Inviscid instabilities in rotating ellipsoids on eccentric Kepler orbits

Jérémie Vidal (1) , David Cébron (1) , Nathanaël Schaeffer (1)

1 Géodynamo

Because of their spin and tidal interactions, fluid layers are ellipsoidal in most celestial bodies, such as planets, moons or stars. This departure from a spherical shape can lead to inertial instabilities, and thus volume-filling turbulence. Theoretical studies mainly consider weakly deformed spheres, while experimental or numerical studies use strongly deformed ellipsoids because of technical constraints. To bridge the gap, we present a general and versatile computational framework to perform linear global stability analysis of incompressible flows in arbitrary rotating ellipsoids. We present the uniform vorticity basic flow driven by a mechanical forcing in the limit of vanishing viscosity. Then we describe the inviscid stability analysis method. The latter gives the growth rate and velocity field of the unstable flow. Our framework relies on both symbolic and numeric computations to handle global perturbations of unprecedented complexity. It provides a unified understanding of inertial instabilities in rotating ellipsoids, bringing together and extending several previous studies under a common framework. We apply our method to the case of an orbiting fluid ellipsoid. We recover the two limiting cases, namely the tidally-driven and libration-driven elliptical instabilities. Finally, the general case of an orbiting body on an eccentric Kepler orbit is considered. In this case, several forcing frequencies are present and the ellipsoidal shape of the fluid body evolves in time. These effects give birth to new vigorous orbitally-driven elliptical instabilities.

Mots clés: Rotating flows; Topographic effects; Parametric instability

Domaines: Mécanique des fluides [physics.class-ph]; Planétologie et astrophysique de la terre [astro-ph.EP]; Géophysique [physics.geo-ph]

Jérémie Vidal, David Cébron, Nathanaël Schaeffer. Inviscid instabilities in rotating ellipsoids on eccentric Kepler orbits. 2017. ⟨hal-01498649v1⟩