A systematic numerical study of the tidal instability in a rotating triaxial ellipsoid

TL;DR

This study numerically investigates the non-linear evolution of tidal instability in rotating ellipsoids, providing insights into growth rates, mode selection, and dissipation relevant for planetary core dynamics.

Contribution

It introduces a validated finite element model to systematically analyze tidal instability across various ellipsoid geometries and orientations, addressing previously inaccessible questions.

Findings

Growth rates depend on aspect ratio and inclination.

Quantified saturation amplitude of the flow.

Derived scaling laws for planetary core dissipation.

Abstract

The full non-linear evolution of the tidal instability is studied numerically in an ellipsoidal fluid domain relevant for planetary cores applications. Our numerical model, based on a finite element method, is first validated by reproducing some known analytical results. This model is then used to address open questions that were up to now inaccessible using theoretical and experimental approaches. Growth rates and mode selection of the instability are systematically studied as a function of the aspect ratio of the ellipsoid and as a function of the inclination of the rotation axis compared to the deformation plane. We also quantify the saturation amplitude of the flow driven by the instability and calculate the viscous dissipation that it causes. This tidal dissipation can be of major importance for some geophysical situations and we thus derive general scaling laws which are applied to typical planetary cores.