On the mechanism of wavelength selection of self-organized shoreline sand waves

Abstract

Sandy shorelines exposed to very oblique wave incidence can be unstable and develop self-organized shoreline sand waves. Different types of models predict the formation of these sand waves with an initially dominant alongshore wavelength in the range 1–10 km, which is quite common in nature. Here we investigate the physical reasons for such wavelength selection with the use of a linear stability model. The existence of a minimum wavelength for sand wave growth is explained by an interplay of three physical effects: (a) largest relative (to the local shoreline) wave angle at the downdrift flank of the sand wave, (b) wave energy concentration at the updrift flank due to less refractive energy dispersion, and (c) wave energy concentration slightly downdrift of the crest due to refractive focusing. For small wavelengths, effects (a) and (c) dominate and cause decay, while for larger wavelengths, effect (b) becomes dominant and causes growth. However, the alongshore gradients in sediment transport decrease for increasing wavelength, making the growth rate diminish. There is therefore a growth rate maximum giving a dominant wavelength, LM. In contrast with previous studies, we show that LM scales with λ0/β (λ0 is the wavelength of the offshore waves and β is the mean shoreface slope, from shore to the wave base), an estimate of the order of magnitude of the distance waves travel to undergo appreciable transformation. Our model investigations show that the proportionality constant between LM and λ0/β is typically in the range 0.1–0.4, depending mainly on the wave incidence angle.