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#### Optimal heat transport in rotating Rayleigh-Bénard convection at large Rayleigh numbers

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##### Citation

Hartmann, R., Yerragolam, G., Verzicco, R., Lohse, D., & Stevens, R. (2023). Optimal
heat transport in rotating Rayleigh-Bénard convection at large Rayleigh numbers.* Physical Review Fluids,*
*8*(8): 083501. doi:10.1103/PhysRevFluids.8.083501.

Cite as: https://hdl.handle.net/21.11116/0000-000D-FCBA-6

##### Abstract

The heat transport in rotating Rayleigh-Bénard convection (RBC) can be significantly enhanced for moderate rotation, i.e., for an intermediate range of Rossby numbers Ro, compared to the nonrotating case. At Rayleigh numbers Ra≲5×108, the largest enhancement is achieved when the thicknesses of kinetic and thermal boundary layer are equal. However, experimental and numerical observations show that, at larger Ra (≳5×108), the maximal heat transport starts to deviate from the expected optimal boundary layer ratio and its enhancement amplitude decreases drastically. We present data from direct numerical simulations of rotating RBC in a periodic domain in the range of 107≤Ra≤1010 and 0≤Ro−1≤40 for Prandtl number Pr=4.38 and 6.4 (corresponding to Ekman numbers Ek≳10−6) to identify the reason for the transition to this large-Ra regime of heat transport enhancement. Our analysis reveals that the transition occurs once the bulk flow at the optimal boundary layer ratio changes to geostrophic turbulence for large Ra. In that flow state, the vertically coherent vortices, which support heat transport enhancement by Ekman pumping at smaller Ra, dissolve into vertically decorrelated structures in the bulk such that the enhancing effect of Ekman pumping and the influence of the boundary layer ratio become small. Additionally, more heat leaks out of the Ekman vortices as the fraction of thermal dissipation in the bulk increases. We find that the rotation-induced shearing at the plates helps to increase the thermal dissipation in the bulk and thus acts as a limiting factor for the heat transport enhancement at large Ra: Beyond a certain ratio of wall shear stress to vortex strength, the heat transport decreases irrespectively of the boundary layer ratio. This Pr-dependent threshold, which roughly corresponds to a bulk accounting for ≈1/3 of the total thermal dissipation, indicates the maximal heat transport enhancement and the optimal rotation rate Ro−1opt at large Ra.