NONLINEAR EVOLUTION OF LINEARLY UNSTABLE BAROTROPIC BOUNDARY CURRENTS

The nonlinear evolution of linearly unstable barotropic boundary curre nts, consisting of three piecewise uniform vorticity regions, was inve stigated using the contour dynamics method. A physical interpretation of the nonlinear behavior of the unstable currents is also presented. The contour dynamics experiments reveal that the nonlinear behavior ca n be classified into three regimes dependent on the vorticity distribu tion of the basic how and the wavelength of the unstable wave. In the first breaking wave regime a regular wave train appears with crests br eaking on their upstream side. In the second vortex pair regime the un stable wave evolves into a mushroomlike shape consisting of two vortic es having opposite signs, which, due to self-induced flow, advect coas tal water far away from the boundary. In the third boundary trapped vo rtex regime the vortices generated in both the offshore and coastal sh ear regions remain trapped near the coastal boundary. Differences amon g the three regimes are mainly governed by the temporal change of the phase relationship between the vorticity centers in the piecewise unif orm vorticity regions. The important point to note is that the nonline ar evolution exhibits qualitatively different behavior at different wa velengths, even if the basic currents have the same velocity profiles. In the real ocean, due to coastal topography or external disturbance, the scale of the disturbance is not always determined by the fastest growing mode. Therefore, the nonlinear behavior of an unstable current , which affects the mixing and transport processes, should be studied with attention focused on various wavelengths of the disturbance.