Precession-driven flows in stress-free ellipsoids

TL;DR

This paper investigates precession-driven flows in stress-free ellipsoids, revealing effects on angular momentum and instabilities relevant for planetary fluid dynamics, using asymptotic analysis and numerical validation.

Contribution

It extends the reduced model to stress-free boundary conditions and explores their impact on angular momentum and flow instabilities in precessing ellipsoids.

Findings

Viscosity affects angular momentum evolution in triaxial and some axisymmetric ellipsoids.

Analytical primary flow exhibits a second inviscid resonance in triaxial geometries.

Stress-free boundary conditions facilitate the study of non-viscous instabilities relevant for planetary applications.

Abstract

Motivated by modelling rotating turbulence in planetary fluid layers, we investigate precession-driven flows in ellipsoids subject to stress-free boundary conditions (SF-BC). The SF-BC could indeed unlock numerical constraints associated with the no-slip boundary conditions (NS-BC), but are also relevant for some astrophysical applications. Although SF-BC have been employed in the pioneering work of Lorenzani & Tilgner (J. Fluid Mech., 2003, 492, pp. 363--379), they have scarcely been used due to the discovery of some specific mathematical issues associated with angular momentum conservation. We revisit the problem using asymptotic analysis in the low-viscosity regime, which is validated with numerical simulations. First, we extend the reduced model of uniform-vorticity flows in ellipsoids to account for SF-BC. We show that the long-term evolution of angular momentum is affected by viscosity in triaxial geometries, but also in axisymmetric ellipsoids when the mean rotation axis of the fluid is not the symmetry axis. In a regime relevant to planets, we analytically obtain the primary forced flow in triaxial geometries, which exhibits a second inviscid resonance. Then, we investigate the bulk instabilities existing in precessing ellipsoids. We show that using SF-BC would be useful to explore the non-viscous instabilities (e.g. Kerswell, Geophys. Astrophys. Fluid Dyn., 1993, 72, pp. 107-144), which are presumably relevant for planetary applications but are often hampered in experiments or simulations with NS-BC.