The Hydraulics of an Evolving Upwelling Jet Flowing around a Cape

Abstract

Upwelling jets flow alongshore in approximate geostrophic balance with the onshore pressure gradient induced by coastal upwelling. Observations of such jets have shown that they often move offshore downstream of capes, leaving a pool of upwelled water inshore. Comparisons are made between this behavior and the hydraulic transition of a potential-vorticity-conserving coastal current as it passes a topographic anomaly at which it is exactly critical to long coastal-trapped waves. An analytic 1.5-layer model of coastal hydraulics with constant potential vorticity in each layer predicts flow fields (i.e., jet separation) in critical situations that resemble observations. When scales approximate Cape Blanco on the Oregon coast, separation occurs at a jet transport of around 0.76 ? 106 m3 s?1, similar to observed transports. Time-dependent, semigeostrophic calculations suggest that, during an upwelling season, the jet would evolve from a weak flow, which was subcritical everywhere and symmetric about the cape, to an exactly critical state that made a transition from subcritical to supercritical structure at the head of the cape. The predicted flow field at critical transition consists of a narrow upwelling jet upstream of the cape that moves offshore and broadens at the cape. This critical state would be accompanied by a downstream jump back to subcritical conditions. Further upwelling-favorable winds would lead to transient waves that propagated upstream and downstream, modifying the upstream and downstream conditions and restoring criticality. Thus, the head of the cape exerts hydraulic control on the flow and prevents the jet transport from increasing above its critical level. Inherent in the hydraulic approach is the assumption that alongshore scales are large. For realistic alongshore scales, solutions modified by coastline curvature suggest that the convexity of the head of a cape slightly inhibits the transition to a strongly upwelled downstream state by increasing the required critical transport. In the presence of topographic features with finite alongshore scale, the hydraulic approach can be used to construct a flow field, although this flow field has an inherent error arising from the implicit assumptions regarding scales. Estimation of this error for topography representing Cape Blanco suggests that in places the cape is rather abrupt for hydraulic theory to be valid.