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

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 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 T m = 40 • 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 × 10 9 Ra 7.2 × 10 10 . For small rotation rates and at constant Ra, the reduced Nusselt number Nu red ≡ Nu(1/Ro)/Nu(0) initially increased slightly with increasing 1/Ro, but at 1/Ro = 1/Ro 0 0.5 it suddenly became constant or decreased slightly depending on Ra. At 1/Ro c ≈ 0.85 a second sharp transition occurred in Nu red to a state where Nu red increased with increasing 1/Ro. We know from direct numerical simulation that the transition at 1/Ro c corresponds to the onset of Ekman vortex formation reported before for Γ = 1 at 1/Ro c 0.4 and for Γ = 2 at 1/Ro c = 0.18 (Weiss et al., Phys. Rev. Lett., vol. 105, 2010, 224501). The Γ -dependence of 1/Ro c 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/Ro 0 . Above 1/Ro c , Nu red increased with increasing Γ up to ∼1/Ro = 3. We discuss the Γ -dependence of Nu red 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 Nu red 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 1/Ro, the Taylor-Proudman effect in combination with boundary conditions suppresses fluid flow in the vertical direction.

Regimes of Axisymmetric Flow and Scaling Laws in a Rotating Annulus with Local Convective Forcing

“…Read [16] predicted an aspect ratio dependence of the regime transitions for an annulus with internal heating and observed transitions occurring at lower P for higher aspect ratio in numerical simulations. Aspect ratio dependence of transitions between different behaviours has also been seen in Rayleigh-Bénard convection [53]. As the analysis stands P is independent of the height of the fluid.…”

Exploring the geostrophic regime of rapidly rotating convection with experiments

“…11 and 12. At small enough Ro, experiments and direct numerical simulations (DNSs) of the full Navier-Stokes equations (in the Boussinesq approximation) should give similar results as simulations of the asymptotically reduced equations. Up to now, most of the experiments [13][14][15][16][17][18][19][20][21][22][23] and DNSs 16,18,[24][25][26][27] did not reach deep into the rapidly rotating convection regime. The few experimental and numerical studies that entered decisively into this regime 9,[28][29][30] primarily use the overall heat transfer to characterize rapidly rotating Rayleigh-Bénard convection and identify transitions between flow regimes from changes in the heat-flux scaling.…”

Multiple Transitions in Rotating Turbulent Rayleigh-Bénard Convection

“…However, all of these investigations were carried out on systems with geometrical constraints in all physical directions, and it is not clear whether the sharp transitions are caused by boundary conditions or whether they would survive in an unconstrained system. Indeed for one of these systems, turbulent rotating Rayleigh-Bénard convection, measurements were made as a function of the lateral extent (aspect ratio) of the system, and it was found that the observed transition moves toward zero rotation rate as the lateral system size approaches infinity [12,11]. Here we report measurements of the heat transport, expressed in terms of the Nusselt number N u, and of the temperature gradient near the center of a cylindrical sample of fluid heated from below and rotated about its vertical axis at a rate Ω.…”