Elliptical instability of compressible flow in ellipsoids

Abstract

Elliptical instability is due to a parametric resonance of two inertial modes in a fluid velocity field with elliptical streamlines. This flow is a simple model of the motion in a tidally deformed, rotating body. Elliptical instability typically leads to three-dimensional turbulence. The associated turbulent dissipation together with the dissipation of the large scale mode may be important for the synchronization process in stellar and planetary binary systems. In order to determine the influence of the compressibility on the stability limits of tidal flows in stars or planets, we calculate the growth rates of perturbations in flows with elliptical streamlines within ellipsoidal boundaries of small ellipticity. In addition, the influence of the orbiting frequency of the tidal perturber ${\Omega }_P$ and the viscosity of the fluid are taken into account.

References in corpus (8)

• The mass-radius relationship from solar-type stars to terrestrial planets: a review
• Elliptical instability in terrestrial planets and moons
• Nonlinear evolution of the tidal elliptical instability in gaseous planets and stars
• Elliptical instability in hot Jupiter systems
• Tidal instability in a rotating and differentially heated ellipsoidal shell
• Nonlinear evolution of the elliptical instability in the presence of weak magnetic fields
• A systematic numerical study of the tidal instability in a rotating triaxial ellipsoid
• Magnetohydrodynamic simulations of the elliptical instability in triaxial ellipsoids

Cited by in corpus (4)

• Fossil field decay due to nonlinear tides in massive binaries
• Inviscid instabilities in rotating ellipsoids on eccentric Kepler orbits
• Acoustic and inertial modes in planetary-like rotating ellipsoids
• Precession-driven flows in stress-free ellipsoids