Physics of tidal dissipation in early-type stars and white dwarfs: Hydrodynamical simulations of internal gravity wave breaking in stellar envelopes

In binaries composed of either early-type stars or white dwarfs, the dominant tidal process involves the excitation of internal gravity waves (IGWs), which propagate towards the stellar surface, and their dissipation via non-linear wave breaking. We perform 2D hydrodynamical simulations of this wave breaking process in a stratified, isothermal atmosphere. We find that, after an initial transient phase, the dissipation of the IGWs naturally generates a sharp critical layer, separating the lower stationary region (with no mean flow) and the upper 'synchronized' region (with the mean flow velocity equal to the horizontal wave phase speed). While the critical layer is steepened by absorption of these waves, it is simultaneously broadened by Kelvin-Helmholtz instabilities such that, in steady state, the critical layer width is determined by the Richardson criterion. We study the absorption and reflection of incident waves off the critical layer and provide analytical formulae describing its long-term evolution. The result of this study is important for characterizing the evolution of tidally heated white dwarfs and other binary stars.