Snapshots of an experiment (left) and an inviscid numerical simulation (right) of flow in a rotating annulus. The fluid that lay initially above the drop in depth is visualised using a line of dye in the experiment, and as the interface between the red and blue regions in the simulation.

Schematics of a real ocean shelf break (left) and the idealised shelf break topography used in the theory (right). The theoretical model approximates the shelf as a vertical drop in depth, and neglects  variations of the sea surface by imposing a flat upper surface. The vertical drop in depth is relaxed to a steep slope for the purposes of laboratory experiments and numerical simulations.

My approach to this problem combines nonlinear Rossby wave theory, idealised numerical simulations, and laboratory experiments in an annular channel. In the illustrations below, I have generated a clockwise flow around the annulus, which generates lee waves behind a bump that has been placed in the outer wall. The simulation has been generated by solving the inviscid shallow water quasi-geostrophic equations numerically. The laboratory-generated and numerically-computed flows generate a series strongly nonlinear topographic Rossby waves that tend to break or become unstable.