Vorticity dynamics of coastal fronts
This talk examines how free, long waves propagate along a potential vorticity front beside a vertical coast, using a 1.5-layer quasi-geostrophic model with piecewise-constant potential vorticity. The coastal boundary drives flow via image vorticity and a Kelvin wave, which can either reinforce or oppose Rossby wave dynamics at the front. Front behavior depends on the relative strengths of these three mechanisms, explicitly represented in the model. The richest dynamics—featuring kink solitons (under-compressive shocks) and compound waves—occur when vortical effects dominate. Front evolution follows a fully nonlinear, finite-amplitude equation with first-order dispersion, related to the modified Korteweg–de Vries equation. These behaviours are described analyticaaly via El’s dispersive shock-fitting method. Contour-dynamic simulations confirm that the dispersive long-wave theory accurately captures the full quasi-geostrophic dynamics.
