  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 nonlinear 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.
