TY - JOUR

T1 - Optimal heat transport in rotating Rayleigh-Bénard convection at large Rayleigh numbers

AU - Hartmann, Robert

AU - Yerragolam, Guru S.

AU - Verzicco, Roberto

AU - Lohse, Detlef

AU - Stevens, Richard J. A. M.

N1 - Funding Information:
We thank Yantao Yang for providing us full access to his data, Olga Shishkina for our continuous collaboration (in particular the nice discussions about the details of her scaling theory), and Dominik Krug for giving us helpful advises for the spectral analysis. We further thank Chris Howland for an “epiphany triggering” PoF seminar. This work was funded by the ERC Starting Grant UltimateRB No. 804283. We acknowledge the access to several computational resources, all of which were used for this work: PRACE for awarding us access to MareNostrum 4 based in Spain at the Barcelona Computing Center (BSC) under Projects No. 2020225335, No. 2020235589, and No. 2021250115; the Gauss Centre for Supercomputing e.V. for funding this project by providing computing time on the GCS Supercomputer SuperMUC-NG at Leibniz Supercomputing Centre (LRZ), Project pr74sa; and NWO Science for the use of supercomputer facilities.
Publisher Copyright:
© 2023 American Physical Society.

PY - 2023/8/28

Y1 - 2023/8/28

N2 - 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 Roopt-1 at large Ra.

AB - 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 Roopt-1 at large Ra.

UR - https://arxiv.org/abs/2305.02127

U2 - 10.1103/PhysRevFluids.8.083501

DO - 10.1103/PhysRevFluids.8.083501

M3 - Article

SN - 2469-990X

VL - 8

JO - Physical review fluids

JF - Physical review fluids

IS - 8

M1 - 083501

ER -