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Mean zonal flows induced by weak mechanical forcings in rotating spheroids

Published online by Cambridge University Press:  14 April 2021

David Cébron Open the ORCID record for David Cébron [Opens in a new window] ,
Jérémie Vidal Open the ORCID record for Jérémie Vidal [Opens in a new window] ,
Nathanaël Schaeffer Open the ORCID record for Nathanaël Schaeffer [Opens in a new window] ,
Antonin Borderies  and
Alban Sauret Open the ORCID record for Alban Sauret [Opens in a new window]
David Cébron*
Affiliation:
ISTerre, Université Grenoble Alpes, CNRS, 38000Grenoble, France
Jérémie Vidal
Affiliation:
ISTerre, Université Grenoble Alpes, CNRS, 38000Grenoble, France
Nathanaël Schaeffer
Affiliation:
ISTerre, Université Grenoble Alpes, CNRS, 38000Grenoble, France
Antonin Borderies
Affiliation:
ISTerre, Université Grenoble Alpes, CNRS, 38000Grenoble, France
Alban Sauret
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA93106,USA
*
†Email address for correspondence: [email protected]
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Abstract

The generation of mean flows is a long-standing issue in rotating fluids. Motivated by planetary objects, we consider here a rapidly rotating fluid-filled spheroid, which is subject to weak perturbations of either the boundary (e.g. tides) or the rotation vector (e.g. in direction by precession, or in magnitude by longitudinal librations). Using boundary-layer theory, we determine the mean zonal flows generated by nonlinear interactions within the viscous Ekman layer. These flows are of interest because they survive in the relevant planetary regime of both vanishing forcings and viscous effects. We extend the theory to take into account (i) the combination of spatial and temporal perturbations, providing new mechanically driven zonal flows (e.g. driven by latitudinal librations), and (ii) the spheroidal geometry relevant for planetary bodies. Wherever possible, our analytical predictions are validated with direct numerical simulations. The theoretical solutions are in good quantitative agreement with the simulations, with expected discrepancies (zonal jets) in the presence of inertial waves generated at the critical latitudes (as for precession). Moreover, we find that the mean zonal flows can be strongly affected in spheroids. Guided by planetary applications, we also revisit the scaling laws for the geostrophic shear layers at the critical latitudes, and the influence of a solid inner core.

JFM classification

Geophysical and Geological Flows: Rotating flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , A39
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© The Author(s), 2021. Published by Cambridge University Press

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References

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