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The effect of tidal force and topography on horizontal convection

Published online by Cambridge University Press:  09 December 2021

Guang-Yu Ding Open the ORCID record for Guang-Yu Ding [Opens in a new window] ,
Yu-Hao He  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, Shenzhen518055, PR China Department of Physics, The Chinese University of Hong Kong, Hong Kong, PR China
Yu-Hao He
Affiliation:
Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, 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, Shenzhen518055, PR China Department of Physics, The Chinese University of Hong Kong, Hong Kong, PR China Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Southern University of Science and Technology, Shenzhen518055, PR China
*
†Email address for correspondence: [email protected]
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Abstract

We present a numerical study on how tidal force and topography influence flow dynamics, transport and mixing in horizontal convection. Our results show that local energy dissipation near topography will be enhanced when the tide is sufficiently strong. Such enhancement is related to the height of the topography and increases as the tidal frequency $\omega$ decreases. The global dissipation is found to be less sensitive to the changes in $\omega$ when the latter becomes small and asymptotically approaches a constant value. We interpret the behaviour of the dissipation as a result of the competition among the dominant forces in the system. According to which mechanism prevails, the flow state of the system can be divided into three regimes, which are the buoyancy-, tide- and drag-control regimes. We show that the mixing efficiency $\eta$ for different tidal energy and topography height can be well described by a universal function $\eta \approx \eta _{HC}/(1+\mathcal {R})$, where $\eta _{HC}$ is the mixing efficiency in the absence of tide and $\mathcal {R}$ is the ratio between tidal and available potential energy inputs. With this, one can also determine the dominant mechanism at a certain ocean region. We further derive a power law relationship connecting the mixing coefficient and the tidal Reynolds number.

JFM classification

Convection: Buoyancy-driven instability Geophysical and Geological Flows: Topographic effects
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 932 , 10 February 2022 , A38
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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