Asymptotic Behavior of the Global Attractors to the Boussinesq System for Rayleigh-Bénard Convection at Large Prandtl Number

We study asymptotic behavior of the global attractors to the Boussinesq system for Rayleigh-Bénard convection at large Prandtl number. in particular, we show that the global attractors to the Boussinesq system for Rayleigh-Bénard convection converge to that of the infinite-Prandtl- number model for convection as the Prandtl number approaches infinity. This offers partial justification of the infinite-Prandtl-number model for convection as a valid simplified model for convection at large Prandtl number even in the long-time regime. © 2006 Wiley Periodicals, Inc

Large Prandtl Number Behavior of the Boussinesq System of Rayleigh-Bénard Convection

We establish the validity of the infinite Prandtl number model as an approximation of the Boussinesq system at large Prandtl number on finite and infinite time interval, as well as in some statistical sense. © 2004 Elsevier Ltd. All rights reserved

Standing and travelling waves in cylindrical Rayleigh-Benard convection

The Boussinesq equations for Rayleigh-Benard convection are simulated for a cylindrical container with an aspect ratio near 1.5. The transition from an axisymmetric stationary flow to time-dependent flows is studied using nonlinear simulations, linear stability analysis and bifurcation theory. At a Rayleigh number near 25,000, the axisymmetric flow becomes unstable to standing or travelling azimuthal waves. The standing waves are slightly unstable to travelling waves. This scenario is identified as a Hopf bifurcation in a system with O(2) symmetry

Phenomenology of buoyancy-driven turbulence: Recent results

In this paper, we review the recent developments in the field of buoyancy-driven turbulence. Scaling and numerical arguments show that the stably-stratified turbulence with moderate stratification has kinetic energy spectrum $E_u(k) \sim k^{-11/5}$ and the kinetic energy flux $\Pi_u(k) \sim k^{-4/5}$, which is called Bolgiano-Obukhov scaling. The energy flux for the Rayleigh-B\'{e}nard convection (RBC) however is approximately constant in the inertial range that results in Kolmorogorv's spectrum ($E_u(k) \sim k^{-5/3}$) for the kinetic energy. The phenomenology of RBC should apply to other flows where the buoyancy feeds the kinetic energy, e.g. bubbly turbulence and fully-developed Rayleigh Taylor instability. This paper also covers several models that predict the Reynolds and Nusselt numbers of RBC. Recent works show that the viscous dissipation rate of RBC scales as $\sim \mathrm{Ra}^{1.3}$, where $\mathrm{Ra}$ is the Rayleigh number

Destabilization of free convection by weak rotation

This study offers an explanation of a recently observed effect of destabilization of free convective flows by weak rotation. After studying several models where flows are driven by a simultaneous action of convection and rotation, it is concluded that the destabilization is observed in the cases where centrifugal force acts against main convective circulation. At relatively low Prandtl numbers this counter action can split the main vortex into two counter rotating vortices, where the interaction leads to instability. At larger Prandtl numbers, the counter action of the centrifugal force steepens an unstable thermal stratification, which triggers Rayleigh-B\'enard instability mechanism. Both cases can be enhanced by advection of azimuthal velocity disturbances towards the axis, where they grow and excite perturbations of the radial velocity. The effect was studied considering a combined convective/rotating flow in a cylinder with a rotating lid and a parabolic temperature profile at the sidewall. Next, explanations of the destabilization effect for rotating magnetic field driven flow and melt flow in a Czochralski crystal growth model were derived

Comparison between rough and smooth plates within the same Rayleigh-Bénard cell

International audienceIn a Rayleigh-Bénard cell at high Rayleigh number, the bulk temperature is nearly uniform. The mean temperature gradient differs from zero only in the thin boundary layers close to the plates. Measuring this bulk temperature allows to separately determine the thermal impedance of each plate. In this work, the bottom plate is rough and the top plate is smooth; both interact with the same bulk flow. We compare them and address in particular the question whether the influence of roughness goes through a modification of the bulk flow