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Heat transport by turbulent rotating Rayleigh–Bénard convection and its dependence on the aspect ratio

Published online by Cambridge University Press:  02 September 2011

Stephan Weiss  and
Guenter Ahlers
Stephan Weiss
Affiliation:
Department of Physics, University of California, Santa Barbara, CA 93106, USA
Guenter Ahlers*
Affiliation:
Department of Physics, University of California, Santa Barbara, CA 93106, USA
*
†Email address for correspondence: guenter@physics.ucsb.edu
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Abstract

We report on the influence of rotation about a vertical axis on heat transport by turbulent Rayleigh–Bénard convection in a cylindrical vessel with an aspect ratio ( is the diameter and the height of the sample) and compare the results with those for larger . The working fluid was water at where the Prandtl number  is 4.38. For rotation rates , corresponding to inverse Rossby numbers between zero and twenty, we measured the Nusselt number for six Rayleigh numbers in the range . For small rotation rates and at constant , the reduced Nusselt number initially increased slightly with increasing , but at it suddenly became constant or decreased slightly depending on . At a second sharp transition occurred in to a state where increased with increasing . We know from direct numerical simulation that the transition at corresponds to the onset of Ekman vortex formation reported before for at and for at (Weiss et al., Phys. Rev. Lett., vol. 105, 2010, 224501). The -dependence of can be explained as a finite-size effect that can be described phenomenologically by a Ginzburg–Landau model; this model is discussed in detail in the present paper. We do not know the origin of the transition at . Above , increased with increasing up to . We discuss the -dependence of in this range in terms of the average Ekman vortex density as predicted by the model. At even larger there is a decrease of that can be attributed to two possible effects. First, the Ekman pumping might become less efficient when the Ekman layer is significantly smaller than the thermal boundary layer, and second, for rather large , the Taylor–Proudman effect in combination with boundary conditions suppresses fluid flow in the vertical direction.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Convection: Buoyancy-driven instability

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Papers
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Journal of Fluid Mechanics , Volume 684 , 10 October 2011 , pp. 407 - 426
Copyright
Copyright © Cambridge University Press 2011

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