A systematic numerical study of the tidal instability in a rotating triaxial ellipsoid

Abstract

The full non-linear evolution of the tidal instability is studied numerically in an ellipsoidal fluid domain relevant for planetary cores applications. Our numerical model, based on a finite element method, is first validated by reproducing some known analytical results. This model is then used to address open questions that were up to now inaccessible using theoretical and experimental approaches. Growth rates and mode selection of the instability are systematically studied as a function of the aspect ratio of the ellipsoid and as a function of the inclination of the rotation axis compared to the deformation plane. We also quantify the saturation amplitude of the flow driven by the instability and calculate the viscous dissipation that it causes. This tidal dissipation can be of major importance for some geophysical situations and we thus derive general scaling laws which are applied to typical planetary cores.

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• Tidally driven dynamos in a rotating sphere
• Nonlinear evolution of the elliptical instability in the presence of weak magnetic fields
• Precession-driven flows in non-axisymmetric ellipsoids
• Magnetic fields driven by tidal mixing in radiative stars
• Libration driven elliptical instability
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• Turbulent kinematic dynamos in ellipsoids driven by mechanical forcing
• Nonlinear tides in a homogeneous rotating planet or star: global modes and elliptical instability
• Magnetohydrodynamic simulations of the elliptical instability in triaxial ellipsoids
• Libration driven multipolar instabilities
• Inertial Modes in Near-Spherical Geometries
• Magnetic activity of red giants: correlation between the amplitude of solar-like oscillations and chromospheric indicators
• Elliptical instability of compressible flow in ellipsoids
• Rotational dynamics of planetary cores: instabilities driven by precession, libration and tides
• Did lunar tides sustain the early Earth's dynamo?
• Tilt-over mode in a precessing triaxial ellipsoid