An analytical model to predict dune and cliff notching due to wave impact

A model was developed to calculate the evolution of a notch in a dune or cliff due to wave impact. Analytical solutions were derived to the model for schematized conditions regarding forcing and dune/cliff properties. Comparisons were made with laboratory experiments where the time evolution of the notch was measured. Values of the transport coefficients in the analytical solutions were determined by least-square fitting the solutions to the laboratory data. Some of these coefficients could be related to the ratio between parameters describing the forcing and the dune/cliff strength. The evolution of the dune notch displayed a linear behavior at short times, whereas the cliff notch showed a more complex response for cases where a feedback between the notch and a beach formed seaward of the cliff occurred.