Along-shore Variation of Freshwater Transport in a Buoyant Coastal Current

Dynamical models of buoyant coastal currents often assume along-shore uniform volume and freshwater transport. This assumption is examined for a suite of idealized coastal currents, using a three-dimensional, primitive equation ocean model (ROMS). The numerical model is configured with a river channel connected to a straight, constant sloping shelf and is forced only by riverflow with different magnitudes. When a river plume reattaches to the coast, a coastal current forms and propagates downshelf at a constant speed. The model results show that the freshwater transport in the coastal current decreases toward its propagating head. The sectionally averaged salinity also increases with distance, and its along-shore profiles at different times are self-similar. Consequently, as the coastal current lengthens, a control volume within the coastal current becomes fresher with time. A divergence of freshwater transport is therefore required to support the freshening. In the absence of mixing, a simple kinematic model yields a linearly decreasing freshwater transport, approximately consistent with the model results. Moreover, assuming a geostrophic cross-shore momentum balance and negligible mixing, the decrease of freshwater transport translates to a reduction of coastal current thickness. The along-shore variation of thickness derived from the simple kinematic model is found in reasonable agreement with the prior laboratory experiments by Thomas and Linden (2007).