Evolution of a Potential Vorticity Front over a Topographic Slope

Abstract

Using the methodology of contour dynamics, the evolution of an interface separating two regions of constant potential vorticity is considered. The model equations are those for barotropic nondivergent flow over a topographic slope adjoined by a coastal barrier. The main focus is on the processes which lead to wave breaking for small-amplitude waves and, in general agreement with previous related work, it is found that wave steepening leads to the formation of thin filaments. The key parameter is found to be the ratio of the background potential vorticity to the discontinuity of potential vorticity across the front, with other parameters such as the topographic slope and the distance to the coast playing a relatively less significant role.