The Motion of a Point Vortex near Large-Amplitude Topography in a Two-Layer Fluid

Abstract

This work examines the dynamics of point vortices in a two-layer fluid near large-amplitude, sharply varying topography like that which occurs in continental shelf regions. Topography takes the form of an infinitely long step change in depth, and the two-layer stratification is chosen such that the height of topography in the upper layer is a small fraction of the overall depth, enabling quasigeostrophic theory to be used in both layers. An analytic expression for the dispersion relation of free topographic waves in this system is found. Weak vortices are studied using linear theory and, if located in the lower layer, propagate mainly because of their image in the topography. Depending on their sign, they are able to produce significant topographic wave radiation in their wakes. Upper-layer vortices propagate much slower and produce relatively small amplitude topographic wave radiation. Contour dynamics results are used to investigate the nonlinear regions of parameter space. For lower-layer vortices, linear theory is a good approximation, but for upper-layer vortices complicated features evolve and linear theory is only valid for weak vortices.