Reflection and transmission of internal waves over topography in the presence of a barotropic tide

Internal waves are ubiquitous in the ocean and understanding how these waves change as they pass over topography provides insight into the ocean’s energy budget. Some are generated as a result of barotropic tides passing over topography and radiate away from their generation site, with mode-1 internal waves propagating the furthest. As these mode-1 waves pass over another topographic feature, some of the energy is converted into higher modes, which more rapidly dissipates, while the rest remains in a mode-1 wave that either reflects off the topographic feature or transmits past it. This process is complicated by the persisting barotropic tide, which continues generating internal waves off this second topographic feature. We investigate, analytically and numerically, the modal decomposition of the reflection and transmission process of an incoming mode-1 wave passing over a topographic feature in the presence of a background barotropic tide. Interestingly, despite using a low amplitude mode-1 wave and barotropic tide, the resulting wave field is not simply a superposition of the fields that would have resulted if these features were modeled in isolation. The resulting reflection and transmission of the mode-1 wave depends on its phase difference with the barotropic tide.