The generation of internal tides at abrupt topography

Internal tide generation is examined for a knife-edge ridge and an abrupt step. The energy flux from a knife-edge ridge with a height much less than the water depth is shown to be twice that from a Witch of Agnesi ridge with the same height but a small slope. In contrast, the energy flux from an abrupt step with an infinitesimal depth change compared to the water depth is the same as from a small slope with the same depth change. For larger topographic heights in both cases, the energy flux from the abrupt topography can significantly exceed that from gentle topography. The energy flux generated at a top-hat ridge and top-hat trench is also calculated. A top-hat ridge generates more energy flux than a knife edge of equivalent height, though the increase is large only for ridges whose height is small compared to the total depth. Additionally, the energy flux produced by a top-hat ridge is found to be rather insensitive to the ridge width. In contrast, the energy flux generated at a top-hat trench is strongly dependent on width. A knife-edge ridge of moderate height has much of its energy flux in mode 1. For a height to depth ratio comparable to that of the Hawaiian Ridge this fraction is 75%, consistent with observations. We also show that energy flux estimates based on representing general topography as a number of independent steps are flawed.