On the centrifugal effect in turbulent rotating thermal convection: onset and heat transport

Abstract

The effect of centrifugal force in turbulent rotating Rayleigh–Bénard convection (RRBC) is studied experimentally in an aspect-ratio $\varGamma =1$ cylindrical convection cell and in the ranges of the Froude number $0.004\leq Fr \leq 0.363$ and the Rayleigh number $2.8\times 10^8 \leq Ra \leq 9.5\times 10^9$, and with the Prandtl number fixed at $Pr=4.34$. We use the bulk temperature anomaly to determine the onset Froude number $Fr_c$, beyond which the centrifugal effects cannot be regarded as insignificant. It is found that $Fr_c$ depends on $Ra$ as $Fr_c\sim Ra^{0.53}$, which may be understood qualitatively by the idea of local force balance. For $Fr>Fr_c$, the centrifugal effect is more pronounced for smaller $Ra$, which is also found for larger constant $1/Ro$. This implies that the response of the system to the centrifugal force depends on the flow states, which, in RRBC, is mainly determined by the competition between the buoyancy and Coriolis forces. Detailed analysis of the sidewall temperature signal shows results consistent with those obtained from the bulk temperature. Based on the above results, we propose a different division of the $1/Ro$–$Fr$ phase space than previously suggested. For the heat transport, the results under fixed $1/Ro$ show well-defined $Nu$–$Ra$ scalings, which can provide a better prediction for the heat transport when extrapolating to the unexplored regions in the phase space.