Do nonlinear effects disrupt tidal dissipation predictions in convective envelopes?

TL;DR

This study investigates how nonlinear effects, such as differential rotation and zonal flows, influence tidal dissipation in convective stellar envelopes, revealing significant deviations from linear theory predictions in certain cases.

Contribution

It provides the first detailed 3D nonlinear simulations of tidal flows in convective shells, highlighting the importance of nonlinear effects on tidal dissipation predictions.

Findings

Linear theory approximates dissipation but can be off by a factor of a few.

Nonlinear effects can cause dissipation to differ by orders of magnitude.

Differential rotation and zonal flows significantly impact tidal wave behavior.

Abstract

Most prior works studying tidal interactions in tight star/planet or star/star binary systems have employed linear theory of a viscous fluid in a uniformly-rotating two-dimensional spherical shell. However, compact systems may have sufficiently large tidal amplitudes for nonlinear effects to be important. We compute tidal flows subject to nonlinear effects in a 3D, thin (solar-like) convective shell, spanning the entire frequency range of inertial waves. Tidal frequency-averaged dissipation predictions of linear theory with solid body rotation are approximately reproduced in our nonlinear simulations (though we find it to be reduced by a factor of a few), but we find significant differences, potentially by orders of magnitude, at a fixed tidal frequency corresponding to a specific two-body system at a given epoch. This is largely due to tidal generation of differential rotation (zonal flows) and their effects on the waves.