Spectral simulations of tidal flows in weakly deformed spheres

Jérémie Vidal 1 David Cébron 1
1 Géodynamo
ISTerre - Institut des Sciences de la Terre
Abstract : Celestial fluid bodies (e.g. planets, stars), orbited by gravitational companions, undergo harmonic orbital forcings, such as tides or precession. These orbital forcings deform fluid bodies into ellipsoids and generate fluid instabilities, e.g. the elliptical instability. The nonlinear outcome of these instabilities can sustain a wave turbulence regime and drive self-sustained, dynamo magnetic fields. However, orbitally driven instabilities have only been studied in the achievable range of parameters (i.e. large deformations and overestimated diffusive effects) that is far from the expected regime in geo and astrophysics. We advocate the use of an alternative numerical method to simulate fluid instabilities (i) in weakly deformed non-axisymmetric domains and (ii) in the weak diffusive regime. We have implemented this method within two spectral codes, devoted to linear and nonlinear computations. We report preliminary results benchmarked against the tidal forcing. This method paves the way for more realistic numerical simulations of orbitally driven flows in weakly deformed fluid containers.
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Jérémie Vidal, David Cébron. Spectral simulations of tidal flows in weakly deformed spheres. Comptes-Rendus de la 21ème Rencontre du Non-Linéaire (2018), 2018, Paris, France. ⟨hal-02005416⟩

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