Effect of depth-dependent wave stirring on the final amplitude of shoreface-connected sand ridges

Abstract

A nonlinear morphodynamic model is analysed to gain fundamental knowledge about the initial growth and long-term behaviour of observed shoreface-connected sand ridges. The model describes quasi-steady, depth-averaged flow on a storm-dominated inner shelf with an erodible bottom and a transverse slope. Both bed load and suspended load sediment transport are incorporated. The formulations are linear with respect to the current and account for depth-dependent stirring of sediment by waves as well as for the effect of local bed slopes. A linear stability analysis has already revealed the initial growth of bed forms that resemble observed shoreface-connected ridges. Here, a nonlinear analysis is carried out to study the long-term dynamics of these bed forms. The method is based on an expansion of the flow and the bottom perturbations in a truncated series of eigenfunctions of the linear problem for a coastal stretch with a fixed longshore length. The result is a set of nonlinear algebraic equations, describing the flow over the topography, and differential equations for the bottom amplitudes. Results indicate finite-amplitude behaviour in the mode amplitudes. The long-term bottom pattern shows the observed asymmetries of the ridges with steep bottom gradients on the downstream side. The migration speed of this finite-amplitude perturbation appears to be unaffected by nonlinear effects. Extrapolation of the results to Long Island shelf yields bed forms with a characteristic height of about 4 m in a saturation time of ∼850 yr , which are consistent with observations.