Bifurcation of a Coastal Current at an Escarpment

Abstract

The evolution of a coastal current as it encounters an escarpment depends strongly on whether the geometry of the coast and escarpment is right or left ?handed,? independent of the direction of the coastal current. Handedness is defined such that right-handed means that when looking across the escarpment from the deep to the shallow side, the coast is found on the right. The essential aspects of the difference in behavior of the current in the two geometries are captured by a simple quasigeostrophic model of coastal flow over a step. An exact analytic solution to the nonlinear stationary problem is obtained. This solution shows that, when a coastal current crosses an escarpment in the left-handed geometry, the speed of the current will increase independent of whether the flow is from shallow to deep or from deep to shallow. For the right-handed geometry, the speed of the current decreases, also independent of the direction of the coastal flow. In the left (right)-handed geometry, there is associated to the coastal flow an inshore (offshore) current along the escarpment. These results are explained in terms of linear wave theory and vortex dynamics. Numerical simulations are used to examine the evolution of the flow from the initial encounter to the establishment of a stationary flow. The relevance of this research is discussed in light of recent results from laboratory experiments and oceanic observations.