On the interaction between fast tides and convection

TL;DR

This paper investigates the interaction between fast tides and convection in stellar environments, finding that a recently proposed mechanism for enhanced dissipation does not contribute in realistic models, thus clarifying tidal dissipation processes.

Contribution

The study analytically and numerically shows that the proposed Reynolds stress mechanism for fast tide dissipation vanishes in realistic stellar models, challenging previous suggestions of its significance.

Findings

The new Reynolds stress term vanishes in both Boussinesq and anelastic models.

Fast tide dissipation is not enhanced by the proposed mechanism.

Convection acts as an effective viscosity decreasing quadratically with tidal frequency.

Abstract

The interaction between equilibrium tides and convection in stellar envelopes is often considered important for tidal evolution in close binary and extrasolar planetary systems. Its efficiency for fast tides has however long been controversial, when the tidal frequency exceeds the turnover frequency of convective eddies. Recent numerical simulations indicate that convection can act like an effective viscosity which decays quadratically with tidal frequency for fast tides, resulting in inefficient dissipation in many applications involving pre- and main-sequence stars and giant planets. A new idea was however recently proposed by Terquem (2021), who suggested Reynolds stresses involving correlations between tidal flow components dominate the interaction instead of correlations between convective flow components as usually assumed. They further showed that this can potentially significantly enhance tidal dissipation for fast tides in many applications. Motivated by the importance of this problem for tidal dissipation in stars and planets, we directly compute this new term using analytical arguments and global spherical simulations using Boussinesq and anelastic hydrodynamic models. We demonstrate that the new term proposed by Terquem vanishes identically for equilibrium tides interacting with convection in both Boussinesq and anelastic models; it is therefore unlikely to contribute to tidal dissipation in stars and planets.