Feedback between residual circulations and sediment distribution in highly turbid estuaries: An analytical model

Motivated by field studies of the Ems estuary which show longitudinal gradients in bottom sediment concentration as high as O(0.01 kg/m4), we develop an analytical model for estuarine residual circulation based on currents from salinity gradients, turbidity gradients, and freshwater discharge. Salinity is assumed to be vertically well mixed, while the vertical concentration profile is assumed to result from a balance between a constant settling velocity and turbulent diffusive flux. Width and depth of the model estuary are held constant. Model results show that turbidity gradients enhance tidally averaged circulation upstream of the estuarine turbidity maximum (ETM), but significantly reduce residual circulation downstream, where salinity and turbidity gradients oppose each other. We apply the condition of morphodynamic equilibrium (vanishing sediment transport) and develop an analytical solution for the position of the turbidity maximum and the distribution of suspended sediment concentration (SSC) along a longitudinal axis. A sensitivity study shows great variability in the longitudinal distribution of suspended sediment with the applied salinity gradient and six model parameters: settling velocity, vertical mixing, horizontal dispersion, total sediment supply, fresh water flow, and water depth. Increasing depth and settling velocity move the ETM upstream, while increasing freshwater discharge and vertical mixing move the ETM downstream. Moreover, the longitudinal distribution of SSC is inherently asymmetric around the ETM, and depends on spatial variations in the residual current structure and the vertical profile of SSC.