Formation events of shoreline sand waves on a gravel beach

Kilometric-scale shoreline sand waves (KSSW) have been observed in the north-east flank of the Dungeness Cuspate Foreland (southeastern coast of the UK). They consist of two bumps separated by embayments with a 350–450-m spacing. We have analysed 36 shoreline surveys of 2-km length using the Discrete Fourier Transformation (DFT), from 2005 to 2016, and seven topographic surveys encompassing the intertidal zone, from 2010 to 2016. The data set shows two clear formation events. In order to test the role of high-angle waves on the KSSW formation, the 10-year wave series is propagated from the wave buoy located at 43 m depth up to a location in front of the undulations at 4 m depth using the SWAN wave model. The dominating SW waves arrive with a very high incidence angle (～ 80°) while the NE waves arrive almost shore normal. The ratio R, which measures the degree of dominance of high-angle waves with respect to low-angle waves, correlates well with the shoreline DFT magnitude values of the observed wavelength undulations. In particular, the highest R values coincide with the formation events. Finally, a linear stability model based on the one-line approximation is applied to the Dungeness profile and the 10-year propagated wave series. It predicts accurately the formation moments, with positive growth rates in the correct order of magnitude for wavelengths similar to the observed ones. All these results confirm that the shoreline undulations in Dungeness are self-organized and that the underlying formation mechanism is the high-angle wave instability. The two detected formation events provide a unique opportunity to validate the existing morphodynamic models that include such instability.