On the triggering of the Ultimate Regime of convection

Abstract : Rayleigh-Bénard cells are one of the simplest systems to explore the laws of natural convection in the highly turbulent limit. However, at very high Rayleigh numbers (Ra > 10^{12}) and for Prandtl numbers of order one, experiments fall into two categories : some evidence a steep enhancement of the heat transfer while others do not. The origin of this apparent disagreement is presently unexplained. This puzzling situation motivated a systematic study of the triggering of the regime with an enhanced heat transfer, originally named the ''Ultimate Regime'' of convection. High accuracy heat transfer measurements have been conducted in convection cells with various aspect ratios and different specificities, such as altered boundary conditions or obstacles inserted in the flow. The two control parameters, the Rayleigh and Prandtl numbers have been varied independently to disentangle their relative influence. Among other results, it is found that i) most experiments reaching very high Ra are not in disagreement if small differences in Prandtl numbers are taken into account, ii) the transition is not directly triggered by the large scale circulation present in the cell, iii) the sidewall of the cell have a significant influence on the transition. The characteristics of this Ultimate regime are summarized and compared with R. Kraichnan prediction for the asymptotic regime of convection.
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Philippe-Emmanuel Roche, Frédéric Gauthier, Robert Kaiser, Julien Salort. On the triggering of the Ultimate Regime of convection. New Journal of Physics, Institute of Physics: Open Access Journals, 2010, 12, pp.085014. ⟨10.1088/1367-2630/12/8/085014⟩. ⟨hal-00499652v2⟩

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