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Heat transport and flow morphology of geostrophic rotating Rayleigh–Bénard convection in the presence of boundary flow

Published online by Cambridge University Press:  22 November 2023

Guang-Yu Ding Open the ORCID record for Guang-Yu Ding [Opens in a new window]  and
Ke-Qing Xia Open the ORCID record for Ke-Qing Xia [Opens in a new window]
Guang-Yu Ding
Affiliation:
Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China Department of Physics, The Chinese University of Hong Kong, Hong Kong, PR China
Ke-Qing Xia*
Affiliation:
Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China
*
†Email address for correspondence: xiakq@sustech.edu.cn
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Abstract

Using direct numerical simulations, we investigate the heat transport in bulk and boundary flows separately in rotating Rayleigh–Bénard convection in cylindrical cells. In the bulk we observe a steep scaling relationship between the Nusselt number ($Nu$) and the Rayleigh number ($Ra$), which is consistent with the results from simulations using periodic boundary conditions. For the boundary flow, we observe a power law $Nu_{BF}\sim (Ra/Ra_w)^1$ at the leading order, where $Nu_{BF}$ is the local Nusselt number of the boundary flow and $Ra_w$ is the onset Rayleigh number of the wall mode. We develop a model using the boundary layer marginal stability theory to explain this power law, and further show that a more precise description of the data can be obtained if a higher-order correction is introduced. A striking finding of our study is the observation of a sharp transition in flow state, manifested by a sudden drop in $Nu_{BF}$ with a corresponding collapse of the boundary flow coherency. After the transition, the boundary flow breaks into vortices, leading to a reduction in flow coherency and heat transport efficiency. As the physical properties of the vortices should not depend on the aspect ratio, $Nu_{BF}$ for all aspect ratios collapse together after the transition. Moreover, the centrifugal force helps trigger the breakdown of the coherent boundary flow state. For this reason, $Nu_{BF}$ for the cases with non-zero centrifugal force collapse together. We further develop a method that enables us to separate the contributions from the bulk and boundary flows in the global Nusselt number using only the global $Nu$ and it does not require the centrifugal force to be absent.

JFM classification

Geophysical and Geological Flows: Rotating flows Turbulent Flows: Turbulent convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 975 , 25 November 2023 , A46
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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