On the Alongshelf Evolution of an Idealized Density Front

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Abstract
Observations reveal a strong tendency for fronts to locate over the outer continental shelf and the upper portions of the continental slope. In this paper, we consider a model of the alongshelf evolution of a quasi-steady density front which separates relatively light nearshore water from the offshore. Results show how, in the absence of any external forcing, the frictional stress associated with bottom geostrophic velocities can result in the cross-shelf migration of a front as one progresses down the shelf in the direction of long coastal-trapped wave propagation. The primary results are derived for the hypothetical case of a flat shelf adjoining a very deep offshore region. In this case, the rate of cross-shelf migration of a density front is similar to that of a passive scalar front in a barotropic fluid. The offshore displacement of a front, separating the lighter inshore from the heavier offshore water, increases exponentially in the direction of shelf-wave propagation on the frictional decay scale of a damped barotropic shelf wave. Beyond a point of abrupt increase in depth, density variations play a more important role. There is a transfer of alongshelf transport from the barotropic inshore region to a baroclinic current in the upper layer water above the front. Eventually all of the transport carried by the lighter layer is shifted to the frontal region and the intersection of front with the bottom stops deepening. Interfacial friction continues to result in a seaward spreading of the frontal transport and the interface consequently slowly flattens over time. The results suggest slow cross-shelf migration for a nearshore front, more rapid migration across the outer shelf and then stalling at a depth where all of the transport is carried in the frontal region. While the model is highly idealized it is suggested that the physical mechanisms considered may be partially responsible for the fact that fronts are most often observed either nearshore or near the shelf break. Some important limitations are discussed.

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