Penetrative convection at high Rayleigh numbers

Srikanth Toppaladoddi and John S. Wettlaufer
Phys. Rev. Fluids 3, 043501 – Published 3 April 2018
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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=106,108 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 nondimensional parameter, Λ, which is the ratio of temperature difference between the stable and unstable regions of the flow; larger values of Λ denote increased stability of the upper stable layer. We study the effects of Λ 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 Λ=0.01,4, we find that for a fixed Ra the Nusselt number, Nu, increases with decreasing Λ. We also investigate the effects of Λ on the vertical variation of convective heat flux and the Brunt-Väisälä frequency. Our results clearly indicate that in the limit Λ0 the problem reduces to that of the classical Rayleigh-Bénard convection.

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  • Received 2 June 2017

DOI:https://doi.org/10.1103/PhysRevFluids.3.043501

©2018 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Srikanth Toppaladoddi1,2,3,4 and John S. Wettlaufer1,4,5,*

  • 1Yale University, New Haven, Connecticut 06520, USA
  • 2All Souls College, University of Oxford, Oxford OX1 4AL, United Kingdom
  • 3Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
  • 4Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
  • 5Nordita, Royal Institute of Technology and Stockholm University, Stockholm 106 91, Sweden

  • *john.wettlaufer@yale.edu

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Issue

Vol. 3, Iss. 4 — April 2018

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