Do nonlinear effects disrupt tidal dissipation predictions in convective envelopes?

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.