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

Abstract 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 spatially and temporally variable stratification. Here, we explore the effects of supercritical, finite amplitude bottom topography, which is difficult to solve analytically. We conduct a suite of 2D linear numerical simulations of the barotropic tide interacting with a uniform alongshore coastal shelf, representing the tidal forcing by a body force derived from the vertical displacement of the isopycnals by the gravest coastal trapped wave (of which a Kelvin wave is a close approximation). We explore the effects of latitude, topographic parameters, and nonuniform stratification on the baroclinic tidal energy flux propagating into the deep ocean away from the shelf. By varying the pycnocline depth and thickness, we extend previous studies of shallow and infinitesimally thin pycnoclines to include deep permanent pycnoclines. We find that scaling laws previously derived in terms of continental shelf width and depth for shallow and thin pycnoclines generally hold for the deeper and thicker pycnoclines considered in this study. We also find that baroclinic tidal energy flux is more sensitive to topographic than stratification parameters. Interestingly, we find that the slope of the shelf itself is an important parameter but not the width of the continental slope in the case of these steep topographies. Significance Statement The objective of this study is to better understand how vertical density stratification, which can vary seasonally in the ocean, affects the interaction of tides with steep coastal topography and the generation of waves that travel away from the coast in the ocean interior. These waves in the interior can travel over long distances, carrying energy offshore into the deep ocean. Our results suggest that the amount of energy in these internal waves is more sensitive to changes in topography and latitude than to the vertical density profile. The scaling laws found in this study suggest which parameters are important for calculating global estimates of the energy lost from the tide to the ocean interior at the coastal margins.