Recent zbMATH articles in MSC 76R05https://zbmath.org/atom/cc/76R052021-06-15T18:09:00+00:00WerkzeugExhausting 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.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.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.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.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.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.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.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.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.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.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.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.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 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.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)].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.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.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.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.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.