Modeling the formation of undulations of the coastline: the role of tides

An idealized model is developed and analyzed to investigate the relevance of tidal motion for the emergence of undulations of a sandy coastline. The model describes feedbacks between tidal and steady flow on the inner shelf, sand transport in the nearshore zone and an irregular coastline. It is demonstrated that an initially straight coastline can become unstable with respect to perturbations with a rhythmic structure in the alongshore direction. The mechanism causing the growth of these perturbations is explained in terms of vorticity concepts. The relative importance of tide-related and wave-driven sediment fluxes in generating undulations of the coastline is investigated for the Dutch coast. Using parameter values that are appropriate for the Dutch coast it is found that tides can render a straight coastline unstable. The model predicts a fastest growing mode (FGM) with a wavelength that is in the order of the observed length of barrier islands. The mode grows on a time scale of 50 yr and it migrates 200 m per year. The wavelength of the FGM decreases with increasing amplitude of the tidal currents. This result is consistent with data of tides, waves and the lengths of barrier islands that are located along the Dutch and German Wadden coast.