Internal wave generation by tidal flow over random topography

Internal waves (IW) generated by tidal flow over ocean topography contain a significant fraction of the energy in the oceans. For topography of small scales resolved with high spatial resolution, the topographic slopes are steeper than with low resolution. Previous studies suggested that these small-scale topographies could contribute significantly to the total IW power in oceans. Here we conduct two-dimensional direct numerical simulations for tidal flow of stratified fluids over synthetic random topographies resolved down to small scales; these topographies have the spectrum of ocean topography. We determine the IW power as a function of the parameters characterizing the topography and the fluid stratification. Wave interference between neighboring topographic peaks of steep slopes suppresses IW power to a level less than that predicted by the linear theory. The suppressed power is found to exhibit a linear dependence on the rms topographic height, in contrast to a quadratic height dependence given by the linear theory for topographies of small slopes. The suppressed power has a weak dependence on the fluid stratification. These results suggest that the generated IW power is negligible for topographic features smaller than a cutoff length scale. Our results should help in developing accurate estimates of the total IW power in oceans.