Turbulent convection in the interiors of the Sun and the Earth occurs at high Rayleigh numbers Ra, low Prandtl numbers Pr, and different levels of rotation rates. To understand the combined qualitative effects better, we study rotating turbulent convection for Pr = 0.021, and varying Rossby numbers Ro, using direct numerical simulations in a slender cylinder of diameter one-tenth its height. This confinement allows us to attain high enough Rayleigh numbers. We are motivated by the earlier finding in the absence of rotation that heat transport at high enough Ra is similar between confined and extended domains. We make comparisons with higher aspect ratio data where possible. We study the effects of rotation on the global transport of heat and momentum as well as flow structures for increasing rotation at a few fixed values of Ra as well as for increasing Ra (up to 10^{10}) at the fixed, low Ekman number of 1.45 \times 10^{-6}. 

We find that the flow structure, which is initially helical, develops progressively finer components with increasing thermal forcing. The flow structure feels the rotation strongly near the onset, with suppressed variation along the vertical direction. With increasing Rayleigh numbers, however, the resilience increases and the flow configuration shows a strong resemblance to its non-rotating counterpart at high Rayleigh numbers. In spite of this feature, the essentially isothermal bulk region, observed to exist in wider convection domains, is absent in the slender cell. Yet the heat transport scaling is the same as in wider cells for a given high Rayleigh number, which shows the secondary role of the bulk flow for global heat transport. For instance, we observed that the Nusselt number in the rotating cell scales as Ra^{0.95} for Ra between 10^8 and 10^9, which is close to that found in a wider cell at a similar Prandtl number. 

We obtained the mean temperature gradient in the bulk region of the rotating slender cells and found that its variation with Ra is similar to that in extended domains. We also analysed the width of the Ekman layer and the velocity profile in the region near the horizontal plates, and observed very similar behaviour to that in rapidly rotating convective flows in wider domains. Thus the effects of rotation on the slender convection are similar to those in extended convection, even though the non-rotating case exhibits differing behaviour, as long as Ra is high enough. We find that the effects of rotation diminish with increasing Rayleigh number. These results and comparison studies suggest that, for high enough Rayleigh numbers, rotation alters convective flows in a similar manner for small and large aspect ratios, and so useful insights on the effects of high thermal forcing on convection can be obtained by considering slender domains.

Reference:

Pandey, A. & Sreenivasan, K. R. 2024. Turbulent convection in rotating slender cells. J. Fluid Mech. 999, A28.