Comments on Barker and Astoul (2021)

TL;DR

This paper defends the validity of the $D_R$ energy transfer formulation in tidal interactions, correcting misinterpretations in Barker and Astoul's recent critique based on Boussinesq and anelastic models.

Contribution

It clarifies the correct energy transfer term in tidal dissipation models and refutes Barker and Astoul's claim that $D_R$ is invalid, emphasizing the importance of appropriate boundary conditions.

Findings

$D_R$ remains a valid energy transfer term in tidal dissipation.

Barker and Astoul's boundary condition assumptions are inappropriate for stars and planets.

The critique based on Boussinesq models does not invalidate the $D_R$ formulation.

Abstract

The tidal evolution of interacting binaries when the orbital period is short compared to the primary star's convective time scale is a problem of long-standing. Terquem (2021) has argued that, when this temporal ordering scheme is obeyed, the rate of energy transfer from tides to convection (denoted $D_R$) is given by the product of the averaged Reynolds stress associated with the tidal velocity and the mean shear associated with the convective flow. In a recent response, Barker and Astoul (2021, hereafter BA21) claim to show that $D_R$ (in this form) cannot contribute to tidal dissipation. Their analysis is based on a study of Boussinesq and anelastic models. Here, we demonstrate that BA21 misidentify the correct term responsible for energy transfer between tides and convection. As a consequence, their anelastic calculations do not prove that the $D_R$ formulation is invalidated as an energy-loss coupling between tides and convection. BA21 also carry out a calculation in the Boussinesq approximation. Here, their claim that $D_R$ once again does not contribute is based on boundary conditions that do not apply to any star or planet that radiates energy from its surface, which is a key dissipational process in the problem we consider.