Formation mechanisms for self-organized km-scale shoreline sand waves
Abstract
The feedbacks between morphology and waves through the sediment transport are investigated as a source of km-scale shoreline sand waves. In particular, the observed sand waves along Srd. Holmslands Tange, Denmark, are examined. We use a linear stability model based on the one-line approximation, linking the bathymetry to the perturbed shoreline. Previous models that consider the link by shifting the equilibrium profile and neglecting the curvature of the depth contours predict a positive feedback only if the offshore wave incidence angle (θc) is above a threshold, θc≃42°. Considering curvilinear depth contours and using a linearly decaying perturbation in bed level we find that θc can vary over the range 0 − 90° depending on the background bathymetric profile and the depth of closure, Dc. Associated to the perturbed wave refraction there are two sources of instability: the alongshore gradients in wave angle, wave-angle mechanism, and the alongshore gradients in wave energy induced by wave crest stretching, wave-energy mechanism. The latter are usually de-stabilizing but the former are de-stabilizing only for large enough Dc, steep foreshores and gently sloping shorefaces. The critical angle comes out from the competition between both mechanisms, but when both are de-stabilizing, θc=0. In contrast with earlier studies, the model predicts instability for the Holmslands Tange coast so that the observed sand waves could have emerged from such instability. The key point is considering a larger Dc that is reasonably supported by both observations and wave climate, which brings the wave-angle mechanism near the de-stabilizing threshold.