Tidally Averaged Models of the Gravitationally Driven Estuarine Circulation with Lateral Transport

Abstract This study investigates the impact of lateral tidal mixing and advection by tidally averaged vertical and lateral currents on the gravitationally driven estuarine circulation. The nondimensionalized conservation equations for the estuarine salinity and three-dimensional velocity are analyzed, and illustrative numeric solutions are obtained. The estuarine circulation depends on two nondimensional numbers which control the effects of lateral advection and mixing. The first one, earlier introduced as Fischer number, describes the ratio of lateral to vertical tidal mixing. The second number, referred to as advection parameter, characterizes the importance of advection relative to vertical tidal mixing. For greater Fischer number, tidal mixing dominates consistent with earlier solutions without advection. For sufficiently small depth to width aspect ratio, both the Fischer number and advection parameter become small. In this case, an earlier perturbation expansion analysis is applicable, and the salinity distribution is controlled by lateral transport with mixing being more important than advection in shallower water. For many common estuaries, the Fischer number and advection parameter are, however, not small despite small depth to width aspect ratio. For greater advection parameter, lateral transport greatly reduces lateral salinity gradients that drive lateral flows, suggesting a negative feedback so that the impact of advection on the salinity and along-estuary velocity distributions approaches a limit. In this case, the exchange flow resembles modified classic estuarine circulation solutions, although advection is still a principal term in the governing conservation equations. Overall, this study demonstrates that the estuarine exchange flow fundamentally depends on lateral transport processes.