25T18:46:10.358925Z "Vaddi, Ravi Sankar" https://zbmath.org/authors/?q=ai:vaddi.ravi-sankar "Guan, Yifei" https://zbmath.org/authors/?q=ai:guan.yifei "Mamishev, Alexander" https://zbmath.org/authors/?q=ai:mamishev.alexander-v "Novosselov, Igor" https://zbmath.org/authors/?q=ai:novosselov.igor Summary: Electrohydrodynamic (EHD) thrust is produced when ionized fluid is accelerated in an electric field due to the momentum transfer between the charged species and neutral molecules. We extend the previously reported analytical model that couples space charge, electric field and momentum transfer to derive thrust force in one-dimensional planar coordinates. The electric current density in the model can be expressed in the form of Mott-Gurney law. After the correction for the drag force, the EHD thrust model yields good agreement with the experimental data from several independent studies. The EHD thrust expression derived from the first principles can be used in the design of propulsion systems and can be readily implemented in the numerical simulations. Small deformation theory for two leaky dielectric drops in a uniform electric field https://zbmath.org/1472.78016 2021-11-25T18:46:10.358925Z "Zabarankin, Michael" https://zbmath.org/authors/?q=ai:zabarankin.michael Summary: A small deformation theory for two non-identical spherical drops freely suspended in an ambient fluid and subjected to a uniform electric field is presented. The three phases are assumed to be leaky dielectric (slightly conducting) viscous incompressible fluids and the nonlinear effects of inertia and surface charge convection are neglected. The deformed shapes of the drops are linearized with respect to the electric capillary number that characterizes the balance between the electric stress and the surface tension. When the two drops are sufficiently far apart, their deformed shapes are predicted by Taylor's small deformation theory---depending on Taylor's discriminating function, the drops may become prolate, oblate or remain spherical. When the two drops get closer to each other, in addition to becoming prolate/oblate, they start translating and developing an egg shape. (Since there is no net charge, the centre of mass of the two drops remains stationary.) The extent of each of these modes' of deformation depends on the distance between the drops' centres and on drop-to-ambient fluid ratios of electric conductivities, dielectric constants and viscosities. The predictions of the small deformation theory for two drops perfectly agree with the existing results of two-drop dynamics simulation based on a boundary-integral equation approach. Moreover, while previous works observed only three types of behaviour for two identical drops---the drops may either become prolate or oblate and move towards each other or become prolate and move away from each other---the small deformation theory predicts that non-identical drops may, in fact, become oblate and move away from each other when the drop-to-ambient fluid conductivity ratios are reciprocal and the drop-to-ambient fluid viscosity ratios are sufficiently large. The presented theory also readily yields an analytical insight into the interplay among different modes of drop deformation and can be used to guide the selection of the phases' electromechanical properties for two-drop dynamics simulations. Covariant kinetic theory and transport coefficients for Gribov plasma https://zbmath.org/1472.81272 2021-11-25T18:46:10.358925Z "Jaiswal, Amaresh" https://zbmath.org/authors/?q=ai:jaiswal.amaresh "Haque, Najmul" https://zbmath.org/authors/?q=ai:haque.najmul Summary: Gribov quantization is a method to improve the infrared dynamics of Yang-Mills theory. We study the thermodynamics and transport properties of a plasma consisting of gluons whose propagator is improved by the Gribov prescription. We first construct thermodynamics of Gribov plasma using the gauge invariant Gribov dispersion relation for interacting gluons. When the Gribov parameter in the dispersion relation is temperature dependent, one expects a mean field correction to the Boltzmann equation. We formulate covariant kinetic theory for the Gribov plasma and determine the mean-field contribution in the Boltzmann equation. This leads to a quasiparticle like framework with a bag correction to pressure and energy density which mimics confinement. The temperature dependence of the Gribov parameter and bag pressure is fixed by matching with lattice results for a system of gluons. Finally we calculate the temperature dependence of the transport coefficients, i.e., bulk and shear viscosities. On the effect of fractional statistics on quantum ion acoustic waves https://zbmath.org/1472.81327 2021-11-25T18:46:10.358925Z "Ourabah, Kamel" https://zbmath.org/authors/?q=ai:ourabah.kamel Summary: In this paper, I study the effect of a small deviation from the Fermi-Dirac statistics on the quantum ion acoustic waves. For this purpose, a quantum hydrodynamic model is developed based on the Polychronakos statistics, which allows for a smooth interpolation between the Fermi and Bose limits, passing through the case of classical particles. The model includes the effect of pressure as well as quantum diffraction effects through the Bohm potential. The equation of state for electrons obeying fractional statistics is obtained and the effect of fractional statistics on the kinetic energy and the coupling parameter is analyzed. Through the model, the effect of fractional statistics on the quantum ion acoustic waves is highlighted, exploring both linear and weakly nonlinear regimes. It is found that fractional statistics enhance the amplitude and diminish the width of the quantum ion acoustic waves. Furthermore, it is shown that a small deviation from the Fermi-Dirac statistics can modify the type structures, from bright to dark soliton. All known results of fully degenerate and non-degenerate cases are reproduced in the proper limits. On the boundary layer equations with phase transition in the kinetic theory of gases https://zbmath.org/1472.82011 2021-11-25T18:46:10.358925Z "Bernhoff, Niclas" https://zbmath.org/authors/?q=ai:bernhoff.niclas "Golse, François" https://zbmath.org/authors/?q=ai:golse.francois In the present paper, the authors deal with the nonlinear half-space problem for the Boltzmann equation written in terms of the relative fluctuation of distribution function about the normalized Maxwellian $$M$$ $\left\{ \begin{array}{cc} (\xi _i+u)\partial _xf_u+\mathcal{L}f_u, & \xi \in \mathbb{R}^3,x>0, \\ f_u(0,\xi )=f_b(\xi ), & \xi _i+u>0. \end{array} \right.$ The authors prove the existence of the curve $$C$$ corresponding to solutions of the equations given in some neighborhood of the point $$(1, 0, 1)$$ converging as $$x\rightarrow \infty$$ with exponential speed uniformly in $$u$$. The authors provides a self-contained construction of the solution to the Nicolaenko-Thurber generalized eigenvalue problem near $$u = 0$$. Then, the authors introduce the penalization method, and formulate the problem to be solved by a fixed point argument. The linearized penalized problem is studied. Also, the authors investigate the (weakly) nonlinear penalized problem by a fixed point argument. The authors give an alternative, possibly simpler proof of one of the results discussed in [\textit{T.-P. Liu} and \textit{S.-H. Yu}, Arch. Ration. Mech. Anal. 209, No. 3, 869--997 (2013; Zbl 1290.35181)]. On the Nernst-Planck-Navier-Stokes system https://zbmath.org/1472.82037 2021-11-25T18:46:10.358925Z "Constantin, Peter" https://zbmath.org/authors/?q=ai:constantin.peter "Ignatova, Mihaela" https://zbmath.org/authors/?q=ai:ignatova.mihaela In this paper the authors study and obtain results about global existence and stability properties and convergence properties to Boltzmann states of a model for ionic electrodiffusion in fluids, in bounded domains for various boundary conditions and a wide class of initial data. For the Nernst-Planck-Navier-Stokes model the Navier-Stokes and Poisson equations are considered. This extends earlier known results for smaller classes of initial data and local existence. The model has various applications in the physics literature. Liquid crystals on deformable surfaces https://zbmath.org/1472.82040 2021-11-25T18:46:10.358925Z "Nitschke, Ingo" https://zbmath.org/authors/?q=ai:nitschke.ingo "Reuther, Sebastian" https://zbmath.org/authors/?q=ai:reuther.sebastian "Voigt, Axel" https://zbmath.org/authors/?q=ai:voigt.axel Summary: Liquid crystals with molecules constrained to the tangent bundle of a curved surface show interesting phenomena resulting from the tight coupling of the elastic and bulk-free energies of the liquid crystal with geometric properties of the surface. We derive a thermodynamically consistent Landau-de Gennes-Helfrich model which considers the simultaneous relaxation of the $$Q$$-tensor field and the surface. The resulting system of tensor-valued surface partial differential equation and geometric evolution laws is numerically solved to tackle the rich dynamics of this system and to compute the resulting equilibrium shape. The results strongly depend on the intrinsic and extrinsic curvature contributions and lead to unexpected asymmetric shapes. Gravitational edge modes, coadjoint orbits, and hydrodynamics https://zbmath.org/1472.83011 2021-11-25T18:46:10.358925Z "Donnelly, William" https://zbmath.org/authors/?q=ai:donnelly.william "Freidel, Laurent" https://zbmath.org/authors/?q=ai:freidel.laurent "Moosavian, Seyed Faroogh" https://zbmath.org/authors/?q=ai:moosavian.seyed-faroogh "Speranza, Antony J." https://zbmath.org/authors/?q=ai:speranza.antony-j Summary: The phase space of general relativity in a finite subregion is characterized by edge modes localized at the codimension-2 boundary, transforming under an infinite-dimensional group of symmetries. The quantization of this symmetry algebra is conjectured to be an important aspect of quantum gravity. As a step towards quantization, we derive a complete classification of the positive-area coadjoint orbits of this group for boundaries that are topologically a 2-sphere. This classification parallels Wigner's famous classification of representations of the Poincaré group since both groups have the structure of a semidirect product. We find that the total area is a Casimir of the algebra, analogous to mass in the Poincaré group. A further infinite family of Casimirs can be constructed from the curvature of the normal bundle of the boundary surface. These arise as invariants of the little group, which is the group of area-preserving diffeomorphisms, and are the analogues of spin. Additionally, we show that the symmetry group of hydrodynamics appears as a reduction of the corner symmetries of general relativity. Coadjoint orbits of both groups are classified by the same set of invariants, and, in the case of the hydrodynamical group, the invariants are interpreted as the generalized enstrophies of the fluid. Dynamics of the Szekeres system https://zbmath.org/1472.83014 2021-11-25T18:46:10.358925Z "Llibre, Jaume" https://zbmath.org/authors/?q=ai:llibre.jaume "Valls, Claudia" https://zbmath.org/authors/?q=ai:valls.claudia Summary: The Szekeres model is a differential system in $$\mathbb{R}^4$$ that provides the solutions of the Einstein field equations in the presence of irrotational dust. This differential system is integrable with two rational first integrals and one analytic first integral. We characterize the qualitative behavior of all the orbits of the Szekeres system in the function of the values of the two rational first integrals. {\copyright 2021 American Institute of Physics} A simple description of holographic domain walls in confining theories --- extended hydrodynamics https://zbmath.org/1472.83083 2021-11-25T18:46:10.358925Z "Janik, Romuald A." https://zbmath.org/authors/?q=ai:janik.romuald-a "Järvinen, Matti" https://zbmath.org/authors/?q=ai:jarvinen.matti "Sonnenschein, Jacob" https://zbmath.org/authors/?q=ai:sonnenschein.jacob Summary: In the context of theories with a first order phase transition, we propose a general covariant description of coexisting phases separated by domain walls using an additional order parameter-like degree of freedom. In the case of a holographic Witten model with a confining and deconfined phase, the resulting model extends hydrodynamics and has a simple formulation in terms of a spacetime action with corresponding expressions for the energy-momentum tensor. The proposed description leads to simple analytic profiles of domain walls, including expressions for surface tension density, which agree nicely with holographic numerical solutions, despite the apparent complexity of those gravitational backgrounds. Correspondence of cosmology from non-extensive thermodynamics with fluids of generalized equation of state https://zbmath.org/1472.83120 2021-11-25T18:46:10.358925Z "Nojiri, Shin'ichi" https://zbmath.org/authors/?q=ai:nojiri.shinichi "Odintsov, Sergei D." https://zbmath.org/authors/?q=ai:odintsov.sergei-d "Saridakis, Emmanuel N." https://zbmath.org/authors/?q=ai:saridakis.emmanuel-n "Myrzakulov, R." https://zbmath.org/authors/?q=ai:myrzakulov.ratbay Summary: We show that there is a correspondence between cosmology from non-extensive thermodynamics and cosmology with fluids of redefined and generalized equation of state. We first establish the correspondence in the case of basic non-extensive thermodynamics, and then we proceed by investigating the more consistent case, from the quantum field theoretical point of view, of varying exponent, namely depending on the scale. The obtained duality provides a way of explaining the complicated phenomenological forms of the effective fluid equation-of-state parameters that are being broadly used in the literature, since their microphysical origin may indeed lie in the non-extensive thermodynamics of spacetime. Finally, concerning the cosmological behavior, we show that at late times the effective fluid may drive the universe acceleration even in the absence of an explicit cosmological constant, and even if the initial fluid is the standard dust matter one. Similarly, at early times we obtain an effective cosmological constant which is enhanced through screening, and hence it can drive a successful inflation without spoiling the correct late-time acceleration. Cosmology from Newton-Chern-Simons gravity https://zbmath.org/1472.85004 2021-11-25T18:46:10.358925Z "Lepe, S." https://zbmath.org/authors/?q=ai:lepe.samuel "Rubio, G." https://zbmath.org/authors/?q=ai:rubio.gregorio|rubio.gerardo|rubio.gustavo|rubio.gonzalo|rubio.guillermo-j "Salgado, P." https://zbmath.org/authors/?q=ai:salgado.paulo|salgado.patricio|salgado.pablo|salgado.pilar Summary: We study a five-dimensional non-relativistic gravity theory whose action is composed of a gravitational sector and a sector of matter where the gravitational sector is given by the so called Newton-Chern-Simons gravity and where the matter sector is described by a perfect fluid. At time to do cosmology, the obtained field equations shows a close analogy with the projectable version of the Hořava-Lifshitz theory in $$(3+1)$$-dimensions. Solutions and their asymptotic limits are found. In particular a phantom solution with a future singularity reminiscent of a Litlle Big Rip future singularity is obtained. Modeling Ocean currents through complex random fields indexed in time https://zbmath.org/1472.86004 2021-11-25T18:46:10.358925Z "Cappello, Claudia" https://zbmath.org/authors/?q=ai:cappello.claudia "De Iaco, Sandra" https://zbmath.org/authors/?q=ai:de-iaco.sandra "Maggio, Sabrina" https://zbmath.org/authors/?q=ai:maggio.sabrina "Posa, Donato" https://zbmath.org/authors/?q=ai:posa.donato Summary: Surface ocean currents are often of interest in environmental monitoring. These vectorial data can be reasonably treated as a finite realization of a complex-valued random field, where the decomposition in modulus (current speed) and direction (current direction) of the current field is natural. Moreover, when observations are also available for different time points (other than at several locations), it is useful to evaluate the evolution of their complex correlation over time (rather than in space) and the corresponding modeling which is required for estimation purposes. This paper illustrates a first approach where the temporal profile of surface ocean currents is considered. After introducing the fundamental aspects of the complex formalism of a random field indexed in time, a new class of models suitable for including the temporal component is proposed and applied to describe the time-varying complex covariance function of current data. The analysis concerns ocean current observations, taken hourly on 30 April 2016 through high frequency radar systems at some stations located in the Northeastern Caribbean Sea. The selected complex covariance model indexed in time is used for estimation purposes and its reliability is confirmed by a numerical analysis. Uncoupling electrokinetic flow solutions https://zbmath.org/1472.86006 2021-11-25T18:46:10.358925Z "Kuhlman, Kristopher L." https://zbmath.org/authors/?q=ai:kuhlman.kristopher-l "Malama, Bwalya" https://zbmath.org/authors/?q=ai:malama.bwalya Summary: The continuum-scale electrokinetic porous-media flow and excess charge redistribution equations are uncoupled using eigenvalue decomposition. The uncoupling results in a pair of independent diffusion equations for intermediate'' potentials subject to modified material properties and boundary conditions. The fluid pressure and electrostatic potential are then found by recombining the solutions to the two intermediate uncoupled problems in a matrix-vector multiplication. Expressions for the material properties or source terms in the intermediate uncoupled problem may require extended precision or careful rewriting to avoid numerical cancellation, but the solutions themselves can typically be computed in double precision. The approach works with analytical or gridded numerical solutions and is illustrated through two examples. The solution for flow to a pumping well is manipulated to predict streaming potential and electroosmosis, and a periodic one-dimensional analytical solution is derived and used to predict electroosmosis and streaming potential in a laboratory flow cell subjected to low frequency alternating current and pressure excitation. The examples illustrate the utility of the eigenvalue decoupling approach, repurposing existing analytical solutions or numerical models and leveraging solutions that are simpler to derive for coupled physics. Mechanics of bed particle saltation in turbulent wall-shear flow https://zbmath.org/1472.86007 2021-11-25T18:46:10.358925Z "Padhi, Ellora" https://zbmath.org/authors/?q=ai:padhi.ellora "Ali, Sk Zeeshan" https://zbmath.org/authors/?q=ai:ali.sk-zeeshan "Dey, Subhasish" https://zbmath.org/authors/?q=ai:dey.subhasish Summary: In this paper, we explore the mechanics of bed particle saltation in turbulent wall-shear flow, analysing the forces on a particle to perform saltation. The hydrodynamic drag encompasses the form drag and turbulent drag. The hydrodynamic lift comprises the Saffman lift, Magnus lift and turbulent lift. The subtle role of the Basset force in governing the particle trajectory is accounted for in the analysis. The bedload flux, emanating from the mathematical analysis of bed particle saltation, is determined. The results reveal that for the particle parameter range 20-100, the transport stage function equalling unity corroborates the threshold of bed particle saltation, where the saltation height and length are 1.3 and 9 times the particle size. For a given transport stage function, the relative saltation height and length decrease with an increase in particle parameter. For the particle parameter range 20-100, the relative saltation height and length increase with an increase in transport stage function, reaching their peaks, and then, they decrease. For a given particle parameter, the peak and mean particle densimetric Froude numbers increase as the transport stage function increases. The bedload flux curves for particle parameters 26 and 63 produce the upper and lower bound curves, respectively. Nonlinear MHD Rossby wave interactions and persistent geomagnetic field structures https://zbmath.org/1472.86019 2021-11-25T18:46:10.358925Z "Raphaldini, Breno" https://zbmath.org/authors/?q=ai:raphaldini.breno "Raupp, Carlos F. M." https://zbmath.org/authors/?q=ai:raupp.carlos-f-m Summary: The geomagnetic field presents several stationary features that are thought to be linked to inhomogeneities at the core-mantle boundary. Particularly important stationary structures of the geomagnetic field are the flux lobes, which appear in pairs in mid- to high mid- to high latitudes. A recently discovered stratified layer at the top of the Earth's core poses important constraints on the dynamics at this layer and on the interaction of the core dynamics and the base of the mantle. In this article, we introduce the linear and nonlinear theories of magnetic Rossby waves in a thin shell at the top of the Earth's core. We study the nonlinear interaction of these waves in the presence of prescribed forcings at the base of the mantle of both a thermal and a topographic nature. We show that the combined effects of forcing and nonlinear interaction can lead the wave phases to be locked around a particular geographical longitude, generating a quasi- stationary flow pattern with a significant meridional component. The solutions of the system are shown to be analogous to atmospheric blocking phenomena. Therefore, we argue that persistent and long-lived structures of the geomagnetic field, such as the geomagnetic lobes, might be associated with a blocking at the top of the Earth's core due to nonlinear stationary waves. Acoustic and inertial modes in planetary-like rotating ellipsoids https://zbmath.org/1472.86020 2021-11-25T18:46:10.358925Z "Vidal, Jérémie" https://zbmath.org/authors/?q=ai:vidal.jeremie "Cébron, David" https://zbmath.org/authors/?q=ai:cebron.david Summary: The bounded oscillations of rotating fluid-filled ellipsoids can provide physical insight into the flow dynamics of deformed planetary interiors. The inertial modes, sustained by the Coriolis force, are ubiquitous in rapidly rotating fluids and \textit{S. Vantieghem} [Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 470, No. 2168, Article ID 20140093, 22 p. (2014; Zbl 1371.76157)] pioneered a method to compute them in incompressible fluid ellipsoids. Yet, taking density (and pressure) variations into account is required for accurate planetary applications, which has hitherto been largely overlooked in ellipsoidal models. To go beyond the incompressible theory, we present a Galerkin method in rigid coreless ellipsoids, based on a global polynomial description. We apply the method to investigate the normal modes of fully compressible, rotating and diffusionless fluids. We consider an idealized model, which fairly reproduces the density variations in the Earth's liquid core and Jupiter-like gaseous planets. We successfully benchmark the results against standard finite-element computations. Notably, we find that the quasi-geostrophic inertial modes can be significantly modified by compressibility, even in moderately compressible interiors. Finally, we discuss the use of the normal modes to build reduced dynamical models of planetary flows. Accurate computation of fracture density variations: a new approach tested on fracture corridors https://zbmath.org/1472.86032 2021-11-25T18:46:10.358925Z "Viseur, Sophie" https://zbmath.org/authors/?q=ai:viseur.sophie "Lamarche, Juliette" https://zbmath.org/authors/?q=ai:lamarche.juliette "Akriche, Clément" https://zbmath.org/authors/?q=ai:akriche.clement "Chatelée, Sébastien" https://zbmath.org/authors/?q=ai:chatelee.sebastien "Mombo Mouketo, Metzger" https://zbmath.org/authors/?q=ai:mombo-mouketo.metzger "Gauthier, Bertrand" https://zbmath.org/authors/?q=ai:gauthier.bertrand Summary: Fracture density is an important parameter for characterizing fractured reservoirs. Stochastic object-based simulation algorithms that generate fracture networks commonly rely on a fracture density to populate the reservoir zones with individual fracture surfaces. Reservoirs, including fracture corridors, represent particular challenges in petroleum reservoir studies. Indeed, it is difficult to identify fracture corridor zones objectively and precisely along one-dimensional well data, which are characterized by high fracture densities compared to diffuse fractures. To estimate fracture density, a common practice is to graphically depict only fracture corridors on fracture cumulative intensity curves. In this paper, an approach is proposed to formalize this technique using hypothesis testing. This method precisely compartmentalizes the well data into several zones having specific fracture densities. The method consists of the following steps: (i) dividing the diagram into zones depending on \textit{a priori} drastic changes in density, (ii) computing the local accurate fracture density for each zone and (iii) clustering the zones characterized by similar densities statistically. The key point is to couple regression and hypothesis testing. The regression aims at computing local average fracture density and the hypothesis testing aims at clustering zones for which the densities are statistically the most similar. The proposed approach is dedicated to one-dimensional fracture surveys, such as well data and outcrop scanlines. First, a synthetic case study is presented to prove the ability to highlight changes in fracture density. Second, the procedure is applied on a scanline dataset collected in a quarry (Calvisson, SE France) to show the usefulness of characterizing fracture corridors. Ice sheet flow with thermally activated sliding. I: The role of advection https://zbmath.org/1472.86038 2021-11-25T18:46:10.358925Z "Mantelli, E." https://zbmath.org/authors/?q=ai:mantelli.elisa "Haseloff, M." https://zbmath.org/authors/?q=ai:haseloff.m "Schoof, C." https://zbmath.org/authors/?q=ai:schoof.christian Summary: Flow organization into systems of fast-moving ice streams is a well-known feature of ice sheets. Fast motion is frequently the result of sliding at the base of the ice sheet. Here, we consider how this basal sliding is first initiated as the result of changes in bed temperature. We show that an abrupt sliding onset at the melting point, with no sliding possible below that temperature, leads to rapid drawdown of cold ice and refreezing as the result of the increased temperature gradient within the ice, and demonstrate that this result holds regardless of the mechanical model used to describe the flow of ice. Using this as a motivation, we then consider the possibility of a region of subtemperate sliding' in which sliding at reduced velocities occurs in a narrow range of temperatures just below the melting point. We confirm that this prevents the rapid drawdown of ice and refreezing of the bed, and construct a simple numerical method for computing steady-state ice sheet profiles that include a subtemperate region. The stability of such an ice sheet is analysed in a companion paper. The Part II, see [the first and the third author, Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 475, No. 2231, Article ID 20190411, 25 p. (2019; Zbl 1472.86039)]. Ice sheet flow with thermally activated sliding. II: The stability of subtemperate regions https://zbmath.org/1472.86039 2021-11-25T18:46:10.358925Z "Mantelli, E." https://zbmath.org/authors/?q=ai:mantelli.elisa "Schoof, C." https://zbmath.org/authors/?q=ai:schoof.christian Summary: The onset of sliding in ice sheets may not take the form of a sharp boundary between regions at the melting point, in which sliding is permitted, and regions below that temperature, in which there is no slip. Such a hard switch leads to the paradox of the bed naturally wanting to refreeze as soon as sliding has commenced. A potential alternative structure is a region of subtemperate sliding. Here temperatures are marginally below the melting point and sliding velocities slower than they would if the bed was fully temperate. Rather than being controlled by a standard sliding law, sliding velocities are then constrained by the need to maintain energy balance. This thermal structure arises in temperature-dependent sliding laws in the limit of strong sensitivity to temperature. Here, we analyse the stability of such subtemperate regions, showing that they are subject to a set of instabilities that occur at all length scales between ice thickness and ice sheet length. The fate of these instabilities is to cause the formation of patches of frozen bed, raising the possibility of highly complicated cold-to-temperate transitions with spatial structures at short length scales that cannot be resolved in large-scale ice sheet simulation codes. For Part I, see [the authors et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 475, No. 2230, Article ID 20190410, 26 p. (2019; Zbl 1472.86038)]. Tear film dynamics with blinking and contact lens motion https://zbmath.org/1472.92091 2021-11-25T18:46:10.358925Z "Anderson, Daniel M." https://zbmath.org/authors/?q=ai:anderson.daniel-m "Corsaro, Maria" https://zbmath.org/authors/?q=ai:corsaro.maria "Horton, Jonathan" https://zbmath.org/authors/?q=ai:horton.jonathan "Reid, Tim" https://zbmath.org/authors/?q=ai:reid.tim "Seshaiyer, Padmanabhan" https://zbmath.org/authors/?q=ai:seshaiyer.padmanabhan Summary: We develop a lubrication theory-based mathematical model that describes the dynamics of a tear film during blinking and contact lens (CL) wear. The model extends previous work on pre-corneal tear film dynamics during blinking by coupling the partial differential equation for tear film thickness to a dynamic model for CL motion. We explore different models for eyelid motion and also account for possible voluntary and involuntary globe (eyeball) rotation that may accompany blinking. Boundary conditions for mass flux at the eyelids are also adapted to account for the presence and motion of the CL. Our predictions for CL motion compare reasonably with existing data. Away from the eyelids the pre-lens tear film (PrLTF) is shifted, relative to its pre-corneal counterpart, in the direction of CL motion. Near the eyelids, the inflow/outflow of fluid under the eyelids also influences the PrLTF profile. We also compare our PrLTF dynamics to existing \textit{in vivo} tear film thickness measurements. An implicit approach to the micropolar fluid model of blood flow under the effect of body acceleration https://zbmath.org/1472.92092 2021-11-25T18:46:10.358925Z "Haghighi, Ahmad Reza" https://zbmath.org/authors/?q=ai:haghighi.ahmad-reza "Aliashrafi, Nooshin" https://zbmath.org/authors/?q=ai:aliashrafi.nooshin "Asl, Mohammad Shahbazi" https://zbmath.org/authors/?q=ai:shahbazi-asl.mohammad Summary: In the present study, the problem of simulating a non-Newtonian and two-dimensional blood flow in a flexible stenosed artery is examined by an implicit finite difference method. The streaming blood in the human artery is represented as a micropolar fluid. The governing nonlinear partial differential equations are modeled in cylindrical coordinates system and following a suitable radial coordinate transformation, they are solved numerically employing a Crank-Nicolson method with a suitable choice of initial and boundary conditions. An implicit approach is obtained for velocity distribution and the numerical solutions of flow rate and resistance impedance at the stenosis throat are founded by using velocity distribution. Effects of different types of tapered arteries, the stenosis and the amplitudes of body acceleration on the blood flow characteristics are presented graphically and discussed briefly. The motion of the arterial wall is paid due attention by comparing the blood flow characteristics through the elastic artery with the rigid ones. It is observed that the obtained results are in good agreement with previously conducted studies. Arterial blood stealing as a mechanism of negative BOLD response: from the steady-flow with nonlinear phase separation to a windkessel-based model https://zbmath.org/1472.92094 2021-11-25T18:46:10.358925Z "Suarez, Alejandro" https://zbmath.org/authors/?q=ai:suarez.alejandro "Valdes-Hernandez, Pedro A." https://zbmath.org/authors/?q=ai:valdes-hernandez.pedro-a "Moshkforoush, Arash" https://zbmath.org/authors/?q=ai:moshkforoush.arash "Tsoukias, Nikolaos" https://zbmath.org/authors/?q=ai:tsoukias.nikolaos-m "Riera, Jorge" https://zbmath.org/authors/?q=ai:riera.jorge-daniel Summary: Blood oxygen level dependent (BOLD) signal indirectly characterizes neuronal activity by measuring hemodynamic and metabolic changes in the nearby microvasculature. A deeper understanding of how localized changes in electrical, metabolic and hemodynamic factors translate into a BOLD signal is crucial for the interpretation of functional brain imaging techniques. While positive BOLD responses (PBR) are widely considered to be linked with neuronal activation, the origins of negative BOLD responses (NBR) have remained largely unknown. As NBRs are sometimes observed in close proximity of regions with PBR, a blood stealing'' effect, i.e., redirection of blood from a passive periphery to the area with high neuronal activity, has been postulated. In this study, we used the Hagen-Poiseuille equation to model hemodynamics in an idealized microvascular network that account for the particulate nature of blood and nonlinearities arising from the red blood cell (RBC) distribution (i.e., the Fåhraeus, Fåhraeus-Lindqvist and the phase separation effects). Using this detailed model, we evaluate determinants driving this stealing'' effect in a microvascular network with geometric parameters within physiological ranges. Model simulations predict that during localized cerebral blood flow (CBF) increases due to neuronal activation -- hyperemic response, blood from surrounding vessels is reallocated towards the activated region. This stealing effect depended on the resistance of the microvasculature and the uneven distribution of RBCs at vessel bifurcations. A parsimonious model consisting of two-connected windkessel regions sharing a supplying artery was proposed to simulate the stealing effect with a minimum number of parameters. Comparison with the detailed model showed that the parsimonious model can reproduce the observed response for hematocrit values within the physiological range for different species. Our novel parsimonious model promise to be of use for statistical inference (top-down analysis) from direct blood flow measurements (e.g., arterial spin labeling and laser Doppler/Speckle flowmetry), and when combined with theoretical models for oxygen extraction/diffusion will help account for some types of NBRs. Models of bacteria swimming in a nematic liquid crystal https://zbmath.org/1472.92142 2021-11-25T18:46:10.358925Z "Duan, Mochong" https://zbmath.org/authors/?q=ai:duan.mochong "Walkington, Noel J." https://zbmath.org/authors/?q=ai:walkington.noel-j Summary: Models of dilute systems of bacteria swimming in a nematic liquid crystal are developed and analyzed. The motion and orientation of the bacteria are simulated using ordinary differential equations coupled with the partial differential equations modeling the nematic liquid crystal (Ericksen Leslie equations). The analysis and numerical simulations of this system are shown to predict interesting phenomena observed experimentally. Fluid dynamic simulation suggests hopping locomotion in the Ordovician trilobite \textit{Placoparia} https://zbmath.org/1472.92251 2021-11-25T18:46:10.358925Z "Esteve, Jorge" https://zbmath.org/authors/?q=ai:esteve.jorge "López, Matheo" https://zbmath.org/authors/?q=ai:lopez.matheo "Ramírez, Carlos-Guillermo" https://zbmath.org/authors/?q=ai:ramirez.carlos-guillermo "Gómez, Iván" https://zbmath.org/authors/?q=ai:gomez.ivan Summary: Colonization of the water column by animals occurred gradually during the early Palaeozoic. However, the morphological and functional changes that took place during this colonization are poorly understood. The fossil record provides clear evidence of animals that were well adapted for swimming near the seafloor or in the open ocean, but recognising transitional forms is more problematic. Trilobites are a good model to explore the colonization of marine ecosystems. Here, we use computational fluid dynamics (CFD) to test between competing functional hypotheses in the Ordovician trilobite \textit{Placoparia}. The CFD simulations exhibits hydrodynamics that promote detachment from the seafloor but also promote return to the seafloor following detachment, this is compatible with hopping locomotion. The results suggest that \textit{Placopara} was not able to swim, but its hydrodynamics allowed it to hop long distances. This is consistent with the fossil record, as some ichnofossils show evidence of hopping. This type of locomotion could be useful to avoid predators as an escape mechanism. In addition, CFD simulation shows how the morphology of \textit{Placoparia} is adapted to protect anterior appendices of the trunk and generate a ventral vortex that send food particles directly to the trilobite mouth. Adaptations in \textit{Placoparia} allowed the first steps to evolved a new ecological habitat and consequently nektonization during the GOBE. A fully coupled subwavelength resonance approach to filtering auditory signals https://zbmath.org/1472.94022 2021-11-25T18:46:10.358925Z "Ammari, Habib" https://zbmath.org/authors/?q=ai:ammari.habib-m "Davies, Bryn" https://zbmath.org/authors/?q=ai:davies.bryn Summary: The aim of this paper is to understand the behaviour of a large number of coupled subwavelength resonators. We use layer potential techniques in combination with numerical computations to study an acoustic pressure wave scattered by a graded array of subwavelength resonators. Using this approach, the spatial frequency separation properties of such an array can be understood. Our set-up is inspired by the graded structure of cochlear hair cells on the surface of the basilar membrane. We compute the resonant modes of the system and explore the model's ability to decompose incoming signals. We propose a mathematical explanation for phenomena identified with the cochlea's travelling wave' behaviour and tonotopic frequency map.