Internal tides at the coast: interpreting baroclinic energy flux in the presence of coastal trapped waves

The steep bathymetry of the continental shelf break supports the generation and propagation of coastal trapped waves, providing an important energy pathway that links astronomical forcing to turbulent dissipation and mixing at the ocean's boundaries. These waves have been observed at all frequencies, forming fully trapped waves when the tide is subinertial, and "leaky" modes when the tide is superinertial. Unlike open ocean internal tides, coastal modes cannot be isolated by a barotropic-baroclinic decomposition, as the wave modes couple both motions. Furthermore, in general coastal modes are not orthogonal. Here we examine coastal internal tide energy pathways, first discussing the interpretations of barotropic-baroclinic conversion and baroclinic flux over the steep topography of the shelf break, and then showing specific examples of tidal energy pathways at a range of idealized and realistic coastal topographies. We show that in the presence of along-shelf topographic variability, energy from the gravest Kelvin mode is readily scattered into higher modes with significant along-shelf baroclinic energy flux, though in general this is a notable underestimate of the total wave mode flux.