Lateral transport controls the tidally averaged gravitationally driven estuarine circulation: Tidal mixing effects

Abstract In classic models of the tidally averaged gravitationally driven estuarine circulation, denser salty oceanic water moves up the estuary near the bottom while less dense riverine water flows towards the ocean near the surface. Traditionally, it is assumed that the associated pressure gradient forces and salt advection are balanced by vertical mixing. This study, however, demonstrates that lateral (across the estuary width) transport processes are essential for maintaining the estuarine circulation. This is because for realistic estuarine bathymetry, the depth-integrated salt transport up the estuary is enhanced in the deeper estuary channel. A closed salt budget then requires the lateral transport of this excess salt in the deeper channel towards the estuarine flanks. To understand how such lateral transport affects the estuarine salt and momentum balances, we devise an idealized model with explicit lateral transport focusing on tidally-averaged lateral mixing effects. Solutions for the along-estuary velocity and salinity are non-dimensionalized to depend only on one single non-dimensional parameter, referred to as Fischer number, which describes the relative importance of lateral to vertical tidal mixing. For relatively strong lateral tidal mixing (greater Fischer number), salinity and velocity variations are predominantly vertical. For relatively weak lateral tidal mixing (smaller Fischer number), salinity and velocity variations are predominantly lateral. Overall, lateral transport greatly affects the estuarine circulation and controls the estuarine salinity intrusion length, which is demonstrated to scale inversely with Fischer number.