The adjustment of a rotating fluid to a geostrophic equilibrium is now a classical problem in the theory of rotating fluids and is associated with the name of Rossby because of his pioneering work in this subject. The case of particular interest here is the one where the fluid is initially at rest but has a discontinuity in surface elevation along a certain line. If the bottom is flat, the adjustment gives rise to a jet flowing along the line of the initial discontinuity, the width of the jet being the Rossby radius of deformation. This paper examines how the flow is modified when the bottom is not flat, but has a step-like discontinuity running perpendicular to the line of the initial jump in surface elevation, giving rise to double Kelvin waves which propagate along the step. Flow is thus diverted parallel to the step, and behind the wave front there is no mass flux across the step.The effect of adding a vertical coast perpendicular to the step is also considered. When the double Kelvin wave propagates offshore, it leaves behind a state with no transport across the step. With propagation toward the coast, however, there is pinching of the longshore current into a narrow boundary layer.The problem is examined using (a) linear analysis, (b) laboratory experiments, and (c) numerical experiments.
Gill, A. E., M. K. Davey, E. R. Johnson, and P. F. Linden. 1986. "Rossby adjustment over a step." Journal of Marine Research 44, (4). https://elischolar.library.yale.edu/journal_of_marine_research/1833