Asymptotic behavior of heat transport for a class of exact solutions in rotating Rayleigh-Benard convection

作者：Grooms Ian^*

来源：Geophysical and Astrophysical Fluid Dynamics, 2015, 109(2): 145-158.

DOI：10.1080/03091929.2015.1036054

• Rapid rotation
• Rayleigh-Benard
• Single-mode

The non-hydrostatic, quasigeostrophic approximation for rapidly rotating Rayleigh-Benard convection admits a class of exact "single mode" solutions. These solutions correspond to steady laminar convection with a separable structure consisting of a horizontal planform characterized by a single wavenumber multiplied by a vertical amplitude profile, with the latter given as the solution of a nonlinear boundary value problem. The heat transport associated with these solutions is studied in the regime of strong thermal forcing (large reduced Rayleigh number <br xmlns:set="http://exslt.org/sets">[GRAPHICS]
). It is shown that the Nusselt number
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, a nondimensional measure of the efficiency of heat transport by convection, for this class of solutions is bounded below by
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, independent of the Prandtl number, in the limit of large reduced Rayleigh number. Matching upper bounds include only logarithmic corrections, showing the accuracy of the estimate. Numerical solutions of the nonlinear boundary value problem for the vertical structure are consistent with the analytical bounds. The single mode solutions are typically unstable to perturbations and, for Prandtl numbers greater than unity give way to turbulent dynamics with smaller
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(behavior of the turbulent dynamics for smaller Prandtl numbers in the non-hydrostatic quasigeostrophic approximation remains unexplored).

• 出版日期2015-3-4