Residual currents in tidally dominated, well-mixed estuaries

Abstract

An analytical model is developed to investigate the residual circulation originating from the interaction of the density field, river flow, and the nonlinear rectification of the periodic tides, in tidally-dominated, well-mixed estuaries. These residual flows effect the density field, which in turn drives the estuarine gravitational circulation. Previous analytical studies have excluded the tidal dynamics and have either imposed the density structure, thereby decoupling the problem, or assumed similarity solutions valid for specific regions within the estuary. Here, a theoretical model is developed that calculates, via a perturbation analysis, the lowest-order density field established from tidal mixing, tidally-induced residual flow, river runoff, and diffusion. Two special cases are considered, a long tidal river and a finite length, variable-breadth estuary. Once the density field is determined for each case, the density driven flow is calculated and added to the rectified tidal and river induced flows for both the Eulerian and Lagrangian reference frames.