Nonlinear evolution of the tidal elliptical instability in gaseous planets and stars

TL;DR

This study uses 3D hydrodynamical simulations to investigate the nonlinear evolution of the elliptical instability in tidally deformed gaseous planets and stars, revealing vortex formation that limits energy dissipation.

Contribution

First nonlinear analysis of elliptical instability in astrophysical fluids showing vortex formation and its impact on tidal energy dissipation.

Findings

Long-lived vortices form under weak tidal deformation.

Vortices suppress the elliptical instability and reduce energy dissipation.

Insufficient dissipation to explain tidal evolution in current models.

Abstract

Tidally distorted rotating stars and gaseous planets are subject to a well-known linear fluid instability -- the elliptical instability. It has been proposed that this instability might drive enough energy dissipation to solve the long-standing problem of the origin of tidal dissipation in stars and planets. But the nonlinear outcome of the elliptical instability has yet to be investigated in the parameter regime of interest, and the resulting turbulent energy dissipation has not yet been quantified. We do so by performing three dimensional hydrodynamical simulations of a small patch of a tidally deformed fluid planet or star subject to the elliptical instability. We show that when the tidal deformation is weak, the nonlinear outcome of the instability leads to the formation of long-lived columnar vortices aligned with the axis of rotation. These vortices shut off the elliptical instability, and the net result is insufficient energy dissipation to account for tidal dissipation. However, further work is required to account for effects neglected here, including magnetic fields, turbulent convection, and realistic boundary conditions.