Shoreline instability under low-angle wave incidence

Abstract

The growth of megacusps as shoreline instabilities is investigated by examining the coupling between wave transformation in the shoaling zone, longshore transport in the surf zone, cross-shore transport, and morphological evolution. This coupling is known to drive a potential positive feedback in case of very oblique wave incidence, leading to an unstable shoreline and the consequent formation of shoreline sand waves. Here, using a linear stability model based on the one-line concept, we demonstrate that such instabilities can also develop in cases of low-angle or shore normal incidence under certain conditions (small enough wave height and/or large enough beach slope). The wavelength and growth timescales are much smaller than those of high-angle wave instabilities and are nearly in the range of those of surf zone rhythmic bars, O(102–103 m) and O(1–10 days). The feedback mechanism is based on (1) wave refraction by a shoal (defined as a cross-shore extension of the shoreline perturbation) leading to wave convergence shoreward of it; (2) longshore sediment flux convergence between the shoal and the shoreline, resulting in megacusp formation; and (3) cross-shore sediment flux from the surf to the shoaling zone, feeding the shoal. Even though the present model is based on a crude representation of nearshore dynamics, a comparison of model results with existing depth-averaged two-dimensional model output and laboratory experiments suggests that the instability mechanism is plausible. Additional work is required to fully assess whether and under which conditions this mechanism exists in nature.