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Precession-driven flows in stress-free ellipsoids

Published online by Cambridge University Press:  23 December 2022

Jérémie Vidal Open the ORCID record for Jérémie Vidal [Opens in a new window]  and
David Cébron Open the ORCID record for David Cébron [Opens in a new window]
Jérémie Vidal*
Affiliation:
Université Grenoble Alpes, CNRS, ISTerre, 38000 Grenoble, France
David Cébron
Affiliation:
Université Grenoble Alpes, CNRS, ISTerre, 38000 Grenoble, France
*
†Email address for correspondence: jeremie.vidal@univ-grenoble-alpes.fr
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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., vol. 492, 2003, 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., vol. 72, 1993, pp. 107–144), which are presumably relevant for planetary applications but are often hampered in experiments or simulations with NS-BC.

JFM classification

Geophysical and Geological Flows: Rotating flows Geophysical and Geological Flows: Waves in rotating fluids
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 954 , 10 January 2023 , A5
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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