Reflection of an internal gravity wave beam off a horizontal free-slip surface

The reflection of a planar finite-amplitude internal gravity wave beam off a free-slip flat horizontal surface is investigated numerically in a uniformly stratified Boussinesq fluid. Nonlinear effects such as mean currents and harmonics are observed in the wave reflection zone. Mean currents form a stationary, vertically oscillatory, layered structure under the free-slip reflecting surface. The vertical wavelength of the mean-flow layers equals half of the vertical wavelength of the reflecting wave. An empirical predictive model for the steady-state mean flow strength, based on the degree of wave nonlinearity and hydrostaticity, is proposed and subsequently compared to the weakly-nonlinear theory by Tabaei \textit{et al.}, \textit{J. Fluid Mech.}, 2005, \textit{vol.} 526, \textit{pp.} 217-243. Both propagating and evanescent superharmonics are observed, and for waves with steepness of $O$(5\%), subharmonic instabilities can occur in the late-time of reflection. Other complications to the basic set-up, such as addition of a subsurface mixed layer and spanwise localization of beam, will also be discussed.