Journal
PHYSICAL REVIEW FLUIDS
Volume 3, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevFluids.3.043501
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Funding
- University of Oxford
- Yale University
- Office of Naval Research [OCE-1332750]
- NASA Graduate Research Fellowship
- NASA [NNH13ZDA001N-CRYO]
- Swedish Research Council [638-2013-9243]
- Royal Society Wolfson Research Merit Award
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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 = [10(6),10(8)] 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, 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 = [0.01,4], 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-Vaisala frequency. Our results clearly indicate that in the limit Lambda -> 0 the problem reduces to that of the classical Rayleigh-Benard convection.
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