Investigation of a self‐organization model for beach cusp formation and development

A recent numerical investigation of “self‐organization” [ Werner and Fink , 1993] suggests that the feedback process between currents and sediment response can result in “self‐organized” patterns and can be used to predict beach cusp formation and spacing. A similar model based on self‐organization is tested here in order to understand the processes occurring during beach cusp formation and development, to evaluate the sensitivity toward the parameters used, and to examine how the model might relate to field observations. Results obtained confirm the validity of the self‐organization approach and its capacity to predict beach cusp spacing, with values in fair agreement with the available field measurements, with most of the input parameters primarily affecting the rate of the process rather than the final spacing. However, changes in the random seed and runs for large numbers of swash cycles reveal a dynamical system with significant unpredictable behavior. Cusp spacing tends to change with time, and cusp regularity shows large long‐term variations. Cusps are found to be accretionary in the swash zone, and in agreement with most observations, mean flows are horn divergent over developed topography. Simulations over nonplanar slopes characterized by the presence of preexisting nonrhythmic or cuspate features have been performed. Results indicate that preexisting large‐amplitude cusps are destroyed if their spacing is substantially different from that expected under self‐organization and that the final spacing is consistent with that predicted by the model for an equivalent plane beach. These findings support the hypothesis that self‐organization is a robust mechanism for beach cusp formation.