Nonlinear tides in a homogeneous rotating planet or star: global simulations of the elliptical instability

TL;DR

This paper presents the first global hydrodynamical simulations of the elliptical instability in tidally deformed gaseous planets, revealing turbulence bursts, spin synchronization, and differential rotation effects relevant to hot Jupiter tidal evolution.

Contribution

It introduces nonlinear simulations of the elliptical instability in a free-surface, homogeneous planet model, showing turbulence, spin alignment, and differential rotation effects.

Findings

Elliptical instability causes turbulence bursts and drives planets toward synchronism.

Spin-orbit alignment occurs if the initial spin is anti-aligned.

Dissipation from the instability explains short-period hot Jupiter orbit circularization.

Abstract

I present results from the first global hydrodynamical simulations of the elliptical instability in a tidally deformed gaseous planet (or star) with a free surface. The elliptical instability is potentially important for tidal evolution of the shortest-period hot Jupiters. I model the planet as a spin-orbit aligned or anti-aligned, and non-synchronously rotating, tidally deformed, homogeneous fluid body. A companion paper presented an analysis of the global modes and instabilities of such a planet. Here I focus on the nonlinear evolution of the elliptical instability. This is observed to produce bursts of turbulence that drive the planet towards synchronism with its orbit in an erratic manner. If the planetary spin is initially anti-aligned, the elliptical instability also drives spin-orbit alignment on a similar timescale as the spin synchronisation. The instability generates differential rotation inside the planet in the form of zonal flows, which play an important role in the saturation of the instability, and in producing the observed burstiness. These results are broadly consistent with the picture obtained using a local Cartesian model (where columnar vortices played the role of zonal flows). I also simulate the instability in a container that is rigid (but stress-free) rather than free, finding broad quantitative agreement. The dissipation resulting from the elliptical instability could explain why the shortest-period hot Jupiters tend to have circular orbits inside about 2-3 days, and predicts spin-synchronisation (and spin-orbit alignment) out to about 10-15 days. However, other mechanisms must be invoked to explain tidal circularisation for longer orbital periods.