Buoyant discharge on the inner continental shelf: A frontal model

A steady state, frontal model of the arrested topographic wave type (Csanady, 1978) is developed for application to buoyant coastal discharge of large-scale and weak stratification, typically found on the inner continental shelf. The across-shore momentum balance is geostrophic, while the alongshore momentum balance includes wind stress and bottom or interfacial friction. The dynamics thus has semi-geostrophic character. No mixing dynamics is present. The model has two major purposes: first, to serve as the vehicle for a process study requiring only moderate computing resources, and second, to inquire into the general consequences of extending the original single-layer model of Csanady (1978) into a two-layer, frontal model for application to buoyant coastal discharge. Analysis of the flow near the frontal bottom intersection shows that the bottom stresses on each side of the front must be equal and match as well the interfacial stress just above. Similar analysis near the surface front shows that static stability there requires the presence of only downwelling-favorable wind stress. This implies that a statically stable, steady state is not possible for upwelling-favorable winds. The model possesses an asymptotic downshelf state that is termed frictionally adjusted flow in which alongshore gradients and across-shore velocities vanish and bottom, interfacial, and wind stresses all are equal. The front then becomes trapped to the local isobaths. Numerical experiments showed that the model contains possible spatially growing instability because of the frontal boundary. Weaker baroclinic strength and diminished bottom slopes tended to increase flow stability. Stable flows were computed in their evolution from a prescribed upshelf state intended to simulate estuarine outflow of buoyant discharge and adjacent inflow of denser ambient shelf water. A turning region developed where the front moved first offshore then back nearer the coast. Experiments showed that the turning region was a joint product of the turning isobath geometry imposed near the estuary mouth and the estuarine inflow of shelf water. Comparisons of model results with recent observations of the Delaware Coastal Current showed general qualitative agreement, but highlight the lack of model mixing processes.