Analytic modeling and applications of barotropic flows over sloping topographies using similarity solutions.

The continental slope is a region in the ocean that consists of a strong sloping topography. The slope acts as a barrier to large scale geophysical transport, but small scale mechanisms are not well understood. Studies are mostly limited to large scale simulations and spatially limited field measurements. I developed an analytic method to obtain a base flow field for regions of the continental slope. Using scaling arguments, I reduce the system to the leading order dynamical balances and apply a similarity method to find solutions of the flow. It is possible to retain the nonlinear terms for a special case, which provides insight into the base nonlinear dynamics of the flow. I show that the solutions are relevant to regions of the continental slope using bathymetry data from the National Oceanic and Atmospheric Administration.