TOPOGRAPHICALLY FORCED LONG WAVES ON A SHEARED COASTAL CURRENT .2. FINITE-AMPLITUDE WAVES

This paper analyses the finite-amplitude flow of a constant-vorticity current past coastal topography in the long-wave limit. A forced finit e-amplitude long-wave equation is derived to describe the evolution of the vorticity interface. An analysis of this equation shows that thre e distinct near-critical regimes occur. In the first the upstream flow is restricted, with overturning of the vorticity interface for suffic iently large topography. In the second quasi-steady nonlinear waves fo rm downstream of the topography with weak upstream influence. In the t hird regime the upstream rotational fluid is partially blocked. Blocki ng and overturning are enhanced at headlands with steep rear faces and decreased at headlands with steep forward faces. For certain paramete r values both overturning and partially blocked solutions are possible and the long-time evolution is critically dependent on the initial co nditions. The reduction of the problem to a one-dimensional nonlinear wave equation allows solutions to be followed to much longer times and parameter space to be explored more finely than in the related pionee ring contour-dynamical integrations of Stern (1991).