Simultaneous generation and scattering of internal waves by bottom topography

Dissipation mechanisms of low-mode internal tides, which travel far from their topographic generation sites, are an important consideration for the large-scale circulation and energy budget in the ocean. Modelling studies often decouple scattering and generation, i. e. study scattering in the absence of a local barotropic tide, or study generation in the absence of an incident internal tide. In this two-dimensional study using a semi-analytical Green function approach, we model the combined effects of internal wave generation by a barotropic forcing and scattering of an incident mode-1 internal wave, at an isolated Gaussian bottom topography in uniform stratification. Four different parameters govern the energetics – the non-dimensional topographic height (height ratio h^*) and slope (criticality), and the normalised amplitude (U₀) and phase () of the barotropic forcing with respect to the incident mode-1 internal wave. The theory is first quantitatively validated by comparisons with numerical simulations for three different combinations of (h^*, ), followed by a detailed parametric sweep. For a given topography and U₀, on an average across, the total internal wave energy flux is the sum of the energy fluxes associated with generation in the presence of the barotropic forcing alone and the incident mode-1. For a given, however, the total energy flux can deviate significantly from its mean value due to constructive/destructive interferences of the individual modes; this occurs over a surprisingly wide range of U₀, h^* and. Depending on U₀, these deviations can be interpreted as either the extent to which a background barotropic forcing affects internal wave scattering, or the extent to which an incident mode-1 internal wave influences internal wave generation by barotropic forcing. The presence of barotropic forcing can significantly modify the scattering characteristics, including the possibility of losing a non-negligible fraction of the incident internal wave energy to another form. Similarly, internal wave generation characteristics can be sensitively dependent on the presence of an incident internal wave. These energy flux loss or gain effects are typically found for short subcritical (h^* 0. 4, 1) and sufficiently steep, tall (h^* 0. 4) topographies.