Penetrative Convection at High Rayleigh Numbers

Abstract

We study penetrative convection of a fluid confined between two horizontal plates, the temperatures of which are such that a temperature of maximum density lies between them. The range of Rayleigh numbers studied is $Ra=\left[10^6,10^8\right]$ and the Prandtl numbers are $Pr=1$ and $11.6$. An evolution equation for the growth of the convecting region is obtained through an integral energy balance. We identify a new non-dimensional parameter, $\Lambda$, which is the ratio of temperature difference between the stable and unstable regions of the flow; larger values of $\Lambda$ denote increased stability of the upper stable layer. We study the effects of $\Lambda$ on the flow field using well-resolved lattice Boltzmann simulations, and show that the characteristics of the flow depend sensitively upon it. For the range $\Lambda =\left[0.01,4\right]$, we find that for a fixed $Ra$ the Nusselt number, $Nu$, increases with decreasing $\Lambda$. We also investigate the effects of $\Lambda$ on the vertical variation of convective heat flux and the Brunt-Väisälä frequency. Our results clearly indicate that in the limit $\Lambda \to 0$ the problem reduces to that of the classical Rayleigh-Bénard convection.

12 pages, 19 figures

References in corpus (6)

• A Comparison of Turbulent Thermal Convection Between Conditions of Constant Temperature and Constant Flux
• Roughness as a Route to the Ultimate Regime of Thermal Convection
• Seismic Sounding of Convection in the Sun
• Spectrum and amplitudes of internal gravity waves excited by penetrative convection in solar-type stars
• Penetrative internally heated convection in two and three dimensions
• Dynamics of Mixed Convective--Stably-Stratified Fluids

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