On geometry effects in Rayleigh-Benard convection

Details On geometry effects in Rayleigh-Benard convection On geometry effects in Rayleigh-Benard convection

2002-12-05

arxiv.org/abs/nlin/0212012v1

Nonlinear Sciences

Chaotic Dynamics

4 pages, 1 figure

Scientific paper

10.1017/S0022112003004270

Various recent experiments hint at a geometry dependence of scaling relations in Rayleigh-B\'enard convection. Aspect ratio and shape dependences have been found. In this paper a mechanism is offered which can account for such dependences. It is based on Prandtl's theory for laminar boundary layers and on the conservation of volume flux of the large scale wind. The mechanism implies the possibility of different thicknesses of the kinetic boundary layers at the sidewalls and the top/bottom plates, just as experimentally found by Qiu and Xia (Phys. Rev. E58, 486 (1998)), and also different $Ra$-scaling of the wind measured over the plates and at the sidewalls. In the second part of the paper a scaling argument for the velocity and temperature fluctuations in the bulk is developeVarious recent experiments hint at a geometry dependence of scaling relations in Rayleigh-Benard convection. Aspect ratio and shape dependences have been found. In this paper a mechanism is offered which can account for such dependences. It is based on Prandtl's theory for laminar boundary layers and on the conservation of volume flux of the large scale wind. The mechanism implies the possibility of different thicknesses of the kinetic boundary layers at the sidewalls and the top/bottom plates, just as experimentally found by Qiu and Xia (Phys. Rev. E58, 486 (1998)), and also different $Ra$-scaling of the wind measured over the plates and at the sidewalls. In the second part of the paper a scaling argument for the velocity and temperature fluctuations in the bulk is develope

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