Acoustic and inertial modes in planetary-like rotating ellipsoids

TL;DR

This paper develops a polynomial-based Galerkin method to analyze acoustic and inertial modes in rotating ellipsoids with density variations, advancing planetary interior modeling beyond incompressible assumptions.

Contribution

It introduces a global polynomial Galerkin approach for fully compressible rotating ellipsoids, enabling more accurate planetary interior mode analysis.

Findings

Compressibility significantly alters inertial modes.

Method accurately benchmarks against finite-element results.

Relevance to Earth's core and Jupiter-like planets.

Abstract

The bounded oscillations of rotating fluid-filled ellipsoids can provide physical insight into the flow dynamics of deformed planetary interiors. The inertial modes, sustained by the Coriolis force, are ubiquitous in rapidly rotating fluids and Vantieghem (2014, Proc. R. Soc. A, 470, 20140093, doi:10.1098/rspa.2014.0093) pioneered a method to compute them n incompressible fluid ellipsoids. Yet, taking density (and pressure) variations into account is required for accurate planetary applications, which has hitherto been largely overlooked in ellipsoidal models. To go beyond the incompressible theory, we present a Galerkin method in rigid coreless ellipsoids, based on a global polynomial description. We apply the method to investigate the normal modes of fully compressible, rotating and diffusionless fluids. We consider an idealized model, which fairly reproduces the density variations in the Earth's liquid core and Jupiter-like gaseous planets. We successfully benchmark the results against standard finite-element computations. Notably, we find that the quasi-geostrophic inertial modes can be significantly modified by compressibility, even in moderately compressible interiors. Finally, we discuss the use of the normal modes to build reduced dynamical models of planetary flows.