SEPARATION OF BOUNDARY CURRENTS DUE TO BOTTOM TOPOGRAPHY

The effect of a large step (running oblique to the coast) on a nonlinear boundary current is examined using an inviscid, baratropic model on an f-plane and a set of laboratory experiments. Attention is focused on two cases: a step-down case in which the depth beyond the step (looking downstream) is infinite, and a step-up case in which the downstream depth is finite. Before examining these two cases in detail, the step matching conditions, analogous to the so-called Rankine-Hugoniot conditions for shock waves, are derived. These derivations show that, in contrast to our expectations, the sea-level on the two sides of the step should not necessarily be matched. On the basis of the newly derived step conditions, steady solutions for the step-down case are obtained analytically by considering the conservation of potential vorticity and mass, the Bernoulli integral and the integrated momentum equation. These solutions are constructed by connecting the upstream and downstream fields without solving for the complicated region in between. It is found that, upon encountering a large step down, the upstream jet turns offshore, and that there is an "entrainment" of water from the deep region into the shallow area. The entrainment current also flows offshore along the step. For the finite step-up case, the method of connecting the upstream and downstream fields without solving for the area in between cannot be easily applied and, consequently, a detailed solution is not obtained. However, a qualitative analysis suggests that, as in the infinitely deep step-down case, the current turns offshore. Simple laboratory experiments on a rotation table were performed for both the step-down and step-up cases. These experiments support the findings mentioned above. A qualitative application of our study to the response of the flow off the Shelikof Strait to the local topography is discussed.