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The effect of velocity boundary conditions on $2D$ Rayleigh-B\'enard turbulence

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Rayleigh-Bénard (RB) convection, the flow between a cold top plate and a hot bottom plate, is commonly used to model natural convection. Experimental realizations of RB usually consist of low aspect-ratio geometries and are limited to no-slip velocity boundary conditions. This is not representative of most geo- and astrophysical systems we wish to model. In this contribution, the effect of aspect-ratio and velocity boundary conditions on a 2D RB system have been studied by varying the sidewall boundary conditions between no-slip, stress-free and periodic, and the differences in the heat transport are measured. Heat transport is found to be larger for stress-free and periodic cells than for the no-slip case. Aspect ratio plays a small role in periodic cells, as long as the aspect ratio is larger than a certain threshold. For stress-free and no-slip cells, aspect ratio plays opposing roles. Thinner cells have larger heat transport than square cells when the sidewalls are stress-free. In contrast, for cells with no-slip walls, square cells have a larger heat transport than thin cells.

Author(s):

Rodolfo Ostilla Mónico    
Physics of Fluids, University of Twente
Netherlands

Erwin P. van der Poel    
Physics of Fluids, University of Twente
Netherlands

Roberto Verzicco    
Dipartimento di Ingegneria Meccanica, University of Rome Tor Vergata
Italy

Detlef Lohse    
Physics of Fluids, University of Twente
Netherlands