2010 On internal wave breaking and tidal dissipation near the centre of a solar-type star. Monthly Notices of the Royal Astronomical Society 404

We study the fate of internal gravity waves approaching the centre of an initially non-rotating solar-type star, primarily using two-dimensional numerical simulations based on a cylindrical model. A train of internal gravity waves is excited by tidal forcing at the interface between the convection and radiation zones of such a star. We derive a Boussinesq-type model of the central region of a star and find a nonlinear wave solution that is steady in the frame rotating with the angular pattern speed of the tidal forcing. We then use spectral methods to integrate the equations numerically, with the aim of studying at what amplitude the wave is subject to instabilities. These instabilities are found to lead to wave breaking whenever the amplitude exceeds a critical value. Below this critical value, the wave reflects perfectly from the centre of the star. Wave breaking leads to mean flow acceleration, which corresponds to a spin up of the central region of the star, and the formation of a critical layer, which acts as an absorbing barrier for subsequent ingoing waves. As these waves continue to be absorbed near the critical layer, the star is spun up from the inside out. Our results point to an important amplitude dependence of the (modified) tidal quality factor Q′, since nonlinear effects are responsible for dissipation at the centre of the star. If the amplitude of the tidal forcing exceeds the critical amplitude for wave breaking to occur, then this mechanism produces efficient dissipation over a continuous range of tidal frequencies. This requires m