Topographic amplitude dependence of internal wave generation by tidal forcing over idealized three‐dimensional topography

Abstract

This numerical study using the Princeton Ocean Model investigates the conversion of energy from an eastward propagating surface tide to the internal wave field as an oscillating tidal current flows over and around idealized three‐dimensional Gaussian seamounts. In particular, the relationship between the energy flux in the internal wave field and the height of the topography is explored using a range of horizontal aspect ratios. In agreement with theory, the energy flux is found to increase as the square of the topographic amplitude ho for subcritical topography. For supercritical topographies the functional relationship is more complex aspect ratio dependent. It increases more rapidly than ho2 for near‐critical topography. For larger circular seamounts the energy flux increases much more slowly, with the rate of increase dropping with amplitude. As the seamounts are elongated in the cross‐tidal wave (north‐south) direction the energy flux increases more rapidly with height and, for a two‐dimensional ridge, increases as approximately ho2.2. The directional dependence of the energy flux also depends on the aspect ratio and amplitude of the seamount. For circular seamounts, energy flux has its maximum in directions between 20° and 45° counterclockwise from the east‐west axis (Northern Hemisphere). For elongated seamounts the energy flux is directed in the east‐west direction.