Turbulent convection in rotating slender cells

TL;DR

This study investigates how rotation influences turbulent convection at very high Rayleigh numbers in slender cylindrical cells, revealing that rotation effects diminish at high thermal forcing, with implications for understanding natural convection in planetary interiors.

Contribution

The paper provides new insights into the effects of rotation on turbulent convection at high Rayleigh numbers using direct numerical simulations in slender domains, extending previous understanding to more extreme conditions.

Findings

Rotation effects decrease as Rayleigh number increases.

Flow structures in slender and wider domains show similar responses to rotation at high Ra.

High Ra convection can be effectively studied in slender geometries.

Abstract

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 effects better, we study rotating turbulent convection for $Pr = 0.021$ (for which some laboratory data corresponding to liquid metals are available), and varying Rossby numbers $Ro$, using direct numerical simulations (DNS) in a slender cylinder of aspect ratio 0.1; 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 (a) for increasing rotation at a few fixed values of $Ra$ and (b) for increasing $Ra$ (up to $10^{10}$) at the fixed, low Ekman number of $1.45 \times 10^{-6}$. We compare the results with those from unity $Pr$ simulations for the same range of $Ra$ and $Ro$, and with the non-rotating case over the same range of $Ra$ and low $Pr$. We find that the effects of rotation diminish with increasing $Ra$. These results and comparison studies suggest that, for high enough $Ra$, 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.