Internal tides generated in straits and small ocean basins: when is their response amplified?

When they interact with topography in the presence of stratification, astronomically driven barotropic tides lose part of their energy to internal tides. Numerical and observational studies on internal tide generation often focus on either generation at ocean ridges and isolated topographical features or generation at the open coast, but not in semi-enclosed basins. Because of their long wavelengths, potentially comparable to horizontal basin scales, internal tides may be resonant with natural basin modes, which would explain previous observations of large amplitude internal tides in some basins. Yet, what is an appropriate basin geometry to elicit a resonant response is poorly understood. Interaction of vertical stratification with coastal bathymetry is likely to have an impact on the generation and dynamics of internal waves. We conduct a series of idealized 3D numerical simulations of semi-enclosed, continuously vertically stratified basins with coastal shelf bathymetry. We force these basins with a periodic barotropic flow to investigate under what physical characteristics of a basin internal tides can be characterized as resonant basin modes rather than freely propagating waves. We identify relevant nondimensional parameters that can be used to find characteristics of a basin resonant to a particular frequency. We also find that in the presence of coastal bathymetry, there is a coupling between the basin mode and coastal trapped waves that modifies the dynamics of the resonant response.