An analytic model for the prediction of wave setup, longshore currents and sediment transport on beaches with seawalls

Abstract

An analytic model is developed to predict the time- and depth-averaged cross-shore and longshore hydrodynamics as well as the longshore sediment transport on a planar beach backed by a seawall. Similar to the classical no seawall derivations of the problem, the model assumes shallow water, small angle of wave incidence, and spilling breakers. The reflected wave energy flux is conserved while the increased energy in the surf zone due to the reflected wave is assumed to be dissipated in the incident wave. A partial standing wave develops in front of the seawall causing modulations of the radiation stresses, the bottom stress, and the resulting wave setup, longshore current and longshore sediment transport. The influence of these modulations increases as the beach slope decreases due to a greater number of standing waves that develop across the wider surf zone. The total water depth slope (including wave setup) is steeper on a beach with a seawall than on a non-armored beach. Both the longshore current and the longshore sediment transport are strongly influenced by the cross-shore location of the seawall. On steep beaches, the total sediment transport is less than that for a natural beach. For milder sloped beaches, the modulations due to partial standing waves become significant and the transport may be either more or less than that for a beach with no wall, depending on the location of the seawall. These mixed results help to explain some of the confusion and contradictions found in the available seawall literature and may aid in focusing future research on the seawall problem.