Cross-shore sediment transport and the equilibrium morphology of mudflats under tidal currents

We describe a mathematical model of suspended sediment transport under cross-shore tidal currents on an intertidal mudflat. We employ a Lagrangian formulation to obtain periodic solutions for the sediment transport over idealized bathymetries and use these to investigate the process of settling lag. In deep water away from the shoreline the concentration of suspended sediment tends to a constant value, and we may invert the relation between bathymetry and offshore concentration to estimate how the gradient of a flat in a state of equilibrium varies with the sediment properties and supply. These analytical estimates are compared successfully with the numerical experiments of previous studies. We discuss the robustness of our modeling framework and demonstrate its application to different descriptions of sediment transport and tidal regimes.