Analytical Solution for Dune Erosion by Storms

Abstract

Beach and dune erosion due to a storm is analyzed as a one‐dimensional unsteady problem assuming uniformity in the alongshore direction. The eroded dune face is treated as a vertical receding front, whereas the sediment deposited in the vicinity of the breaker point causes the offshore advancement of the breaker point. The continuity equation of bottom sediment combined with an empirical sediment transport relationship is used to obtain the temporal and shore‐normal variations of the beach and dune profile inside the breaker point. An analytical solution for an idealized initial beach and dune profile is derived for the case of a rectangular storm surge hydrograph. The temporal variations of the dune recession and eroded sediment volume are expressed in terms of the given initial profile, storm surge, breaker depth, and sediment characteristics. The analytical solution is shown to be in agreement with limited field data on dune erosion due to a hurricane. However, more extensive calibration and verification are required for actual applications.