Recent zbMATH articles in MSC 76Rhttps://zbmath.org/atom/cc/76R2021-06-15T18:09:00+00:00WerkzeugConvective plumes in rotating systems.https://zbmath.org/1460.860512021-06-15T18:09:00+00:00"Deremble, Bruno"https://zbmath.org/authors/?q=ai:deremble.brunoSummary: Convective plumes emanating from fixed buoyant sources such as volcanoes, hot springs and oil spills are common in the atmosphere and the ocean. Most of what we know about their dynamics comes from scaling laws, laboratory experiments and numerical simulations. A plume grows laterally during its ascent mainly due to the process of turbulent entrainment of fluid from the environment into the plume. In an unstratified system, nothing hampers the vertical motion of the plume. By contrast, in a stratified system, as the plume rises, it reaches and overshoots the neutral buoyancy height -- due to the non-zero momentum at that height. This rising fluid is then dense relative to the environment and slows down, ceases to rise and falls back to the height of the intrusion. For buoyant plumes occurring in the ocean or atmosphere, the rotation of the Earth adds an additional constraint via the conservation of angular momentum. In fact, the effect of rotation is still not well understood, and we addressed this issue in the study reported here. We looked for the steady states of an axisymmetric model in both the rotating and non-rotating cases. At the non-rotating limit, we isolated two regimes of convection depending on the buoyancy flux/momentum flux ratio at the base of the plume, in agreement with scaling laws. However, the inclusion of rotation in the model strongly affects these classical convection patterns: the lateral extension of the plume is confined at the intrusion level by the establishment of a geostrophic balance, and non-trivial swirl speed develops in and around the plume.The first 180 Lyapunov exponents for two-dimensional complex Ginzburg-Landau-type equation.https://zbmath.org/1460.763002021-06-15T18:09:00+00:00"Kozitskiy, S. B."https://zbmath.org/authors/?q=ai:kozitskii.s-bSummary: Dynamic patterns of three-dimensional double-diffusive convection in horizontally infinite liquid layer at large Rayleigh numbers have been simulated with the use of the previously derived system of complex Ginzburg-Landau-type amplitude equations valid in the neighborhoods of Hopf bifurcation points. For the special case of convection the first 180 Lyapunov exponents of the system have been calculated and 164 of them are positive. The spatial autocorrelation function is shown to be localized. Thus the system exhibits spatiotemporal chaos.On the dynamics of air bubbles in Rayleigh-Bénard convection.https://zbmath.org/1460.767922021-06-15T18:09:00+00:00"Kim, Jin-Tae"https://zbmath.org/authors/?q=ai:kim.jintae"Nam, Jaewook"https://zbmath.org/authors/?q=ai:nam.jaewook"Shen, Shikun"https://zbmath.org/authors/?q=ai:shen.shikun"Lee, Changhoon"https://zbmath.org/authors/?q=ai:lee.changhoon|lee.changhoon.1|lee.changhoon.2"Chamorro, Leonardo P."https://zbmath.org/authors/?q=ai:chamorro.leonardo-pSummary: The dynamics of air bubbles in turbulent Rayleigh-Bénard (RB) convection is described for the first time using laboratory experiments and complementary numerical simulations. We performed experiments at \(Ra=5.5\times 10^9\) and \(1.1\times 10^{10}\), where streams of 1 mm bubbles were released at various locations from the bottom of the tank along the path of the roll structure. Using three-dimensional particle tracking velocimetry, we simultaneously tracked a large number of bubbles to inspect the pair dispersion, \(R^2(t)\), for a range of initial separations, \(r\), spanning one order of magnitude, namely \(25 \eta \leqslant r\leqslant 225 \eta\); here \(\eta\) is the local Kolmogorov length scale. Pair dispersion, \(R^2(t)\), of the bubbles within a quiescent medium was also determined to assess the effect of inhomogeneity and anisotropy induced by the RB convection. Results show that \(R^2(t)\) underwent a transition phase similar to the ballistic-to-diffusive \((t^2\)-to-\(t^1)\) regime in the vicinity of the cell centre; it approached a bulk behavior \(t^{3/2}\) in the diffusive regime as the distance away from the cell centre increased. At small \(r, R^2(t)\propto t^1\) is shown in the diffusive regime with a lower magnitude compared to the quiescent case, indicating that the convective turbulence reduced the amplitude of the bubble's fluctuations. This phenomenon associated to the bubble path instability was further explored by the autocorrelation of the bubble's horizontal velocity. At large initial separations, \(R^2(t)\propto t^2\) was observed, showing the effect of the roll structure.Ricocheting inclined layer convection states.https://zbmath.org/1460.767292021-06-15T18:09:00+00:00"Tuckerman, Laurette S."https://zbmath.org/authors/?q=ai:tuckerman.laurette-sSummary: Inclining a fluid layer subjected to a temperature gradient introduces a profusion of fascinating patterns and regimes. Previous experimental and computational studies form the starting point for an extensive numerical bifurcation study by \textit{F. Reetz} and \textit{T. M. Schneider} [ibid. 898, Article ID A22, 31 p. (2020; Zbl 1460.76333)] and \textit{F. Reetz} et al. [ibid. 898, Article ID A23, 38 p. (2020; Zbl 1460.76725)]. Intricate trajectories passing through multiple steady and periodic states organize the dynamics. The consequences for chaotic patterns in large geometries is discussed.Scaling in concentration-driven convection boundary layers with transpiration.https://zbmath.org/1460.767652021-06-15T18:09:00+00:00"Ramareddy, G. V."https://zbmath.org/authors/?q=ai:ramareddy.g-v"Joshy, P. J."https://zbmath.org/authors/?q=ai:joshy.p-j"Nair, Gayathri"https://zbmath.org/authors/?q=ai:nair.gayathri"Puthenveettil, Baburaj A."https://zbmath.org/authors/?q=ai:puthenveettil.baburaj-aSummary: We study concentration-driven natural convection boundary layers on horizontal surfaces, subjected to a weak, surface normal, uniform blowing velocity \(V_i\) for three orders of range of the dimensionless blowing parameter \(10^{-8}\le J=Re_x^3/Gr_x\leq 10^{-5}\), where \(Re_x\) and \(Gr_x\) are the local Reynolds and Grashof numbers at the horizontal location \(x\), based respectively on \(V_i\) and \(\Delta C\), the concentration difference across the boundary layer. We formulate the integral boundary layer equations, with the assumption of no concentration drop within the species boundary layer, which is valid for weak blowing into the thin species boundary layers that occur at the high Schmidt number \((Sc \simeq 600)\) of concentration-driven convection. The equations are then numerically solved to show that the species boundary layer thickness \(\delta_d = 1.6x (Re_x/Gr_x)^{1/4}\), the velocity boundary layer thickness \(\delta_v=\delta_d Sc^{1/5}\), the horizontal velocity \(u = V_i(Gr_x/Re_x)^{1/4}f(\eta)\), where \(\eta =y/\delta_v\), and the drag coefficient based on \(V_i\), \(C_D = 2.32/\sqrt{J}\). We find that the vertical profile of the horizontally averaged dimensionless concentration across the boundary layer becomes, surprisingly, independent of the blowing and the species diffusion effects to follow a \(Gr_y^{2/3}\) scaling, where \(Gr_y\) is the Grashof number based on the vertical location \(y\) within the boundary layer. We then show that the above profile matches the experimentally observed mean concentration profile within the boundary layers that form on the top surface of a membrane, when a weak flow is forced gravitationally from below the horizontal membrane that has brine above it and water below it. A similar match between the theoretical scaling of the species boundary layer thickness and its experimentally observed variation is also shown to occur.Onset of Darcy-Bénard convection in a horizontal layer of dual-permeability medium with isothermal boundaries.https://zbmath.org/1460.767412021-06-15T18:09:00+00:00"Afanasyev, Andrey"https://zbmath.org/authors/?q=ai:afanasev.a-aSummary: The onset of natural convection in an infinite horizontal layer of a fractured-porous medium is investigated. The breakdown of local equilibrium between the low-permeability matrix and fractures embedded in the matrix is accounted for by applying the dual-porosity dual-permeability model. The symmetric case of impermeable and isothermal boundaries of the layer is examined in detail. By means of linear perturbation analysis, the dispersion equation is derived, and its solutions are investigated numerically as well as analytically in a few asymptotic cases. It is determined that the critical Rayleigh number depends only on the permeability, heat conductivity ratios and the coefficient of heat and mass transfer between fractures and matrix. It is shown that the convection exhibits a rich variety of flow patterns at near-critical conditions. Nine flow regimes can arise with co-rotating or counter-rotating convection cells in the fractures and matrix. These modes can bifurcate to the plane flow regime, in which only cross-medium convection occurs. The complete classification of the flow regimes is provided and plotted in a solution map. Finally, the theoretical analysis is supported by the numerical modelling of the convection by using a reservoir simulator.Reduced-order modelling of radiative transfer effects on Rayleigh-Bénard convection in a cubic cell.https://zbmath.org/1460.767272021-06-15T18:09:00+00:00"Soucasse, Laurent"https://zbmath.org/authors/?q=ai:soucasse.laurent"Podvin, Bérengère"https://zbmath.org/authors/?q=ai:podvin.berengere"Rivière, Philippe"https://zbmath.org/authors/?q=ai:riviere.philippe"Soufiani, Anouar"https://zbmath.org/authors/?q=ai:soufiani.anouarSummary: This paper presents a reduced-order modelling strategy for Rayleigh-Bénard convection of a radiating gas, based on the proper orthogonal decomposition (POD). Direct numerical simulation (DNS) of coupled natural convection and radiative transfer in a cubic Rayleigh-Bénard cell is performed for an air/H\(_2\)O/CO\(_2\) mixture at room temperature and at a Rayleigh number of \(10^7\). It is shown that radiative transfer between the isothermal walls and the gas triggers a convection growth outside the boundary layers. Mean and turbulent kinetic energy increase with radiation, as well as temperature fluctuations to a lesser extent. As in the uncoupled case, the large-scale circulation (LSC) settles in one of the two diagonal planes of the cube with a clockwise or anticlockwise motion, and experiences occasional brief reorientations which are rotations of \(\pi /2\) of the LSC in the horizontal plane. A POD analysis is conducted and reveals that the dominant POD eigenfunctions are preserved with radiation while POD eigenvalues are increased. Two POD-based reduced-order models including radiative transfer effects are then derived: the first one is based on coupled DNS data while the second one is an \textit{a priori} model based on uncoupled DNS data. Owing to the weak temperature differences, radiation effects on mode amplitudes are linear in the models. Both models capture the increase in energy with radiation and are able to reproduce the low-frequency dynamics of reorientations and the high-frequency dynamics associated with the LSC velocity observed in the coupled DNS.Invariant states in inclined layer convection. II: Bifurcations and connections between branches of invariant states.https://zbmath.org/1460.767252021-06-15T18:09:00+00:00"Reetz, Florian"https://zbmath.org/authors/?q=ai:reetz.florian"Subramanian, Priya"https://zbmath.org/authors/?q=ai:subramanian.priya"Schneider, Tobias M."https://zbmath.org/authors/?q=ai:schneider.tobias-mSummary: Convection in a layer inclined against gravity is a thermally driven non-equilibrium system, in which both buoyancy and shear forces drive spatio-temporally complex flows. As a function of the strength of thermal driving and the angle of inclination, a multitude of convection patterns is observed in experiments and numerical simulations. Several observed patterns have been linked to exact invariant states of the fully nonlinear three-dimensional Oberbeck-Boussinesq equations. These exact equilibria, travelling waves and periodic orbits reside in state space and, depending on their stability properties, are transiently visited by the dynamics or act as attractors. To explain the dependence of observed convection patterns on control parameters, we study the parameter dependence of the state space structure. Specifically, we identify the bifurcations that modify the existence, stability and connectivity of invariant states. We numerically continue exact invariant states underlying spatially periodic convection patterns at \(Pr=1.07\) under changing control parameters for a temperature difference between the walls and inclination angle. The resulting state branches cover various inclinations from horizontal layer convection to vertical layer convection and beyond. The collection of all computed branches represents an extensive bifurcation network connecting 16 different invariant states across control parameter values. Individual bifurcation structures are discussed in detail and related to the observed complex dynamics of individual convection patterns. Together, the bifurcations and associated state branches indicate at what control parameter values which invariant states coexist. This provides a nonlinear framework to explain the multitude of complex flow dynamics arising in inclined layer convection.
For part I, see [\textit{F. Reetz} and \textit{T. M. Schneider}, ibid. 898, Paper No. A22, 31 p. (2020; Zbl 1460.76333)].Tenacious wall states in thermal convection in rapidly rotating containers.https://zbmath.org/1460.768982021-06-15T18:09:00+00:00"Shishkina, Olga"https://zbmath.org/authors/?q=ai:shishkina.olga-andreevnaSummary: Convection in a container, heated from below, cooled from above and rapidly rotated around a vertical axis, starts from its sidewall. When the imposed vertical temperature gradient is not sufficiently large for bulk modes to set in, thermal convection can start in the form of wall modes, which are observed near the sidewall as pairs of hot ascending and cold descending plumes that drift along the wall. With increasing temperature gradient, different wall and bulk modes occur and interact, leading finally to turbulence. A recent numerical study by \textit{B. Favier} and \textit{E. Knobloch} [ibid. 895, Article ID R1, 15 p. (2020; Zbl 1460.76719)] reveals an extreme robustness of the wall states. They persist above the onset of bulk modes and turbulence, thereby relating them to the recently discovered boundary zonal flows in highly turbulent rotating thermal convection. More exciting is that the wall modes can be thought of as topologically protected states, as they are robust with respect to the sidewall shape. They stubbornly drift along the wall, following its contour, independent of geometric obstacles.Global-in-time existence for liquid mixtures subject to a generalised incompressibility constraint.https://zbmath.org/1460.352802021-06-15T18:09:00+00:00"Druet, Pierre-Etienne"https://zbmath.org/authors/?q=ai:druet.pierre-etienneSummary: We consider a system of partial differential equations describing diffusive and convective mass transport in a fluid mixture of \(N > 1\) chemical species. A weighted sum of the partial mass densities of the chemical species is assumed to be constant, which expresses the incompressibility of the fluid, while accounting for different reference sizes of the involved molecules. This condition is different from the usual assumption of a constant total mass density, and it leads in particular to a non-solenoidal velocity field in the Navier-Stokes equations. In turn, the pressure gradient occurs in the diffusion fluxes, so that the PDE-system of mass transport equations and momentum balance is fully coupled. Another striking feature of such incompressible \textit{mixtures} is the algebraic formula connecting the pressure and the densities, which can be exploited to prove a pressure bound in \(L^1\). In this paper, we consider incompressible initial states with bounded energy and show the global existence of weak solutions with defect measure.Turbulent Rayleigh-Bénard convection in a strong vertical magnetic field.https://zbmath.org/1460.769182021-06-15T18:09:00+00:00"Akhmedagaev, R."https://zbmath.org/authors/?q=ai:akhmedagaev.r"Zikanov, O."https://zbmath.org/authors/?q=ai:zikanov.oleg-yu"Krasnov, D."https://zbmath.org/authors/?q=ai:krasnov.dmitry|krasnov.d-s"Schumacher, J."https://zbmath.org/authors/?q=ai:schumacher.jorgSummary: Direct numerical simulations are carried out to study the flow structure and transport properties in turbulent Rayleigh-Bénard convection in a vertical cylindrical cell of aspect ratio one with an imposed axial magnetic field. Flows at the Prandtl number \(0.025\) and Rayleigh and Hartmann numbers up to \(10^9\) and \(1400\), respectively, are considered. The results are consistent with those of earlier experimental and numerical data. As anticipated, the heat transfer rate and kinetic energy are suppressed by a strong magnetic field. At the same time, their growth with Rayleigh number is found to be faster in flows at high Hartmann numbers. This behaviour is attributed to the newly discovered flow regime characterized by prominent quasi-two-dimensional structures reminiscent of vortex sheets observed earlier in simulations of magnetohydrodynamic turbulence. Rotating wall modes similar to those in Rayleigh-Bénard convection with rotation are found in flows near the Chandrasekhar linear stability limit. A detailed analysis of the spatial structure of the flows and its effect on global transport properties is reported.Natural convection of Newtonian liquids and nanoliquids confined in low-porosity enclosures.https://zbmath.org/1460.767362021-06-15T18:09:00+00:00"Siddheshwar, P. G."https://zbmath.org/authors/?q=ai:siddheshwar.pradeep-g"Lakshmi, K. M."https://zbmath.org/authors/?q=ai:lakshmi.k-mNatural convection of nanoliquids confined in a low-porosity enclosure when the lateral walls are subject to constant heat and mass fluxes is studied analytically using modified Buongiorno-Darcy model and Oseen linearised approximation. For the study the authors have considered water-copper nanoliquid and aluminium foam, glass balls as porous materials. The effective thermophysical properties are calculated using phenomenological laws and mixture theory. An analytical solution is obtained for boundary layer velocity and Nusselt number. The study shows that dilute concentration of high thermal conductivity nanoparticles significantly facilitates enhanced the heat transport.
For the entire collection see [Zbl 1410.65005].
Reviewer: Ioan Pop (Cluj-Napoca)Stability of ice lenses in saline soils.https://zbmath.org/1460.767632021-06-15T18:09:00+00:00"Peppin, S. S. L."https://zbmath.org/authors/?q=ai:peppin.stephen-s-lSummary: A model of the growth of an ice lens in a saline porous medium is developed. At high lens growth rates the pore fluid becomes supercooled relative to its equilibrium Clapeyron temperature. Instability occurs when the supercooling increases with distance away from the ice lens. Solute diffusion in the pore fluid significantly enhances the instability. An expression for the segregation potential of the soil is obtained from the condition for marginal stability of the ice lens. The model is applied to a clayey silt and a glass powder medium, indicating parameter regimes where the ice lens stability is controlled by viscous flow or by solute diffusion. A mushy layer, composed of vertical ice veins and horizontal ice lenses, forms in the soil in response to the instability. A marginal equilibrium condition is used to estimate the segregated ice fraction in the mushy layer as a function of the freezing rate and salinity.Characteristics of a precessing flow under the influence of a convecting temperature field in a spheroidal shell.https://zbmath.org/1460.769012021-06-15T18:09:00+00:00"Vormann, Jan"https://zbmath.org/authors/?q=ai:vormann.jan"Hansen, Ulrich"https://zbmath.org/authors/?q=ai:hansen.ulrichSummary: We present results from direct numerical simulations of flows in spherical and oblate spheroidal shells, driven both by precession and thermal convection, with Ekman number \(Ek=10^{-4}\), non-diffusive Rayleigh numbers from \(Ra=0.1\) to \(Ra=10\) and unity Prandtl number. The applied precessional forcing spans seven orders of magnitude. Our experiments show a clear transition between a convective state and a precessing flow that can be approximated by a reduced dynamical model. The change in the flow is apparent in visualizations and a decomposition of the velocity into symmetric and antisymmetric components. For the flow dominated by precession, some parameter combinations show two stable solutions that can be realized by a hysteresis or a strong thermal forcing. An increase of the Rayleigh number at a constant precession rate exhibits established scaling properties for the heat transfer, with exponents \(2/7\) and \(6/5\).Mathematical model for degradation and drug release from an intravitreal biodegradable implant.https://zbmath.org/1460.769522021-06-15T18:09:00+00:00"Ferreira, J. A."https://zbmath.org/authors/?q=ai:ferreira.jose-augusto"Gonçalves, M. B."https://zbmath.org/authors/?q=ai:goncalves.m-b"Gudiño, E."https://zbmath.org/authors/?q=ai:gudino.elias"Maia, M."https://zbmath.org/authors/?q=ai:maia.mariana|maia.moreira|maia.manuel"Oishi, C. M."https://zbmath.org/authors/?q=ai:oishi.cassio-mSummary: In this paper we study from a mathematical point of view the drug release and the degradation process in the context of biodegradable intravitreal implants. In particular, two different clinical situations are considered: non-vitrectomized and vitrectomized eyes. In the former case we assume that the vitreous humor is replaced by a saline solution or a silicone oil. In intravitreal space, the intravitreal liquid enters the implant by non-Fickian diffusion causing the degradation of the poly(lactic-co-glycolic acid) based implant. Then, drug in the implant dissolves and diffuses out of the polymeric matrix. The transport of drug in the vitreous chamber and retina is modeled by Fickian diffusion and convection generated by the flow of the vitreous humor. In order to numerically solve the system of partial differential equations that define the model, we propose an Implicit-Explicit finite element method that allows for the decoupling of the solution reducing the computational cost of the simulations. Several numerical experiments showing the effectiveness of the proposed numerical schemes are also included. The proposed mathematical model may be useful to optimize patient specific treatments in clinical practice.The convective Stefan problem: shaping under natural convection.https://zbmath.org/1460.800162021-06-15T18:09:00+00:00"Pegler, Samuel S."https://zbmath.org/authors/?q=ai:pegler.samuel-s"Davies Wykes, Megan S."https://zbmath.org/authors/?q=ai:wykes.megan-s-daviesSummary: What is the shape formed by a body that is melting or dissolving into an ambient fluid? We present a theoretical analysis of the dynamics of melting or dissolving bodies in the common situation where the transfer of heat or solute at the surface creates a thin thermal or solutal convective boundary layer along its surface. By conducting a general analysis of a mathematical model describing the shape evolution of such bodies [the authors, ibid. 900, Paper No. A35, 42 p. (2020; Zbl 1460.86047)], we reveal new phenomena relating to the emergence of fundamental similarity solutions, asymptotic transitions, tip structure and the conditions for the development of sharp versus blunted tips. A universal regime diagram is developed showing asymptotic transitions between two different classes of similarity solutions. With \(t\) time, the tip of initially rectangular bodies is found to descend as \(t^{4/3}\) at early times, but transitions to the considerable faster power of \(t^4\) at long times, for example. Surprisingly, the tips of certain shapes, including initially rectangular bodies, sharpen continuously, whilst those of others, including initially conic bodies, blunt for all times. For the former case, the tip curvature grows rapidly as \(t^{12}\), forming a needle-like shape. More general initial shapes can produce multiple transitions between sharpening and blunting. These results provide foundational understanding of buoyancy-driven fluid sculpting that underlies numerous natural and industrial applications.Robust wall states in rapidly rotating Rayleigh-Bénard convection.https://zbmath.org/1460.767192021-06-15T18:09:00+00:00"Favier, Benjamin"https://zbmath.org/authors/?q=ai:favier.benjamin"Knobloch, Edgar"https://zbmath.org/authors/?q=ai:knobloch.edgarSummary: We show, using direct numerical simulations with experimentally realizable boundary conditions, that wall modes in Rayleigh-Bénard convection in a rapidly rotating cylinder persist even very far from their linear onset. These nonlinear wall states survive in the presence of turbulence in the bulk and are robust with respect to changes in the shape of the boundary of the container. In this sense, these states behave much like the topologically protected states present in two-dimensional chiral systems even though rotating convection is a three-dimensional nonlinear driven dissipative system. We suggest that the robustness of this nonlinear state may provide an explanation for the strong zonal flows observed recently in experiments and simulations of rapidly rotating convection at high Rayleigh number.New bounds on the vertical heat transport for Bénard-Marangoni convection at infinite Prandtl number.https://zbmath.org/1460.767182021-06-15T18:09:00+00:00"Fantuzzi, Giovanni"https://zbmath.org/authors/?q=ai:fantuzzi.giovanni"Nobili, Camilla"https://zbmath.org/authors/?q=ai:nobili.camilla"Wynn, Andrew"https://zbmath.org/authors/?q=ai:wynn.andrewSummary: We prove a new rigorous upper bound on the vertical heat transport for Bénard-Marangoni convection of a two- or three-dimensional fluid layer with infinite Prandtl number. Precisely, for Marangoni number \(Ma\gg 1\) the Nusselt number \(Nu\) is bounded asymptotically by \(Nu\leqslant \text{const.}\times Ma^{2/7}(\ln Ma)^{-1/7}\). Key to our proof are a background temperature field with a hyperbolic profile near the fluid's surface and new estimates for the coupling between temperature and vertical velocity.Bidispersive thermal convection with relatively large macropores.https://zbmath.org/1460.767492021-06-15T18:09:00+00:00"Gentile, M."https://zbmath.org/authors/?q=ai:gentile.maurizio|gentile.marc"Straughan, B."https://zbmath.org/authors/?q=ai:straughan.brianSummary: We derive linear instability and nonlinear stability thresholds for a problem of thermal convection in a bidispersive porous medium with a single temperature when Darcy theory is employed in the micropores whereas Brinkman theory is utilized in the macropores. It is important to note that 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. The coincidence of the linear and nonlinear stability boundaries is established under general thermal boundary conditions.Settling-driven large-scale instabilities in double-diffusive convection.https://zbmath.org/1460.768532021-06-15T18:09:00+00:00"Ouillon, Raphael"https://zbmath.org/authors/?q=ai:ouillon.raphael"Edel, Philip"https://zbmath.org/authors/?q=ai:edel.philip"Garaud, Pascale"https://zbmath.org/authors/?q=ai:garaud.pascale"Meiburg, Eckart"https://zbmath.org/authors/?q=ai:meiburg.eckart-hSummary: When the density of a gravitationally stable fluid depends on a fast diffusing scalar and a slowly diffusing scalar of opposite contribution to the stability, `double diffusive' instabilities may develop and drive convection. When the slow diffuser settles under gravity, as is for instance the case for small sediment particles in water, settling-driven double-diffusive instabilities can additionally occur. Such instabilities are relevant in a variety of naturally occurring settings, such as particle-laden river discharges, or underground inflows in lakes. Inspired by the dynamics of the more traditional thermohaline double-diffusive instabilities, we ask whether large-scale `mean-field' instabilities can develop as a result of sedimentary double-diffusive convection. We first apply the mean-field instability theory of \textit{A. Traxler} et al. [ibid. 677, 530--553 (2011; Zbl 1241.76229)] to high-Prandtl-number fluids, and find that these are unstable to Radko's layering instability, yet collectively stable. We then extend the theory of Traxler et al. [loc. cit.] to include settling and study its impact on the development of the collective instability. We find that two distinct regimes exist. At low settling velocities, the double-diffusive turbulence in the fingering regime is relatively unaffected by settling and remains stable to the classical collective instability. It is, however, unstable to a new instability in which large-scale gravity waves are excited by the phase shift between the salinity and particle concentration fields. At higher settling velocities, the double-diffusive turbulence is substantially affected by settling, and becomes unstable to the classic collective instability. Our findings, validated by direct numerical simulations, reveal new opportunities to observe settling-driven layering in laboratory and field experiments.The Nusselt numbers of horizontal convection.https://zbmath.org/1460.767262021-06-15T18:09:00+00:00"Rocha, Cesar B."https://zbmath.org/authors/?q=ai:rocha.cesar-b"Constantinou, Navid C."https://zbmath.org/authors/?q=ai:constantinou.navid-c"Llewellyn Smith, Stefan G."https://zbmath.org/authors/?q=ai:llewellyn-smith.stefan-g"Young, William R."https://zbmath.org/authors/?q=ai:young.william-rSummary: In the problem of horizontal convection a non-uniform buoyancy, \(b_s(x,y)\), is imposed on the top surface of a container and all other surfaces are insulating. Horizontal convection produces a net horizontal flux of buoyancy, \(\mathbf{J}\), defined by vertically and temporally averaging the interior horizontal flux of buoyancy. We show that \(\overline{\mathbf{J}\cdot\nabla b_s}=-\kappa \langle |\nabla b|^2\rangle\); the overbar denotes a space-time average over the top surface, angle brackets denote a volume-time average and \(\kappa\) is the molecular diffusivity of buoyancy \(b\). This connection between \(\mathbf{J}\) and \(\kappa\langle | \nabla b|^2\rangle\) justifies the definition of the horizontal-convective Nusselt number, \(Nu\), as the ratio of \(\kappa\langle | \nabla b|^2\rangle\) to the corresponding quantity produced by molecular diffusion alone. We discuss the advantages of this definition of \(Nu\) over other definitions of horizontal-convective Nusselt number. We investigate transient effects and show that \(\kappa \langle | \nabla b|^2\rangle\) equilibrates more rapidly than other global averages, such as the averaged kinetic energy and bottom buoyancy. We show that \(\kappa \langle | \nabla b|^2\rangle\) is the volume-averaged rate of Boussinesq entropy production within the enclosure. In statistical steady state, the interior entropy production is balanced by a flux through the top surface. This leads to an equivalent `surface Nusselt number', defined as the surface average of vertical buoyancy flux through the top surface times the imposed surface buoyancy \(b_s(x,y)\). In experimental situations it is easier to evaluate the surface entropy flux, rather than the volume integral of \(| \nabla b|^2\) demanded by \(\kappa\langle | \nabla b|^2\rangle \).Rotation of anisotropic particles in Rayleigh-Bénard turbulence.https://zbmath.org/1460.763542021-06-15T18:09:00+00:00"Jiang, Linfeng"https://zbmath.org/authors/?q=ai:jiang.linfeng"Calzavarini, Enrico"https://zbmath.org/authors/?q=ai:calzavarini.enrico"Sun, Chao"https://zbmath.org/authors/?q=ai:sun.chaoSummary: Inertialess anisotropic particles in a Rayleigh-Bénard turbulent flow show maximal tumbling rates for weakly oblate shapes, in contrast with the universal behaviour observed in developed turbulence where the mean tumbling rate monotonically decreases with the particle aspect ratio. This is due to the concurrent effect of turbulent fluctuations and of a mean shear flow whose intensity, we show, is determined by the kinetic boundary layers. In Rayleigh-Bénard turbulence prolate particles align preferentially with the fluid velocity, while oblate ones orient with the temperature gradient. This analysis elucidates the link between particle angular dynamics and small-scale properties of convective turbulence and has implications for the wider class of sheared turbulent flows.Flow regimes of Rayleigh-Bénard convection in a vertical magnetic field.https://zbmath.org/1460.769442021-06-15T18:09:00+00:00"Zürner, Till"https://zbmath.org/authors/?q=ai:zurner.till"Schindler, Felix"https://zbmath.org/authors/?q=ai:schindler.felix"Vogt, Tobias"https://zbmath.org/authors/?q=ai:vogt.tobias"Eckert, Sven"https://zbmath.org/authors/?q=ai:eckert.sven"Schumacher, Jörg"https://zbmath.org/authors/?q=ai:schumacher.jorgSummary: The effects of a vertical static magnetic field on the flow structure and global transport properties of momentum and heat in liquid metal Rayleigh-Bénard convection are investigated. Experiments are conducted in a cylindrical convection cell of unity aspect ratio, filled with the alloy GaInSn at a low Prandtl number of \(Pr=0.029\). Changes of the large-scale velocity structure with increasing magnetic field strength are probed systematically using multiple ultrasound Doppler velocimetry sensors and thermocouples for a parameter range that is spanned by Rayleigh numbers of \(10^6\leqslant Ra\leqslant 6\times 10^7\) and Hartmann numbers of \(Ha\leqslant 1000\). Our simultaneous multi-probe temperature and velocity measurements demonstrate how the large-scale circulation is affected by an increasing magnetic field strength (or Hartmann number). Lorentz forces induced in the liquid metal first suppress the oscillations of the large-scale circulation at low \(Ha\), then transform the one-roll structure into a cellular large-scale pattern consisting of multiple up- and downwellings for intermediate \(Ha\), before finally expelling any fluid motion out of the bulk at the highest accessible \(Ha\) leaving only a near-wall convective flow that persists even below Chandrasekhar's linear instability threshold. Our study thus proves experimentally the existence of wall modes in confined magnetoconvection. The magnitude of the transferred heat remains nearly unaffected by the steady decrease of the fluid momentum over a large range of Hartmann numbers. We extend the experimental global transport analysis to momentum transfer and include the dependence of the Reynolds number on the Hartmann number.Stability of three-dimensional columnar convection in a porous medium.https://zbmath.org/1460.767532021-06-15T18:09:00+00:00"Hewitt, Duncan R."https://zbmath.org/authors/?q=ai:hewitt.duncan-r"Lister, John R."https://zbmath.org/authors/?q=ai:lister.john-rSummary: The stability of steady convective exchange flow with a rectangular planform in an unbounded three-dimensional porous medium is explored. The base flow comprises a balance between vertical advection with amplitude \(A\) in interleaving rectangular columns with aspect ratio \(\xi \leqslant 1\) and horizontal diffusion between the columns. Columnar flow with a square planform \(( \xi =1)\) is found to be weakly unstable to a large-scale perturbation of the background temperature gradient, irrespective of \(A\), but to have no stronger instability on the scale of the columns. This result provides a stark contrast to two-dimensional columnar flow \textit{D. R. Hewitt} et al. [ibid. 737, 205--231 (2013; Zbl 1294.76121)], which, as \(A\) is increased, is increasingly unstable to a perturbation on the scale of the columnar wavelength. For rectangular planforms with \(\xi <1\), a critical aspect ratio is identified, below which a perturbation on the scale of the columns is the fastest growing mode, as in two dimensions. Scalings for the growth rate and the structure of this mode are identified, and are explained by means of an asymptotic expansion in the limit \(\xi \rightarrow 0\). The difference between the stabilities of two-dimensional and three-dimensional exchange flow provides a potential explanation for the apparent difference in dominant horizontal scale observed in direct numerical simulations of two-dimensional and three-dimensional statistically steady `Rayleigh-Darcy' convection at high Rayleigh numbers.The effect of double diffusion on the dynamics of horizontal turbulent thermohaline jets.https://zbmath.org/1460.767392021-06-15T18:09:00+00:00"Dadonau, Maksim"https://zbmath.org/authors/?q=ai:dadonau.maksim"Partridge, J. L."https://zbmath.org/authors/?q=ai:partridge.j-l"Linden, P. F."https://zbmath.org/authors/?q=ai:linden.paul-fSummary: We investigate experimentally the effect of double diffusion on the dynamics of initially neutrally buoyant warm and salty turbulent jets discharged horizontally into stationary cooler freshwater ambient. Jets over a range of source Reynolds numbers and source temperature/salinity combinations are examined. In all cases, we observed sinking jet trajectories and the formation of salt fingers along the lower surface of the jet. Increasing the source concentration of both scalar properties led to more pronounced jet sinking trajectories, and to a reduction in the distance between the source and the onset point of salt fingers, demonstrating the significance of the double-diffusive processes. We propose that is it the differential double-diffusive fluxes across the jet-ambient turbulent/non-turbulent interfaces that causes the build-up of negative buoyancy and hence the sinking motion. In addition, we make predictions on the onset point of the salt fingers based on the balance between diffusive processes and the jet entrainment, and compare them with the experimental observations.From zonal flow to convection rolls in Rayleigh-Bénard convection with free-slip plates.https://zbmath.org/1460.767302021-06-15T18:09:00+00:00"Wang, Qi"https://zbmath.org/authors/?q=ai:wang.qi.1|wang.qi.4|wang.qi.3|wang.qi|wang.qi.6|wang.qi.2|wang.qi.5"Chong, Kai Leong"https://zbmath.org/authors/?q=ai:chong.kai-leong"Stevens, Richard J. A. M."https://zbmath.org/authors/?q=ai:stevens.richard-j-a-m"Verzicco, Roberto"https://zbmath.org/authors/?q=ai:verzicco.roberto"Lohse, Detlef"https://zbmath.org/authors/?q=ai:lohse.detlefSummary: Rayleigh-Bénard (RB) convection with free-slip plates and horizontally periodic boundary conditions is investigated using direct numerical simulations. Two configurations are considered, one is two-dimensional (2-D) RB convection and the other one three-dimensional (3-D) RB convection with a rotating axis parallel to the plate, which for strong rotation mimics 2-D RB convection. For the 2-D simulations, we explore the parameter range of Rayleigh numbers \(Ra\) from \(10^7\) to \(10^9\) and Prandtl numbers \(Pr\) from \(1\) to \(100\). The effect of the width-to-height aspect ratio \(\varGamma\) is investigated for \(1\leqslant \varGamma \leqslant 128\). We show that zonal flow, which was observed, for example, by \textit{D. Goluskin} et al. [``Convectively driven shear and decreased heat flux'', ibid. 759, 360--385 (2014; \url{doi:10.1017/jfm.2014.577})] for \(\varGamma =2\), is only stable when \(\varGamma\) is smaller than a critical value, which depends on \(Ra\) and \(Pr\). The regime in which only zonal flow can exist is called the first regime in this study. With increasing \(\varGamma\), we find a second regime in which both zonal flow and different convection roll states can be statistically stable. For even larger \(\varGamma\), in a third regime, only convection roll states are statistically stable and zonal flow is not sustained. How many convection rolls form (or in other words, what the mean aspect ratio of an individual roll is), depends on the initial conditions and on \(Ra\) and \(Pr\). For instance, for \(Ra=10^8\) and \(Pr=10\), the aspect ratio \(\varGamma_r\) of an individual, statistically stable convection roll can vary in a large range between \(16/11\) and \(64\). A convection roll with a large aspect ratio of \(\varGamma_r = 64\), or more generally already with \(\varGamma_r \gg 10\), can be seen as `localized' zonal flow, and indeed carries over various properties of the global zonal flow. For the 3-D simulations, we fix \(Ra=10^7\) and \(Pr=0.71\), and compare the flow for \(\varGamma =8\) and \(\varGamma = 16\). We first show that with increasing rotation rate both the flow structures and global quantities like the Nusselt number \(Nu\) and the Reynolds number \(Re\) increasingly behave like in the 2-D case. We then demonstrate that with increasing aspect ratio \(\varGamma \), zonal flow, which was observed for small \(\varGamma =2\pi\) by \textit{J. von Hardenberg} et al. [``Generation of large-scale winds in horizontally anisotropic convection'', Phys. Rev. Lett. 115, No. 13, Article ID 134501, 5 p. (2015; \url{doi:10.1103/PhysRevLett.115.134501})], completely disappears for \(\varGamma =16\). For such large \(\varGamma\), only convection roll states are statistically stable. In-between, here for medium aspect ratio \(\varGamma = 8\), the convection roll state and the zonal flow state are both statistically stable. What state is taken depends on the initial conditions, similarly as we found for the 2-D case.Formation of drops and rings in double-diffusive sedimentation.https://zbmath.org/1460.767372021-06-15T18:09:00+00:00"Chou, Yi-Ju"https://zbmath.org/authors/?q=ai:chou.yi-ju"Hung, Chen-Yen"https://zbmath.org/authors/?q=ai:hung.chen-yen"Chen, Chien-Fu"https://zbmath.org/authors/?q=ai:chen.chien-fuSummary: We conduct numerical simulations to investigate the formation and evolution of drops and vortex rings of particle-laden fingers in double-diffusive convection in stably stratified environments. We show that the temporal evolution can be divided into double diffusion, acceleration and deceleration phases. The acceleration phase is a result of the vanishing temperature perturbation in the drop during the descent in the layer of uniform temperature. The drop decelerates because it transforms into a vortex ring. A theoretical drag model is presented to predict the speed of the spherical drop with the low drop Reynolds number. By formulating the boundary condition based on the vorticity, our drag model gives a more general form of the drag coefficient for small spherical drops and shows good agreement in predicting the drag coefficient. Drops with five particle sizes are compared, and it is found that although the greater vertical settling enhances vertical transport, the final state differs little among the various sizes. Comparison of our drag model with the simulation results under various bulk conditions and previous experimental results shows good model predictability. Finally, a comparison with the salt-finger case shows that the diffusive nature of the dissolved scalar field, along with the wake effect, can result in an apparent loss of mass from the drop and a permanent presence of the connection between the drop and its parent finger. This makes the observed detachment of the particle-laden drop much less likely in the salt-finger case.Stability of hexagonal pattern in Rayleigh-Bénard convection for thermodependent shear-thinning fluids.https://zbmath.org/1460.760162021-06-15T18:09:00+00:00"Varé, T."https://zbmath.org/authors/?q=ai:vare.t"Nouar, Chérif"https://zbmath.org/authors/?q=ai:nouar.cherif"Métivier, C."https://zbmath.org/authors/?q=ai:metivier.christel"Bouteraa, M."https://zbmath.org/authors/?q=ai:bouteraa.mSummary: Stability of hexagonal patterns in Rayleigh-Bénard convection for shear-thinning fluids with temperature-dependent viscosity is studied in the framework of amplitude equations. The rheological behaviour of the fluid is described by the Carreau model and the relationship between the viscosity and the temperature is of exponential type. Ginzburg-Landau equations including non-variational quadratic spatial terms are derived explicitly from the basic hydrodynamic equations using a multiple scale expansion. The stability of hexagonal patterns towards spatially uniform disturbances (amplitude instabilities) and to long wavelength perturbations (phase instabilities) is analysed for different values of the shear-thinning degree \(\alpha\) of the fluid and the ratio \(r\) of the viscosities between the top and bottom walls. It is shown that the amplitude stability domain shrinks with increasing shear-thinning effects and increases with increasing the viscosity ratio \(r\). Concerning the phase stability domain which confines the range of stable wavenumbers, it is shown that it is closed for low values of \(r\) and becomes open and asymmetric for moderate values of \(r\). With increasing shear-thinning effects, the phase stability domain becomes more decentred towards higher values of the wavenumber. Beyond the stability limits, two different modes go unstable: longitudinal and transverse modes. For the parameters considered here, the longitudinal mode is relevant only in a small region close to the onset. The nonlinear evolution of the transverse phase instability is investigated by numerical integration of amplitude equations. The hexagon-roll transition triggered by the transverse phase instability for sufficiently large reduced Rayleigh number \(\epsilon\) is illustrated.Numerical model of diffusion of impurities in the atmosphere taking into account local meteorological conditions.https://zbmath.org/1460.651312021-06-15T18:09:00+00:00"Ryazanov, V. I."https://zbmath.org/authors/?q=ai:ryazanov.vladimir-i"Shapovalov, A. V."https://zbmath.org/authors/?q=ai:shapovalov.aleksandr-v"Shapovalov, V. A."https://zbmath.org/authors/?q=ai:shapovalov.v-a"Uvizheva, F. Kh."https://zbmath.org/authors/?q=ai:uvizheva.f-kh"Sherieva, M. A."https://zbmath.org/authors/?q=ai:sherieva.m-aSummary: A three-dimensional mathematical model of the diffusion of impurities from a short-term source taking into account meteorological conditions is presented. The model includes the system of equations of hydrothermodynamics describing regional atmospheric processes. The transfer of multicomponent gas impurities is calculated taking into account microphysical processes, precipitation, and fog. Initial information for model initialization is aerological information in the form of actual or forecast fields of meteorological parameters and characteristics of sources of impurities. A numerical analysis of the diffusion of impurities in the near zone of a cosmodrome from short-term sources such as engines of launch vehicles was performed for various meteorological parameters, including wind in the atmosphere.Mammatus cloud formation by settling and evaporation.https://zbmath.org/1460.860282021-06-15T18:09:00+00:00"Ravichandran, S."https://zbmath.org/authors/?q=ai:ravichandran.s"Meiburg, Eckart"https://zbmath.org/authors/?q=ai:meiburg.eckart-h"Govindarajan, Rama"https://zbmath.org/authors/?q=ai:govindarajan.ramaSummary: We show how settling and phase change can combine to drive an instability, as a simple model for the formation of mammatus clouds. Our idealised system consists of a layer (an `anvil') of air mixed with saturated water vapour and monodisperse water droplets, sitting atop dry air. The water droplets in the anvil settle under gravity due to their finite size, evaporating as they enter dry air and cooling the layer of air just below the anvil. The colder air just below the anvil thus becomes denser than the dry air below it, forming a density `overhang', which is unstable. The strength of the instability depends on the density difference between the density overhang and the dry ambient, and the depth of the overhang. Using linear stability analysis and nonlinear simulations in one, two and three dimensions, we study how the amplitude and depth of the density layer depend on the initial conditions, finding that their variations can be explained in terms only of the size of the droplets making up the liquid content of the anvil and by the total amount of liquid water contained in the anvil. We find that the size of the water droplets is the controlling factor in the structure of the clouds: mammatus-like lobes form for large droplet sizes; and small droplet sizes lead to a `leaky' instability resulting in a stringy cloud structure resembling the newly designated \textit{asperitas}.Heat transfer in rapidly rotating convection with heterogeneous thermal boundary conditions.https://zbmath.org/1460.768932021-06-15T18:09:00+00:00"Mound, Jon E."https://zbmath.org/authors/?q=ai:mound.jon-e"Davies, Christopher J."https://zbmath.org/authors/?q=ai:davies.christopher-jSummary: Convection in the metallic cores of terrestrial planets is likely to be subjected to lateral variations in heat flux through the outer boundary imposed by creeping flow in the overlying silicate mantles. Boundary anomalies can significantly influence global diagnostics of core convection when the Rayleigh number, \(Ra\), is weakly supercritical; however, little is known about the strongly supercritical regime appropriate for planets. We perform numerical simulations of rapidly rotating convection in a spherical shell geometry and impose two patterns of boundary heat flow heterogeneity: a hemispherical \(Y_1^1\) spherical harmonic pattern; and one derived from seismic tomography of the Earth's lower mantle. We consider Ekman numbers \(10^{-4}\leqslant E\leqslant 10^{-6}\), flux-based Rayleigh numbers up to \(\sim 800\) times critical, and a Prandtl number of unity. The amplitude of the lateral variation in heat flux is characterised by \(q_L^* =0, 2.3, 5.0\), the peak-to-peak amplitude of the outer boundary heat flux divided by its mean. We find that the Nusselt number, \(Nu\), can be increased by up to \(\sim 25\%\) relative to the equivalent homogeneous case due to boundary-induced correlations between the radial velocity and temperature anomalies near the top of the shell. The \(Nu\) enhancement tends to become greater as the amplitude and length scale of the boundary heterogeneity are increased and as the system becomes more supercritical. This \(Ra\) dependence can steepen the \(Nu\propto Ra^ \gamma\) scaling in the rotationally dominated regime, with \(\gamma\) for our most extreme case approximately 20 \% greater than the equivalent homogeneous scaling. Therefore, it may be important to consider boundary heterogeneity when extrapolating numerical results to planetary conditions.New primal-dual weak Galerkin finite element methods for convection-diffusion problems.https://zbmath.org/1460.651442021-06-15T18:09:00+00:00"Cao, Waixiang"https://zbmath.org/authors/?q=ai:cao.waixiang"Wang, Chunmei"https://zbmath.org/authors/?q=ai:wang.chunmeiSummary: This article devises a new primal-dual weak Galerkin finite element method for the convection-diffusion equation. Optimal order error estimates are established for the primal-dual weak Galerkin approximations in various discrete norms and the standard \(L^2\) norms. A series of numerical experiments are conducted and reported to verify the theoretical findings.Exhausting the background approach for bounding the heat transport in Rayleigh-Bénard convection.https://zbmath.org/1460.767172021-06-15T18:09:00+00:00"Ding, Zijing"https://zbmath.org/authors/?q=ai:ding.zijing"Kerswell, Rich R."https://zbmath.org/authors/?q=ai:kerswell.richard-rSummary: We revisit the optimal heat transport problem for Rayleigh-Bénard convection in which a rigorous upper bound on the Nusselt number, \(Nu\), is sought as a function of the Rayleigh number, \(Ra\). Concentrating on the two-dimensional problem with stress-free boundary conditions, we impose the time-averaged heat equation as a constraint for the bound using a novel two-dimensional background approach thereby complementing the `wall-to-wall' approach of \textit{P. Hassanzadeh} et al. [ibid. 751, 627--662 (2014; Zbl 1329.74253)]. Imposing the same symmetry on the problem, we find correspondence with their maximal result for \(Ra\leqslant Ra_c:=4468.8\) but, beyond that, the results from the two approaches diverge. The bound produced by the two-dimensional background field approaches that produced by the one-dimensional background field from below as the length of computational domain \(L\to\infty\). On lifting the imposed symmetry, the optimal two-dimensional temperature background field reverts to being one-dimensional, giving the best bound \(Nu \leqslant 0.055Ra^{1/2}\) compared to \(Nu\leqslant 0.026Ra^{1/2}\) in the non-slip case. We then show via an inductive bifurcation analysis that introducing two-dimensional temperature and velocity background fields (in an attempt to impose the time-averaged Boussinesq equations) is also unable to lower the bound. This then exhausts the background approach for the two-dimensional (and by extension three-dimensional) Rayleigh-Bénard problem with the bound remaining stubbornly \(Ra^{1/2}\) while data seem more to scale like \(Ra^{1/3}\) for large \(Ra\). Finally, we show that adding a velocity background field to the formulation of \textit{B. Wen} et al. [``Time-stepping approach for solving upper-bound problems: application to two-dimensional Rayleigh-Bénard convection'', Phys. Rev. E (3) 92, No. 4, Article ID 043012, 13 p. (2015; \url{doi:10.1103/PhysRevE.92.043012})], which is able to use an extra vorticity constraint due to the stress-free condition to lower the bound to \(Nu\leqslant O(Ra^{5/12})\), also fails to further improve the bound.Controlling flow reversal in two-dimensional Rayleigh-Bénard convection.https://zbmath.org/1460.767312021-06-15T18:09:00+00:00"Zhang, Shengqi"https://zbmath.org/authors/?q=ai:zhang.shengqi"Xia, Zhenhua"https://zbmath.org/authors/?q=ai:xia.zhenhua"Zhou, Quan"https://zbmath.org/authors/?q=ai:zhou.quan"Chen, Shiyi"https://zbmath.org/authors/?q=ai:chen.shiyiSummary: In this paper, we report that reversals of large-scale circulation in two-dimensional Rayleigh-Bénard convection could be suppressed or enhanced by imposing local constant-temperature control on sidewalls. When the control area is away from the centre of the sidewalls, the control can successfully eliminate the flow reversal if the size of the control region is large enough. With a proper location, the width can be as small as 1 \% of the system size. When the control region is located around the centre, the control may enhance the flow reversal. It may also stimulate the occurrence of a double-roll mode when the control is located in the centre. Explanations are also discussed based on the twofold effects of the control region on the nearby plumes and the concept of symmetry. The present work provides a new way to control the flow reversals in Rayleigh-Bénard convection through modifying sidewall boundary conditions.Exact relations between Rayleigh-Bénard and rotating plane Couette flow in two dimensions.https://zbmath.org/1460.767322021-06-15T18:09:00+00:00"Eckhardt, Bruno"https://zbmath.org/authors/?q=ai:eckhardt.bruno"Doering, Charles R."https://zbmath.org/authors/?q=ai:doering.charles-r"Whitehead, Jared P."https://zbmath.org/authors/?q=ai:whitehead.jared-pSummary: Rayleigh-Bénard convection (RBC) and Taylor-Couette flow (TCF) are two paradigmatic fluid dynamical systems frequently discussed together because of their many similarities despite their different geometries and forcing. Often these analogies require approximations, but in the limit of large radii where TCF becomes rotating plane Couette flow (RPC) exact relations can be established. When the flows are restricted to two spatial independent variables, there is an exact specification that maps the three velocity components in RPC to the two velocity components and one temperature field in RBC. Using this, we deduce several relations between both flows: (i) heat and angular momentum transport differ by \((1-R_\Omega)\), explaining why angular momentum transport is not symmetric around \(R_\Omega=1/2\) even though the relation between \(Ra\), the Rayleigh number, and \(R_\Omega\), a non-dimensional measure of the rotation, has this symmetry. This relationship leads to a predicted value of \(R_\Omega\) that maximizes the angular momentum transport that agrees remarkably well with existing numerical simulations of the full three-dimensional system. (ii) One variable in both flows satisfies a maximum principle, i.e. the fields' extrema occur at the walls. Accordingly, backflow events in shear flow cannot occur in this quasi two-dimensional setting. (iii) For free-slip boundary conditions on the axial and radial velocity components, previous rigorous analysis for RBC implies that the azimuthal momentum transport in RPC is bounded from above by \(Re_S^{5/6}\), where \(Re_S\) is the shear Reynolds number, with a scaling exponent smaller than the anticipated \(Re_S^1\).Regime crossover in Rayleigh-Bénard convection with mixed boundary conditions.https://zbmath.org/1460.767232021-06-15T18:09:00+00:00"Ostilla-Mónico, Rodolfo"https://zbmath.org/authors/?q=ai:ostilla-monico.rodolfo"Amritkar, Amit"https://zbmath.org/authors/?q=ai:amritkar.amitSummary: We numerically simulate three-dimensional Rayleigh-Bénard convection, the flow in a fluid layer heated from below and cooled from above, with inhomogeneous temperature boundary conditions, to explore two distinct regimes described in recent literature. We fix the non-dimensional temperature difference, i.e. the Rayleigh number, to \(\mathrm{Ra}=10^8\), and vary the Prandtl number between 1 and 100. By introducing stripes of adiabatic boundary conditions on the top plate, and making the surface of the top plate only 50\% conducting, we modify the heat transfer, the average temperature profiles and the underlying flow properties. We find two regimes: when the pattern wavelength is small, the flow is barely affected by the stripes. The heat transfer is reduced, but remains a large fraction of that of the unmodified case, and the underlying flow is only slightly modified. When the pattern wavelength is large, the heat transfer saturates to approximately two-thirds of the value of the unmodified problem, the temperature in the bulk increases substantially, and velocity fluctuations in the directions normal to the stripes are enhanced. The transition between the two regimes happens at pattern wavelength around the distance between the two plates, with different quantities transitioning at slightly different wavelength values. This transition is approximately Prandtl-number-independent, even if the statistics in the long-wavelength regime slightly vary.Modelling a surfactant-covered droplet on a solid surface in three-dimensional shear flow.https://zbmath.org/1460.762702021-06-15T18:09:00+00:00"Liu, Haihu"https://zbmath.org/authors/?q=ai:liu.haihu"Zhang, Jinggang"https://zbmath.org/authors/?q=ai:zhang.jinggang"Ba, Yan"https://zbmath.org/authors/?q=ai:ba.yan"Wang, Ningning"https://zbmath.org/authors/?q=ai:wang.ningning"Wu, Lei"https://zbmath.org/authors/?q=ai:wu.lei.2Summary: A surfactant-covered droplet on a solid surface subject to a three-dimensional shear flow is studied using a lattice-Boltzmann and finite-difference hybrid method, which allows for the surfactant concentration beyond the critical micelle concentration. We first focus on low values of the effective capillary number \((Ca_e)\) and study the effect of \(Ca_e\), viscosity ratio \((\lambda)\) and surfactant coverage on the droplet behaviour. Results show that at low \(Ca_e\) the droplet eventually reaches steady deformation and a constant moving velocity \(u_d\). The presence of surfactants not only increases droplet deformation but also promotes droplet motion. For each \(\lambda\), a linear relationship is found between contact-line capillary number and \(Ca_e\), but not between wall stress and \(u_d\) due to Marangoni effects. As \(\lambda\) increases, \(u_d\) decreases monotonically, but the deformation first increases and then decreases for each \(Ca_e\). Moreover, increasing surfactant coverage enhances droplet deformation and motion, although the surfactant distribution becomes less non-uniform. We then increase \(Ca_e\) and study droplet breakup for varying \(\lambda\), where the role of surfactants on the critical \(Ca_e (Ca_{e,c})\) of droplet breakup is identified by comparing with the clean case. As in the clean case, \(Ca_{e,c}\) first decreases and then increases with increasing \(\lambda\), but its minima occurs at \(\lambda =0.5\) instead of \(\lambda =1\) in the clean case. The presence of surfactants always decreases \(Ca_{e,c}\), and its effect is more pronounced at low \(\lambda\). Moreover, a decreasing viscosity ratio is found to favour ternary breakup in both clean and surfactant-covered cases, and tip streaming is observed at the lowest \(\lambda\) in the surfactant-covered case.Dispersion of inertial particles in cellular flows in the small-Stokes, large-Péclet regime.https://zbmath.org/1460.760062021-06-15T18:09:00+00:00"Renaud, Antoine"https://zbmath.org/authors/?q=ai:renaud.antoine"Vanneste, Jacques"https://zbmath.org/authors/?q=ai:vanneste.jacquesSummary: We investigate the transport of inertial particles by cellular flows when advection dominates over inertia and diffusion, that is, for Stokes and Péclet numbers satisfying \(St \ll 1\) and \(Pe \gg 1\). Starting from the Maxey-Riley model, we consider the distinguished scaling \(St\, Pe = O(1)\) and derive an effective Brownian dynamics approximating the full Langevin dynamics. We then apply homogenisation and matched-asymptotics techniques to obtain an explicit expression for the effective diffusivity \(\bar{D}\) characterising long-time dispersion. This expression quantifies how \(\bar{D}\), proportional to \(Pe^{-1/2}\) when inertia is neglected, increases for particles heavier than the fluid and decreases for lighter particles. In particular, when \(St \gg Pe^{-1}\), we find that \(\bar{D}\) is proportional to \(St^{1/2}/(\log ( St\, Pe))^{1/2}\) for heavy particles and exponentially small in \(St\, Pe\) for light particles. We verify our asymptotic predictions against numerical simulations of the particle dynamics.Nonlinear mixed convection flow in an inclined channel with time-periodic boundary conditions.https://zbmath.org/1460.767202021-06-15T18:09:00+00:00"Jha, Basant K."https://zbmath.org/authors/?q=ai:jha.basant-k"Oni, Michael O."https://zbmath.org/authors/?q=ai:oni.michael-oSummary: This article scrutinises the role of nonlinear Boussinesq approximation on mixed convection flow in an inclined channel when one of the walls is kept at constant temperature while is other one is periodically heated. By expanding the Boussinesq approximation up to second degree Taylor series expansion, the governing momentum and energy equations are derived and solved analytically. During the course of graphical and numerical simulations, results show that the role of nonlinear Boussinesq approximation is to increase fluid velocity, interval of reverse flow formation at the walls, pressure drop and fanning frictional factor.On the mechanism responsible for unconventional thermal behaviour during freezing.https://zbmath.org/1460.767582021-06-15T18:09:00+00:00"Kumar, Virkeshwar"https://zbmath.org/authors/?q=ai:kumar.virkeshwar"Abhishek, G. S."https://zbmath.org/authors/?q=ai:abhishek.g-s"Srivastava, Atul"https://zbmath.org/authors/?q=ai:srivastava.atul-kumar"Karagadde, Shyamprasad"https://zbmath.org/authors/?q=ai:karagadde.shyamprasadSummary: In this study, identical experiments of bottom-cooled solidification fluidic mixtures that exhibit faceted and dendritic microstructures were performed. The strength of compositional convection, created due to the rejection of a lighter solute, was correlated with the solidifying microstructure morphology via separate Rayleigh numbers in the mushy and bulk-fluid zones. While the bulk fluid in dendritic solidification experienced a monotonic decrease in the temperature, solidification of the faceted case revealed an unconventional, anomalous temperature rise in the bulk liquid after the formation of a eutectic solid. Based on the bulk-liquid temperatures, three distinct regimes of heat transfer were observed in the liquid, namely, convection-dominated, transition and conduction-dominated. The observations were analysed and verified with the help of different initial compositions and cooling conditions, as well as other mixtures that form faceted morphology upon freezing. The observed temperature rise was further ascertained by performing an energy balance in an indicative control volume ahead of the solid-liquid interface. The plausible mechanism of permeability-driven flow causing a gain in the temperature of the liquid during freezing was generalized with the help of a semi-analytical investigation of a one-dimensional system comprising solid, porous mush and liquid regions. The analytical scaling relations for fluid velocity and vorticity, for the faceted and dentritic cases, revealed contrasting vorticity values, which are much larger in low permeability (faceted case) and cause enhanced mixing in the bulk. The study sheds new insights into the role of microstructural morphology in governing the transport phenomena in the bulk liquid.Isolated buoyant convection in a two-layered porous medium with an inclined permeability jump.https://zbmath.org/1460.767432021-06-15T18:09:00+00:00"Bharath, K. S."https://zbmath.org/authors/?q=ai:bharath.k-s"Sahu, C. K."https://zbmath.org/authors/?q=ai:sahu.chunendra-k"Flynn, M. R."https://zbmath.org/authors/?q=ai:flynn.morris-r|flynn.michael-rSummary: The migration of dense fluid through a saturated, layered porous medium leads to two end-member examples of buoyancy-driven flow, namely plumes and gravity currents. Herein we develop an integrated theoretical model to study this scenario for the special case where the boundary between the permeable layers, in a two-layered porous medium, is inclined at an angle to the horizontal. Far from being a routine detail, the inclination of the permeability jump leads to a symmetry-breaking: up- and downdip flows have different volume fluxes and travel different distances, possibly substantially different distances, before becoming arrested at the point where plume inflow balances basal draining. Our model predicts these associated run-out lengths and the transient approach thereto. Predictions are validated with measurements from similitude laboratory experiments, in which the upper and lower layers are comprised of glass beads of different diameters. Experiments are conducted for a range of inclination angles and also a range of plume source conditions. The experimental data suggest a complicated structure for the gravity currents, whose boundaries are blurred by dispersion in a manner not captured by our (sharp interface) model. This observation has particular significance in predicting the lateral spread of contaminated fluid through real geological formations, particularly in instances where for example groundwater contamination is of particular concern.Flow organization and heat transfer in turbulent wall sheared thermal convection.https://zbmath.org/1460.764292021-06-15T18:09:00+00:00"Blass, Alexander"https://zbmath.org/authors/?q=ai:blass.alexander"Zhu, Xiaojue"https://zbmath.org/authors/?q=ai:zhu.xiaojue"Verzicco, Roberto"https://zbmath.org/authors/?q=ai:verzicco.roberto"Lohse, Detlef"https://zbmath.org/authors/?q=ai:lohse.detlef"Stevens, Richard J. A. M."https://zbmath.org/authors/?q=ai:stevens.richard-j-a-mSummary: We perform direct numerical simulations of wall sheared Rayleigh-Bénard convection for Rayleigh numbers up to \(Ra=10^8\), Prandtl number unity and wall shear Reynolds numbers up to \(Re_w=10\,000\). Using the Monin-Obukhov length \(L_{MO}\) we observe the presence of three different flow states, a buoyancy dominated regime \((L_{MO}\lesssim \lambda_\theta\); with \(\lambda_\theta\) the thermal boundary layer thickness), a transitional regime \((0.5H\gtrsim L_{MO}\gtrsim \lambda_\theta\); with \(H\) the height of the domain) and a shear dominated regime \((L_{MO}\gtrsim 0.5H)\). In the buoyancy dominated regime, the flow dynamics is similar to that of turbulent thermal convection. The transitional regime is characterized by rolls that are increasingly elongated with increasing shear. The flow in the shear dominated regime consists of very large-scale meandering rolls, similar to the ones found in conventional Couette flow. As a consequence of these different flow regimes, for fixed \(Ra\) and with increasing shear, the heat transfer first decreases, due to the breakup of the thermal rolls, and then increases at the beginning of the shear dominated regime. In the shear dominated regime the Nusselt number \(Nu\) effectively scales as \(Nu\sim Ra^\alpha\) with \(\alpha \ll 1/3\), while we find \(\alpha \simeq 0.30\) in the buoyancy dominated regime. In the transitional regime, the effective scaling exponent is \(\alpha >1/3\), but the temperature and velocity profiles in this regime are not logarithmic yet, thus indicating transient dynamics and not the ultimate regime of thermal convection.Nonlinear finite volume discretization for transient diffusion problems on general meshes.https://zbmath.org/1460.766392021-06-15T18:09:00+00:00"Quenjel, El Houssaine"https://zbmath.org/authors/?q=ai:quenjel.el-houssaineSummary: A nonlinear discrete duality finite volume scheme is proposed for time-dependent diffusion equations. The model example is written in a new formulation giving rise to similar nonlinearities for both the diffusion and the potential functions. A natural finite volume discretization is built on this particular problem's structure. The fluxes are generically approximated thanks to a key fractional average. The point of this strategy is to promote coercivity and scheme's stability simultaneously. The existence of positive solutions is guaranteed. The theoretical convergence of the nonlinear scheme is established using practical compactness tools. Numerical results are performed in order to highlight the second order accuracy of the methodology and the positiveness of solutions on distorted meshes.Stability of temperature modulated convection in a vertical fluid layer.https://zbmath.org/1460.763022021-06-15T18:09:00+00:00"Singh, Jitender"https://zbmath.org/authors/?q=ai:singh.jitender"Bajaj, Renu"https://zbmath.org/authors/?q=ai:bajaj.renuSummary: We investigate the effect of time periodic oscillations of the boundary temperatures on the onset of natural convection in a fluid layer bounded by two vertical planes. The fluids with Prandtl number up to 12.5 are considered. For these fluids, the mode of instability with constant temperature gradient is the steady convection mode. The parametric instability of the modulated fluid layer is found to appear either in the form of harmonic oscillations or in the form of subharmonic oscillations, depending upon the modulation parameters and the Prandtl number. The transition of the instability between harmonic and subharmonic oscillations occurs via an intermediate bicritical state in which the fluid layer oscillates with coexistence of distinct harmonic and subharmonic wave numbers. A proper tuning of the modulation parameters offers a good control over the mode of instability in the fluid layer.Suppression of internal waves by thermohaline staircases.https://zbmath.org/1460.767382021-06-15T18:09:00+00:00"Radko, Timour"https://zbmath.org/authors/?q=ai:radko.timourSummary: This study attempts to quantify and explain the systematic weakening of internal gravity waves in fingering and diffusive thermohaline staircases. The interaction between waves and staircases is explored using a combination of direct numerical simulations (DNS) and an asymptotic multiscale model. The multiscale theory makes it possible to express the wave decay rate \((\lambda_d)\) as a function of its wavenumbers and staircase parameters. We find that the decay rates in fully developed staircases greatly exceed values that can be directly attributed to molecular dissipation. They rapidly increase with increasing wavenumbers, both vertical and horizontal. At the same time, \(\lambda_d\) is only weakly dependent on the thickness of layers in the staircase, the overall density ratio and the diffusivity ratio. The proposed physical mechanism of attenuation emphasizes the significance of eddy diffusion of temperature and salinity, whereas eddy viscosity plays a secondary role in damping internal waves. The asymptotic model is successfully validated by the DNS performed in numerically accessible regimes. We also discuss potential implications of staircase-induced suppression for diapycnal mixing by overturning internal waves in the ocean.The local well-posedness to the density-dependent magnetic Bénard system with nonnegative density.https://zbmath.org/1460.353012021-06-15T18:09:00+00:00"Zhong, Xin"https://zbmath.org/authors/?q=ai:zhong.xinSummary: We study the Cauchy problem of density-dependent magnetic Bénard system with zero density at infinity on the whole two-dimensional (2D) space. Despite the degenerate nature of the problem, we show the local existence of a unique strong solution in weighted Sobolev spaces by energy method.Three-dimensional backflow at liquid-gas interface induced by surfactant.https://zbmath.org/1460.767932021-06-15T18:09:00+00:00"Li, Hongyuan"https://zbmath.org/authors/?q=ai:li.hongyuan"Li, Zexiang"https://zbmath.org/authors/?q=ai:li.zexiang"Tan, Xiangkui"https://zbmath.org/authors/?q=ai:tan.xiangkui"Wang, Xiangyu"https://zbmath.org/authors/?q=ai:wang.xiangyu"Huang, Shenglin"https://zbmath.org/authors/?q=ai:huang.shenglin"Xiang, Yaolei"https://zbmath.org/authors/?q=ai:xiang.yaolei"Lv, Pengyu"https://zbmath.org/authors/?q=ai:lv.pengyu"Duan, Huiling"https://zbmath.org/authors/?q=ai:duan.huilingSummary: A liquid-gas interface (LGI) on submerged microstructure surfaces has the potential to achieve large slip velocities, which is significant for underwater applications such as drag reduction. However, surfactants adsorbing on the LGI can cause surface tension gradient against the mainstream, which weakens the flow near the LGI and severely limits drag reduction. The mechanism of the effect of surfactants on two-dimensional flows has already been proposed, while the effect of surfactants on the three-dimensional flow near the LGI is still not clear. In our study, we specifically design an experimental system to directly observe a three-dimensional backflow at the LGI. The formation as well as the behaviour of the backflow are demonstrated to be significantly influenced by the surfactant. Combining experimental measurements, theoretical analyses and numerical simulations, we reveal the underlying mechanism of the backflow, which is a competition between the mainstream and the Marangoni flows generated by the interfacial concentration gradients of surfactant simultaneously in streamwise and spanwise directions, reflecting the three-dimensional feature of the backflow. In addition, a kinematic similarity is obtained to characterize the backflow. The current work provides a model system for investigating the three-dimensional backflow at the LGI with surfactants, which is significant for practical applications such as drag reduction and superhydrophobicity.The effect of thermal boundary conditions on forced convection heat transfer to fluids at supercritical pressure.https://zbmath.org/1460.765532021-06-15T18:09:00+00:00"Nemati, Hassan"https://zbmath.org/authors/?q=ai:nemati.hassan"Patel, Ashish"https://zbmath.org/authors/?q=ai:patel.ashish"Boersma, Bendiks J."https://zbmath.org/authors/?q=ai:boersma.bendiks-jan"Pecnik, Rene"https://zbmath.org/authors/?q=ai:pecnik.reneSummary: We use direct numerical simulations to study the effect of thermal boundary conditions on developing turbulent pipe flows with fluids at supercritical pressure. The Reynolds number based on pipe diameter and friction velocity at the inlet is \(Re_{\tau0}=360\) and Prandtl number at the inlet is \(Pr_{0}=3.19\). The thermodynamic conditions are chosen such that the temperature range within the flow domain incorporates the pseudo-critical point where large variations in thermophysical properties occur. Two different thermal wall boundary conditions are studied: one that permits temperature fluctuations and one that does not allow temperature fluctuations at the wall (equivalent to cases where the thermal effusivity ratio approaches infinity and zero, respectively). Unlike for turbulent flows with constant thermophysical properties and Prandtl numbers above unity -- where the effusivity ratio has a negligible influence on heat transfer -- supercritical fluids shows a strong dependency on the effusivity ratio. We observe a reduction of \(7\%\) in Nusselt number when the temperature fluctuations at the wall are suppressed. On the other hand, if temperature fluctuations are permitted, large property variations are induced that consequently cause an increase of wall-normal velocity fluctuations very close to the wall and thus an increased overall heat flux and skin friction.Evolution of plumes and turbulent dynamics in deep-ocean convection.https://zbmath.org/1460.767242021-06-15T18:09:00+00:00"Pal, Anikesh"https://zbmath.org/authors/?q=ai:pal.anikesh"Chalamalla, Vamsi K."https://zbmath.org/authors/?q=ai:chalamalla.vamsi-kSummary: Three-dimensional numerical simulations are performed to investigate the dynamics of deep-ocean convection. Organized structures of denser fluid moving downwards, known as plumes, are formed during the initial evolution. We propose a scaling for the diameter and velocity of these plumes based on surface flux magnitude \(B_0\) and the thermal/eddy diffusivity. Rotation effects are found to be negligible during this initial evolution. At a later time \(t>2 \pi /f\), where \(f\) is the Coriolis parameter, the flow comes under the influence of rotation, which stabilizes the flow by inhibiting the conversion of potential energy to turbulent kinetic energy. At moderate to low rotation rates, the dense fluid plummets and spreads laterally as a gravity current along the bottom boundary. However, at high rotation rates, the flow reaches a quasi-geostrophic state (before the dense fluid reaches the bottom boundary) with an approximate balance between the pressure gradient and the Coriolis forces. We also see the formation of baroclinic vortices and a rim current at the interface of the mixed and surrounding fluids at high rotation rates. A quantitative analysis of the root-mean-square velocities reveals that higher rotation rates result in lower turbulence intensities. Closure of the turbulent kinetic energy budget is also achieved with an approximate balance between the buoyancy flux and the dissipation rate.Magnetohydrodynamic natural convection flow in a vertical micro-porous-channel in the presence of induced magnetic field.https://zbmath.org/1460.767332021-06-15T18:09:00+00:00"Jha, Basant K."https://zbmath.org/authors/?q=ai:jha.basant-k"Aina, Babatunde"https://zbmath.org/authors/?q=ai:aina.babatundeSummary: In this work, the exact solution for fully developed magnetohydrodynamic natural convection flow of viscous, incompressible, electrically conducting fluid in vertical micro-porous-channel formed by electrically non-conducting infinite vertical parallel porous plates in presence of induced magnetic field is investigated. Effects of velocity slip and temperature jump conditions are taken into account due to their counter effects both on the volume flow rate and the rate of heat transfer. The governing coupled equations responsible for present physical situation are a set of simultaneous ordinary differential equations and their exact solutions in dimensionless form have been obtained for the velocity field, the induced magnetic field and the temperature field subject to the relevant boundary conditions. The expressions for the induced current density and skin friction at the micro-porous-channel surfaces are also obtained. A parametric study of some physical parameters is conducted and a representative set of numerical results for the velocity field, the induced magnetic field, temperature, induced current density, volume flow rate and skin friction are illustrated graphically to show interesting features of the suction/injection, rarefaction, fluid wall interaction, Hartmann number and the magnetic Prandtl number. Result reveals that, for a fixed value of the Hartmann number, the skin frictions at micro-porous-channel surfaces in the presence of induced magnetic field are higher compared to the case when the induced magnetic field is neglected.Plume or bubble? Mixed-convection flow regimes and city-scale circulations.https://zbmath.org/1460.767352021-06-15T18:09:00+00:00"Omidvar, Hamidreza"https://zbmath.org/authors/?q=ai:omidvar.hamidreza"Bou-Zeid, Elie"https://zbmath.org/authors/?q=ai:bou-zeid.elie"Li, Qi"https://zbmath.org/authors/?q=ai:li.qi.1"Mellado, Juan-Pedro"https://zbmath.org/authors/?q=ai:mellado.juan-pedro"Klein, Petra"https://zbmath.org/authors/?q=ai:klein.petraSummary: Large-scale circulations around a city are co-modulated by the urban heat island and by regional wind patterns. Depending on these variables, the circulations fall into different regimes ranging from advection-dominated (plume regime) to convection-driven (bubble regime). Using dimensional analysis and large-eddy simulations, this study investigates how these different circulations scale with urban and rural heat fluxes, as well as upstream wind speed. Two dimensionless parameters are shown to control the dynamics of the flow: (1) the ratio of rural to urban thermal convective velocities that contrasts their respective buoyancy fluxes and (2) the ratio of bulk inflow velocity to the convection velocity in the rural area. Finally, the vertical flow velocities transecting the rural to urban transitions are used to develop a criterion for categorizing different large-scale circulations into plume, bubble or transitional regimes. The findings have implications for city ventilation since bubble regimes are expected to trap pollutants, as well as for scaling analysis in canonical mixed-convection flows.From Rayleigh-Bénard convection to porous-media convection: how porosity affects heat transfer and flow structure.https://zbmath.org/1460.767222021-06-15T18:09:00+00:00"Liu, Shuang"https://zbmath.org/authors/?q=ai:liu.shuang"Jiang, Linfeng"https://zbmath.org/authors/?q=ai:jiang.linfeng"Chong, Kai Leong"https://zbmath.org/authors/?q=ai:chong.kai-leong"Zhu, Xiaojue"https://zbmath.org/authors/?q=ai:zhu.xiaojue"Wan, Zhen-Hua"https://zbmath.org/authors/?q=ai:wan.zhenhua.1"Verzicco, Roberto"https://zbmath.org/authors/?q=ai:verzicco.roberto"Stevens, Richard J. A. M."https://zbmath.org/authors/?q=ai:stevens.richard-j-a-m"Lohse, Detlef"https://zbmath.org/authors/?q=ai:lohse.detlef"Sun, Chao"https://zbmath.org/authors/?q=ai:sun.chaoSummary: We perform a numerical study of the heat transfer and flow structure of Rayleigh-Bénard (RB) convection in (in most cases regular) porous media, which are comprised of circular, solid obstacles located on a square lattice. This study is focused on the role of porosity \(\phi\) in the flow properties during the transition process from the traditional RB convection with \(\phi =1\) (so no obstacles included) to Darcy-type porous-media convection with \(\phi\) approaching 0. Simulations are carried out in a cell with unity aspect ratio, for Rayleigh number \(Ra\) from \(10^5\) to \(10^{10}\) and varying porosities \(\phi\), at a fixed Prandtl number \(Pr=4.3\), and we restrict ourselves to the two-dimensional case. For fixed \(Ra\), the Nusselt number \(Nu\) is found to vary non-monotonically as a function of \(\phi\); namely, with decreasing \(\phi\), it first increases, before it decreases for \(\phi\) approaching 0. The non-monotonic behaviour of \(Nu(\phi)\) originates from two competing effects of the porous structure on the heat transfer. On the one hand, the flow coherence is enhanced in the porous media, which is beneficial for the heat transfer. On the other hand, the convection is slowed down by the enhanced resistance due to the porous structure, leading to heat transfer reduction. For fixed \(\phi\), depending on \(Ra\), two different heat transfer regimes are identified, with different effective power-law behaviours of \(Nu\) versus \(Ra\), namely a steep one for low \(Ra\) when viscosity dominates, and the standard classical one for large \(Ra\). The scaling crossover occurs when the thermal boundary layer thickness and the pore scale are comparable. The influences of the porous structure on the temperature and velocity fluctuations, convective heat flux and energy dissipation rates are analysed, further demonstrating the competing effects of the porous structure to enhance or reduce the heat transfer.Café latte: spontaneous layer formation in laterally cooled double diffusive convection.https://zbmath.org/1460.765362021-06-15T18:09:00+00:00"Chong, Kai Leong"https://zbmath.org/authors/?q=ai:chong.kai-leong"Yang, Rui"https://zbmath.org/authors/?q=ai:yang.rui"Wang, Qi"https://zbmath.org/authors/?q=ai:wang.qi.5|wang.qi.2|wang.qi|wang.qi.3|wang.qi.6|wang.qi.1|wang.qi.4"Verzicco, Roberto"https://zbmath.org/authors/?q=ai:verzicco.roberto"Lohse, Detlef"https://zbmath.org/authors/?q=ai:lohse.detlefSummary: In the preparation of café latte, spectacular layer formation can occur between the espresso shot in a glass of milk and the milk itself. \textit{N. Xue} et al. [``Laboratory layered Latte'', Nat. Commun. 8, Article No. 1960, 1--6 (2017; \url{doi:10.1038/s41467-017-01852-2})] showed that the injection velocity of espresso determines the depth of coffee-milk mixture. After a while, when a stable stratification forms in the mixture, the layering process can be modelled as a double diffusive convection system with a stably stratified coffee-milk mixture cooled from the side. More specifically, we perform (two-dimensional) direct numerical simulations of laterally cooled double diffusive convection for a wide parameter range, where the convective flow is driven by a lateral temperature gradient while stabilized by a vertical concentration gradient. Depending on the strength of stabilization as compared to the thermal driving, the system exhibits different flow regimes. When the thermal driving force dominates over the stabilizing force, the flow behaves like vertical convection in which a large-scale circulation develops. However, with increasing strength of the stabilizing force, a meta-stable layered regime emerges. Initially, several vertically-stacked convection rolls develop, and these well-mixed layers are separated by sharp interfaces with large concentration gradients. The initial thickness of these emerging layers can be estimated by balancing the work exerted by thermal driving and the required potential energy to bring fluid out of its equilibrium position in the stably stratified fluid. In the layered regime, we further observe successive layer merging, and eventually only a single convection roll remains. We elucidate the following merging mechanism: as weakened circulation leads to accumulation of hot fluid adjacent to the hot sidewall, larger buoyancy forces associated with hotter fluid eventually break the layer interface. Then two layers merge into a larger layer, and circulation establishes again within the merged structure.Non-monotonic transport mechanisms in vertical natural convection with dispersed light droplets.https://zbmath.org/1460.767342021-06-15T18:09:00+00:00"Ng, Chong Shen"https://zbmath.org/authors/?q=ai:ng.chong-shen"Spandan, Vamsi"https://zbmath.org/authors/?q=ai:spandan.vamsi"Verzicco, Roberto"https://zbmath.org/authors/?q=ai:verzicco.roberto"Lohse, Detlef"https://zbmath.org/authors/?q=ai:lohse.detlefSummary: We present results on the effect of dispersed droplets in vertical natural convection (VC) using direct numerical simulations based on a two-way fully coupled Euler-Lagrange approach with a liquid phase and a dispersed droplets phase. For increasing thermal driving, characterised by the Rayleigh number, \(Ra\), of the two analysed droplet volume fractions, \(\alpha = 5\times 10^{-3}\) and \(\alpha = 2\times 10^{-2}\), we find non-monotonic responses to the overall heat fluxes, characterised by the Nusselt number, \(Nu\). The \(Nu\) number is larger when the droplets are thermally coupled to the liquid. However, \(Nu\) values remain close to the 1/4-laminar VC scaling, suggesting that the heat transport is still modulated by thermal boundary layers. Local analyses reveal the non-monotonic trends of local heat fluxes and wall-shear stresses: whilst regions of high heat fluxes are correlated to increased wall-shear stresses, the spatio-temporal distribution and magnitude of the increase are non-monotonic, implying that the overall heat transport is obscured by competing mechanisms. Most crucially, we find that the transport mechanisms inherently depend on the dominance of droplet driving to thermal driving that can quantified by (i) the bubblance parameter \(b\), which measures the ratio of energy produced by the dispersed phase and the energy of the background turbulence, and (ii) \(Ra_d/Ra\), where \(Ra_d\) is the droplet Rayleigh number, which we introduce in this paper. When \(b \lesssim O(10^{-1})\) and \(Ra_d/Ra \lesssim O(100)\), the \(Nu\) scaling is expected to recover to the VC scaling without droplets, and comparison with \(b\) and \(Ra_d/Ra\) from our data supports this notion.Thermocapillary effects during the melting of phase-change materials in microgravity: steady and oscillatory flow regimes.https://zbmath.org/1460.800122021-06-15T18:09:00+00:00"Salgado Sánchez, Pablo"https://zbmath.org/authors/?q=ai:salgado-sanchez.pablo"Ezquerro, J. M."https://zbmath.org/authors/?q=ai:ezquerro.jose-m"Fernández, J."https://zbmath.org/authors/?q=ai:fernandez.jose-jesus"Rodríguez, J."https://zbmath.org/authors/?q=ai:rodriguez.jesus-a|rodriguez.j-p-j|rodriguez.jose-angel|rodriguez.jose-gregorio|rodriguez.juan-carlos-sanchez|rodriguez.jose-miguel|rodriguez.jose-s|rodriguez.jorge-tomas|rodriguez.jose-israel|rodriguez.jose-e|rodriguez.john-david|rodriguez.jose-antonio|rodriguez.jose-ignacio|rodriguez.jaime-e-a|rodriguez.j-fernandez|rodriguez.juan-r|rodriguez.jesus-f|rodriguez.jeronimo|rodriguez.joanna|rodriguez.joel-arturo|rodriguez.jose-felix|rodriguez.jose-victor|rodriguez.jose-luis|rodriguez.jose-manuel|rodriguez.juan-manuel|rodriguez.jorge-luis-garcia|rodriguez.juan-angel|rodriguez.judith-s|rodriguez.jesus-m|rodriguez.joana|rodriguez.jose-maria|rodriguez.j-l-hospido|rodriguez.juan-sebastian|rodriguez.juan-gabriel|rodriguez.j-daza|rodriguez.joaquin|rodriguez.josemar|rodriguez.j-noyola|rodriguez.joseph-m|rodriguez.j-tinguaro|rodriguez.jonnathan|rodriguez.jorge-luis-dominguez|rodriguez.jeremy|rodriguez.jorge-p|rodriguez.javier|rodriguez.juan-j|rodriguez-seijo.jose-m|rodriguez.jhan|rodriguez.jeffrey-j|rodriguez.julio|rodriguez.j-c-rodr|rodriguez.juan-p|rodriguez.juan-i|rodriguez-velazquez.juan-alberto|rodriguez.jorge-eSummary: A detailed numerical investigation of thermocapillary effects during the melting of phase-change materials in microgravity is presented. The phase-change transition is analysed for the high-Prandtl-number material n-octadecane, which is enclosed in a two-dimensional rectangular container subjected to isothermal conditions along the lateral walls. The progression of the solid/liquid front during the melting leaves a free surface, where the thermocapillary effect acts driving convection in the liquid phase. The nature of the flow found during the melting depends on the container aspect ratio, \(\Gamma\), and on the Marangoni number, \(Ma\). For large \(\Gamma\), this flow initially adopts a steady return flow structure characterised by a single large vortex, which splits into a series of smaller vortices to create a steady multicellular structure (SMC) with increasing \(Ma\). At larger values of \(Ma\), this SMC undergoes a transition to oscillatory flow through the appearance of a hydrothermal travelling wave (HTW), characterised by the creation of travelling vortices near the cold boundary. For small \(\Gamma\), the thermocapillary flow at small to moderate \(Ma\) is characterised by an SMC that develops initially within a thin layer near the free surface. At larger times, the SMC evolves into a large-scale steady vortical structure. With increasing applied \(Ma\), a complex oscillatory mode is observed. This state, referred to as an oscillatory standing wave (OSW), is characterised by the pulsation of the vortical structure. Finally, for an intermediate \(\Gamma\) both HTW and OSW modes can be found depending on \(Ma\).Wall-to-wall optimal transport in two dimensions.https://zbmath.org/1460.767282021-06-15T18:09:00+00:00"Souza, Andre N."https://zbmath.org/authors/?q=ai:souza.andre-n"Tobasco, Ian"https://zbmath.org/authors/?q=ai:tobasco.ian"Doering, Charles R."https://zbmath.org/authors/?q=ai:doering.charles-rSummary: Gradient ascent methods are developed to compute incompressible flows that maximize heat transport between two isothermal no-slip parallel walls. Parameterizing the magnitude of the velocity fields by a Péclet number \(Pe\) proportional to their root-mean-square rate of strain, the schemes are applied to compute two-dimensional flows optimizing convective enhancement of diffusive heat transfer, i.e. the Nusselt number \(Nu\) up to \(Pe\approx 10^5\). The resulting transport exhibits a change of scaling from \(Nu-1\sim Pe^2\) for \(Pe<10\) in the linear regime to \(Nu\sim Pe^{0.54}\) for \(Pe>10^3\). Optimal fields are observed to be approximately separable, i.e. products of functions of the wall-parallel and wall-normal coordinates. Analysis employing a separable ansatz yields a conditional upper bound \(\lesssim Pe^{6/11}=Pe^{0.\overline{54}}\) as \(Pe\rightarrow \infty\) similar to the computationally achieved scaling. Implications for heat transfer in buoyancy-driven Rayleigh-Bénard convection are discussed.A general criterion for the release of background potential energy through double diffusion.https://zbmath.org/1460.767402021-06-15T18:09:00+00:00"Middleton, Leo"https://zbmath.org/authors/?q=ai:middleton.leo"Taylor, John R."https://zbmath.org/authors/?q=ai:taylor.john-r.1|taylor.john-rSummary: Double diffusion occurs when the fluid density depends on two components that diffuse at different rates (e.g. heat and salt in the ocean). Double diffusion can lead to an up-gradient buoyancy flux and drive motion at the expense of potential energy. Here, we follow the work of \textit{E. N. Lorenz} [``Available potential energy and the maintenance of the general circulation'', Tellus 7, No. 2 2, 157--167 (1955; \url{doi:10.3402/tellusa.v7i2.8796})] and \textit{K. B. Winters} et al. [J. Fluid Mech. 289, 115--128 (1995; Zbl 0858.76095)] for a single-component fluid and define the background potential energy (BPE) as the energy associated with an adiabatically sorted density field and derive its budget for a double-diffusive fluid. We find that double diffusion can convert BPE into available potential energy (APE), unlike in a single-component fluid, where the transfer of APE to BPE is irreversible. We also derive an evolution equation for the sorted buoyancy in a double-diffusive fluid, extending the work of \textit{K. B. Winters} and \textit{E. A. D'Asaro} [ibid. 317, 179--193 (1996; Zbl 0894.76082)] and \textit{N. Nakamura} [``Two-dimensional mixing, edge formation, and permeability diagnosed in an area coordinate'', J. Atmos. Sci. 53, No. 11, 1524--1537 (1996; \url{doi:10.1175/1520-0469(1996)053<1524:TDMEFA>2.0.CO;2})]. The criterion we develop for a release of BPE can be used to analyse the energetics of mixing and double diffusion in the ocean and other multiple-component fluids, and we illustrate its application using two-dimensional simulations of salt fingering.Thermal instability of a micropolar fluid layer with temperature-dependent viscosity.https://zbmath.org/1460.762992021-06-15T18:09:00+00:00"Dhiman, Joginder Singh"https://zbmath.org/authors/?q=ai:dhiman.joginder-singh"Sharma, Nivedita"https://zbmath.org/authors/?q=ai:sharma.niveditaThe authors studied the effect of temperature-dependent viscosity on the onset of thermal convection in micropolar fluid layer heated from below. The validity of principle of exchange of stabilities is investigated for this more general problem by conjugate eigen functions. A single-term Galerkin method is used to find general expressions and dynamically free boundaries. The value of the critical Rayleigh numbers for each condition is computed numerically for the case of stationary convection. The effects of micro-rotation parameters and the viscosity variation parameter on critical Rayleigh numbers are computed numerically.
Reviewer: K. N. Shukla (Gurgaon)Linear stability of katabatic Prandtl slope flows with ambient wind forcing.https://zbmath.org/1460.860302021-06-15T18:09:00+00:00"Xiao, Cheng-Nian"https://zbmath.org/authors/?q=ai:xiao.cheng-nian"Senocak, Inanc"https://zbmath.org/authors/?q=ai:senocak.inancSummary: We investigate the stability of katabatic slope flows over an infinitely wide and uniformly cooled planar surface subject to a downslope uniform ambient wind aloft. We adopt an extension of Prandtl's original model for slope flows [\textit{V. N. Lykosov} and \textit{L. N. Gutman}, ``Turbulent boundary-layer over a sloping underlying surface'', Atmos. Ocean. Phys. 8, No. 8, 799--809 (1972)] to derive the base flow, which constitutes an interesting basic state in stability analysis because it cannot be reduced to a single universal form independent of external parameters. We apply a linear modal analysis to this basic state to demonstrate that for a fixed Prandtl number and slope angle, two independent dimensionless parameters are sufficient to describe the flow stability. One of these parameters is the stratification perturbation number that we have introduced in [the authors, ``Stability of the Prandtl model for katabatic slope flows'', J. Fluid Mech. 865, R2, 14 p. (2019; \url{doi:10.1017/jfm.2019.132})]. The second parameter, which we will henceforth designate the wind forcing number, is hitherto uncharted and can be interpreted as the ratio of the kinetic energy of the ambient wind aloft to the damping due to viscosity and the stabilising effect of the background stratification. For a fixed Prandtl number, stationary transverse and travelling longitudinal modes of instabilities can emerge, depending on the value of the slope angle and the aforementioned dimensionless numbers. The influence of ambient wind forcing on the base flow's stability is complicated, as the ambient wind can be both stabilising as well as destabilising for a certain range of the parameters. Our results constitute a strong counterevidence against the current practice of relying solely on the gradient Richardson number to describe the dynamic stability of stratified atmospheric slope flows.Convection at an isothermal wall in an enclosure and establishment of stratification.https://zbmath.org/1460.765052021-06-15T18:09:00+00:00"Caudwell, T."https://zbmath.org/authors/?q=ai:caudwell.t"Flór, J.-B."https://zbmath.org/authors/?q=ai:flor.jan-bert"Negretti, M. E."https://zbmath.org/authors/?q=ai:negretti.m-elettaSummary: In this experimental-theoretical investigation, we consider a turbulent plume generated by an isothermal wall in a closed cavity and the formation of heat stratification in the interior. The buoyancy of the plume near the wall and the temperature stratification are measured across a vertical plane with the temperature laser induced fluorescence method, which is shown to be accurate and efficient (precision of 0.2\degree C) for experimental studies on convection. The simultaneous measurement of the velocity field with particle image velocimetry allows for the calculation of the flow characteristics such as the Richardson number and Reynolds stress. This enables us to give a refined description of the wall plume, as well as the circulation and evolution of the stratification in the interior. The wall plume is found to have an inner layer close to the heated boundary with a laminar transport of hardly mixed fluid which causes a relatively warm top layer and an outer layer with a transition from laminar to turbulent at a considerable height. The measured entrainment coefficient is found to be dramatically influenced by the increase in stratification of the ambient fluid. To model the flow, the entrainment model of \textit{B. R. Morton} et al. [Proc. R. Soc. Lond., Ser. A 234, 1--23 (1956; Zbl 0074.45402)] has first been adapted to the case of an isothermal wall. Differences due to their boundary condition of a constant buoyancy flux, modelled with salt by \textit{P. Cooper} and \textit{G. R. Hunt} [J. Fluid Mech. 646, 39--58 (2010; Zbl 1189.76106)], turn out to be small. Next, to include the laminar-turbulent transition of the boundary layer, a hybrid model is constructed which is based on the similarity solutions reported by \textit{M. G. Worster} and \textit{A. M. Leitch} [``Laminar free convection in confined regions'', ibid. 156, 301--319 (1985; \url{doi:10.1017/S0022112085002117})] for the laminar part and the entrainment model for the turbulent part. Finally, the observed variation of the global entrainment coefficient, which is due to the increased presence of an upper stratified layer with a relatively low entrainment coefficient, is incorporated into both models. All models show reasonable agreement with experimental measurements for the volume, momentum and buoyancy fluxes as well as for the evolution of the stratification in the interior. In particular, the introduction of the variable entrainment coefficient improves all models significantly.Evaporation-driven turbulent convection in water pools.https://zbmath.org/1460.764362021-06-15T18:09:00+00:00"Hay, William A."https://zbmath.org/authors/?q=ai:hay.william-a"Papalexandris, Miltiadis V."https://zbmath.org/authors/?q=ai:papalexandris.miltiadis-vSummary: In this paper we study turbulent thermal convection driven by free-surface evaporation at the top and a uniformly heated wall at the bottom. More specifically, we report on direct numerical simulations over 1.25 decades of Rayleigh number, \(Ra\). At the top of the cubic domain, a shear-free boundary condition acts as an approximation of a free surface, and different evaporation rates form the basis of a temperature gradient assigned as a non-zero Neumann boundary condition. The corresponding lower wall temperature is fixed and we assess the thermal mixing on the water side of the air-water interface. The set-up is considered a simplified model of the turbulent natural convection in the upper volumes of spent-fuel pools of nuclear power plants. Surface temperatures are investigated over a range of 40 K, resulting in a sixteenfold increase in evaporation rates. Our work allows, for the first time, analysis of the features and mean flow statistics of this particular thermal convection configuration. Results show that a shear-free surface increases heat transfer within the domain; however, the exponent in the diagnosed power-law relation between the Nusselt and Rayleigh numbers, \(Nu=0.178Ra^{0.301}\), is similar to that of classical turbulent Rayleigh-Bénard convection. Further, the free slip accelerates the fluid after impingement on the upper boundary, significantly affecting the structure of the large-scale circulation in the container. Analysis of the flow statistics then shows how the shear-free surface introduces inhomogeneities in thermal boundary layer heights. Overall, the investigated turbulent convection configuration shows unique traits, borrowing from both turbulent Rayleigh-Bénard convection and evaporative cooling.Model for classical and ultimate regimes of radiatively driven turbulent convection.https://zbmath.org/1460.767162021-06-15T18:09:00+00:00"Creyssels, Mathieu"https://zbmath.org/authors/?q=ai:creyssels.mathieuSummary: In a standard Rayleigh-Bénard experiment, a layer of fluid is confined between two horizontal plates and the convection regime is controlled by the temperature difference between the hot lower plate and the cold upper plate. The effect of direct heat injection into the fluid layer itself, for example by light absorption, is studied here theoretically. In this case, the Nusselt number \((Nu)\) depends on three non-dimensional parameters: the Rayleigh \((Ra)\) and Prandtl \((Pr)\) numbers and the ratio between the spatial extension of the heat source \((l)\) and the height of the fluid layer \((h)\). For both the well-known classical and ultimate convection regimes, the theory developed here gives a formula for the variations of the Nusselt number as a function of these parameters. For the classical convection regime, by increasing \(l/h\) from 0 to \(1/2\), \(Nu\) gradually changes from the standard scaling \(Nu \sim Ra^{1/3}\) to an asymptotic scaling \(Nu \sim Ra^\theta\), with \(\theta =2/3\) or \(\theta =1\) by adopting, respectively, the \textit{W. V. R. Malkus} [Proc. R. Soc. Lond., Ser. A 225, 196--212 (1954; Zbl 0058.20203)] theory or the \textit{S. Grossmann} and \textit{D. Lohse} [J. Fluid Mech. 407, 27--56 (2000; Zbl 0972.76045)] theory. For the ultimate convection regime, \(Nu\) gradually changes from \(Nu \sim Ra^{1/2}\) scaling to an asymptotic behaviour seen only at very high \(Ra\) for which \(Nu \sim Ra^2\). This theory is validated by the recent experimental results given by \textit{V. Bouillaut} et al. [ibid. 861, R5, 12 p. (2019; Zbl 1415.76307)] and also shows that for these experiments, \(Ra\) and \(Re\) numbers were too small to observe the ultimate regime. The predictions for the ultimate regime cannot be confirmed at this time due to the absence of experimental or numerical work on convection driven by internal sources and for very large \(Ra\) numbers.On the role of the Prandtl number in convection driven by heat sources and sinks.https://zbmath.org/1460.764392021-06-15T18:09:00+00:00"Miquel, Benjamin"https://zbmath.org/authors/?q=ai:miquel.benjamin"Bouillaut, Vincent"https://zbmath.org/authors/?q=ai:bouillaut.vincent"Aumaître, Sébastien"https://zbmath.org/authors/?q=ai:aumaitre.sebastien"Gallet, Basile"https://zbmath.org/authors/?q=ai:gallet.basileSummary: We report on a numerical study of turbulent convection driven by a combination of internal heat sources and sinks. Motivated by a recent experimental realisation [\textit{S. Lepot} et al., Proc. Natl. Acad. Sci. USA 115, No. 36, 8937--8941 (2018; Zbl 1416.76300)], we focus on the situation where the cooling is uniform, while the internal heating is localised near the bottom boundary, over approximately one tenth of the domain height. We obtain scaling laws \(Nu \sim Ra^\gamma Pr^\chi\) for the heat transfer as measured by the Nusselt number \(Nu\) expressed as a function of the Rayleigh number \(Ra\) and the Prandtl number \(Pr\). After confirming the experimental value \(\gamma \approx 1/2\) for the dependence on \(Ra\), we identify several regimes of dependence on \(Pr\). For a stress-free bottom surface and within a range as broad as \(Pr \in [0.003, 10]\), we observe the exponent \(\chi \approx 1/2\), in agreement with Spiegel's mixing-length theory. For a no-slip bottom surface we observe a transition from \(\chi \approx 1/2\) for \(Pr \leq 0.04\) to \(\chi \approx 1/6\) for \(Pr \geq 0.04\), in agreement with scaling predictions by \textit{V. Bouillaut} et al. [J. Fluid Mech. 861, R5, 12 p. (2019; Zbl 1415.76307)]. The latter scaling regime stems from heat accumulation in the stagnant layer adjacent to a no-slip bottom boundary, which we characterise by comparing the local contributions of diffusive and convective thermal fluxes.Mixed baroclinic convection in a cavity.https://zbmath.org/1460.767212021-06-15T18:09:00+00:00"Kumar, Abhishek"https://zbmath.org/authors/?q=ai:kumar.abhishek"Pothérat, Alban"https://zbmath.org/authors/?q=ai:potherat.albanSummary: We study the convective patterns that arise in a nearly semicylindrical cavity fed in with hot fluid at the upper boundary, bounded by a cold, porous semicircular boundary at the bottom, and infinitely extended in the third direction. While this configuration is relevant to continuous casting processes that are significantly more complex, we focus on the flow patterns associated with the particular form of mixed convection that arises in it. Linear stability analysis (LSA) and direct numerical simulations (DNS) are conducted, using the spectral-element method to identify observable states. The nature of the bifurcations is determined through Stuart-Landau analysis for completeness. The base flow consists of two counter-rotating rolls driven by the baroclinic imbalance due to the curved isothermal boundary. These are, however, suppressed by the through-flow, which is found to have a stabilising influence as soon as the Reynolds number \(Re\) based on the through-flow exceeds 25. For a sufficiently high Rayleigh number, this base flow is linearly unstable to three different modes, depending on \(Re\). For \(Re\leqslant 75\), the rolls destabilise through a supercritical bifurcation into a travelling wave. For \(100\leqslant Re\leqslant 110\), a subcritical bifurcation leads to a standing oscillatory mode, whereas for \(Re\geqslant 150\), the unstable mode is non-oscillatory and grows out of a supercritical bifurcation. The DNS confirm that in all cases the dominant mode returned by the LSA precisely matches the topology and evolution of the flow patterns that arise out of the fully nonlinear dynamics.Shaping of melting and dissolving solids under natural convection.https://zbmath.org/1460.860472021-06-15T18:09:00+00:00"Pegler, Samuel S."https://zbmath.org/authors/?q=ai:pegler.samuel-s"Davies Wykes, Megan S."https://zbmath.org/authors/?q=ai:wykes.megan-s-daviesSummary: How quickly does an ice cube melt or a lump of sugar dissolve? We address the open problem of the shapes of solids left to melt or dissolve in an ambient fluid driven by stable natural convection. The theory forms a convective form of a Stefan problem in which the evolution is controlled by a two-way coupling between the shape of the body and stable convection along its surface. We develop a new model describing the evolution of such bodies in two-dimensional or axisymmetric geometries and analyse it using a combination of numerical and analytical methods. Different initial conditions are found to lead to different fundamental shapes and descent rates. For the cases of initially linear surfaces (wedges or cones), the model admits similarity solutions in which the tip descends from its initial position as \(t^{4/5}\), where \(t\) is time. It is determined that the evolving shape always forms a parabola sufficiently near the tip. For steeply inclined bodies, we establish a general two-tiered asymptotic structure comprising a broad \(4/3\)-power intermediate near-tip region connected to a deeper parabolic region at the finest scale. The model results apply universally for any given relationship between density, viscosity, diffusivity and concentration, including two-component convection. New laboratory experiments involving the dissolution of cones of sugar candy in water are found to collapse systematically onto our theoretically predicted shapes and descent rates with no adjustable parameters.Buoyant Tsuji diffusion flames: global flame structure and flow field.https://zbmath.org/1460.800182021-06-15T18:09:00+00:00"Donini, Mariovane S."https://zbmath.org/authors/?q=ai:donini.mariovane-s"Cristaldo, Cesar F."https://zbmath.org/authors/?q=ai:cristaldo.cesar-f"Fachini, Fernando F."https://zbmath.org/authors/?q=ai:fachini.fernando-fSummary: The present work analyses how buoyancy is impacting the topology of diffusion flames established around a horizontal cylindrical burner. The flow conditions are chosen such that the system is subjected to negative and positive buoyant forces. It is proposed in this study to investigate the effect of a modulation of the balance between these buoyant forces on the flame structure by varying the temperature of the ambient atmosphere. More specifically, conditions are sought for establishing a buoyant Tsuji diffusion flame characterized by a very low level of strain rate in its lower part (i.e. below the burner). To understand the fundamental mechanisms controlling the whole flame topology, a model is proposed which assumes steadiness and incompressibility of the flow while retaining buoyancy effects in the momentum balance. The results showed that an increase of the ambient temperature leads to the appearance of a counterflow zone below the burner where the flame is undergoing very low levels of strain rate. The overall flame proves to be shorter than its counterpart observed in the forced convection regime. In addition, it is shown that an order of magnitude analysis is able to recover the sensitivity of the flame behaviour to the Péclet and Froude numbers as well as to the combustion parameters. In a certain range of the ambient-atmosphere temperature, the flow field changes dramatically: for the same boundary conditions, there are two steady-state solutions which depend on the initial conditions, i.e. the system presents a hysteresis.