Tilt-over mode in a precessing triaxial ellipsoid

TL;DR

This paper extends analytical models of the tilt-over mode in precessing bodies from spheroids to triaxial ellipsoids, relevant for astrophysical objects, and confirms their accuracy with numerical simulations.

Contribution

It develops and validates new analytical models for the tilt-over mode in triaxial ellipsoids, a more complex geometry than previously studied spheroids.

Findings

Analytical models accurately describe stationary flow in triaxial ellipsoids.

Numerical simulations confirm the models' validity up to certain forcing levels.

Models break down when time-dependent flows from instabilities emerge.

Abstract

The tilt-over mode in a precessing triaxial ellipsoid is studied theoretically and numerically. Inviscid and viscous analytical models previously developed for the spheroidal geometry by Poincar\'e [Bull. Astr. 27, 321 (1910)] and Busse [J. Fluid Mech., 33, 739 (1968)] are extended to this more complex geometry, which corresponds to a tidally deformed spinning astrophysical body. As confirmed by three-dimensional numerical simulations, the proposed analytical model provides an accurate description of the stationary flow in an arbitrary triaxial ellipsoid, until the appearance at more vigorous forcing of time dependent flows driven by tidal and/or precessional instabilities.