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Orbital forcings of a fluid ellipsoid. Inertial instabilities and dynamos

Abstract : Inertial instabilities are fluid instabilities excited by mechanical forcings (e.g. tides, precession) in fluid bodies (e.g. planetary liquid cores or stellar envelopes) orbited by celestial companions. The nonlinear outcome of these instabilities can drive self-sustained, dynamo magnetic fields. Thus they could be an alternative to thermo-chemical convection to generate magnetic fields in geophysics and astrophysics. These instabilities have only been studied in idealised models, which challenges the extrapolation towards the relevant regimes in geophysics and astrophysics. Recent laboratory and numerical studies, performed in the achievable range of parameters (i.e. large deformations and overestimated diffusive effects), seem apparently not in agreement with theoretical predictions representative of celestial fluid bodies (i.e. extremely small deformations and vanishing diffusive effects). Several physical ingredients have been also neglected, such as the orbital eccentricity. This could drive additional tidal effects, as a result of the time-dependent forcing. Similarly, density variations have been largely neglected in these models. However, rotationally powered magnetic fields in stably stratified stellar envelopes could reconcile astronomical observations with dynamo models. In this thesis we have adopted more realistic models, by combining theoretical tools (linear stability analyses in unbounded and bounded fluids enclosed in ellipsoids) and numerical ones (direct numerical simulations) to study rotationally driven inertial instabilities. We show, with a linear stability analysis in bounded ellipsoidal geometry, that bulk diffusion cannot be neglected emph{a priori} compared to the boundary layer diffusion in laboratory experiments and simulations. This phenomena is not expected in celestial fluid bodies. We also show that an orbital eccentricity could generate additional instabilities in deformed bodies, for orbital configurations which were believed to be linearly stable. Finally, we have studied the dynamo capability of tidal flows in stably stratified fluid envelopes. These are idealised models of hot, intermediate-mass stars (i.e. with a mass ranging from one to eight solar masses). Approximatively 10~% of hot stars exhibit observable magnetic fields. We show that the tidal instability can drive dynamo magnetic fields of large wavelength in stably stratified fluids. Predictions obtained with this tidal model seem consistent with the ultra-weak magnetism of rapidly rotating, tidally deformed Vega-like stars.
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Jérémie Vidal. Orbital forcings of a fluid ellipsoid. Inertial instabilities and dynamos. Astrophysics [astro-ph]. Université Grenoble Alpes, 2018. English. ⟨NNT : 2018GREAU004⟩. ⟨tel-01782426⟩

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