Mean zonal flows induced by weak mechanical forcings in rotating spheroids

TL;DR

This paper develops a boundary-layer theory to predict mean zonal flows induced by weak mechanical forcings in rotating spheroids, validated by numerical simulations, with implications for planetary fluid dynamics.

Contribution

It extends existing theories to include spheroidal geometries and combined spatial-temporal perturbations, providing new insights into planetary-scale flow generation.

Findings

Analytical predictions match numerical simulations well.

Mean zonal flows are significantly affected by spheroidal geometry.

Critical latitude effects influence flow structures and shear layers.

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.