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. Themodel 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 problemfor 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 B850 yr; which are consistent with observations.