Abstract
A series of new analyses of the problem of the evolution of the internal gravity wave field that is excited when a uniformly stratified fluid flows over monochromatic topography is presented. Results demonstrate that upward-propagating waves overturn and break when they reach sufficient amplitude. The breaking of the wave field may occur due to either one or the other of two main effects, namely, the instability of the propagating wave front and the instability of the wave established behind the advancing front. The analysis of the wave–mean flow momentum transfer process reveals significant differences between these results and the predictions of two main gravity wave drag parameterization schemes (viz., those based upon so-called saturation theory and the spectral theory based on the critical layer absorption mechanism) regarding the dynamics of wave breaking and the spatial distribution of the resulting momentum transfer. The vertical extent and structure of the breaking region and, hence, the momentum transfer from the wave field to the mean flow, are shown to be highly sensitive to the governing parameter aN/U (U and N are, respectively, the velocity and buoyancy frequency characteristic of the upstream incident flow, while a is the wavelength of a quasi-topographic forcing). This nondimensional parameter provides a measure of the importance of nonhydrostatic effects. When the flow is allowed to access the third spatial dimension, the simulations demonstrate that it develops intense three-dimensional motions in the regions of wave breaking. An instability first appears in the form of streamwise-oriented vortices of alternating sign that are consistent with typical convective instability patterns observed previously by different authors. It was observed, however, that two-dimensional coherence of the main flow is still maintained at the coarse-grain scale although the instability does lead to the onset of small-scale turbulence.