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

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 Γ ≡ D/ L= 0. 50 ( D is the diameter and L the height of the sample) and compare the results with those for larger Γ . The working fluid was water at Tₘ = 400.167em ^∘ C where the Prandtl number Pr is 4.38. For rotation rates Ω 1~rad ~s ^- 1 , corresponding to inverse Rossby numbers 1/ Ro between zero and twenty, we measured the Nusselt number Nu for six Rayleigh numbers Ra in the range 2. 2× 10⁹ Ra 7. 2× 10¹⁰ . For small rotation rates and at constant Ra , the reduced Nusselt number Nured ≡ Nu(1/ Ro)/ Nu(0) initially increased slightly with increasing 1/ Ro , but at 1/ Ro= 1/ Ro₀ 0. 5 it suddenly became constant or decreased slightly depending on Ra . At 1/ Roc ≈ 0. 85 a second sharp transition occurred in Nured to a state where Nured increased with increasing 1/ Ro . We know from direct numerical simulation that the transition at 1/ Roc corresponds to the onset of Ekman vortex formation reported before for Γ = 1 at 1/ Roc 0. 4 and for Γ = 2 at 1/ Roc = 0. 18 (Weiss et al. , Phys. Rev. Lett. , vol. 105, 2010, 224501). The Γ -dependence of 1/ Roc 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 1/ Ro₀ . Above 1/ Roc , Nured increased with increasing Γ up to ~ 1/ Ro= 3 . We discuss the Γ -dependence of Nured in this range in terms of the average Ekman vortex density as predicted by the model. At even larger 1/ Ro 3 there is a decrease of Nured