Internal tides at the coast: energy flux of baroclinic tides propagating into the deep ocean in the presence of supercritical shelf topography

The generation of internal tides at coastal margins is an important mechanism for the loss of energy from the barotropic tide. Although some previous studies attempted to quantify energy loss from the barotropic tides into the deep ocean, global estimates are complicated by the coastal geometry and spatio-temporally variable stratification. We explore the effects of supercritical, finite amplitude bottom topography, which is difficult to solve analytically, by conducting a suite of 2D linear numerical simulations of barotropic tide interacting with a coastal shelf that is uniform in the along-shore direction. We explore the effects of latitude, topographic parameters, and non-uniform stratification on the baroclinic tidal energy flux propagating into the deep ocean away from the shelf. By varying the pycnocline depth and width, we approximate the deep permanent pycnocline rather than shallow and infinitesimally thin pycnoclines previously studied. We find that the topographic criticality parameter used in previous studies, i.e., ratio of the topographic slope to the characteristic slope of the mode-1 internal tide, is not a suitable scaling for the baroclinic energy flux magnitude. Instead, we derive a new scaling that combines the latitudinal effects, stratification-dependent barotropic tidal forcing, and various physical parameters that describe the topographic shape.