Calculation of beach change under interacting cross-shore and longshore processes

This paper presents a mathematical approach and numerical model that simulates beach and dune change in response to cross-shore processes of dune growth by wind and dune erosion by storms, and by gradients in longshore sand transport that will alter shoreline position. Sub-aerial transport processes are represented, whereas sub-aqueous transport is neglected. The system is tightly coupled morphologically, with the berm playing a central role. For example, the potential for sand to be transported to the dune by wind depends on berm width, and sand lost in erosion of the dune during storms can widen the berm. Morphologic equilibrium considerations are introduced to improve reliability of predictions and stability of the non-linear model. An analytical solution is given under simplification to illustrate properties of the model. Sensitivity tests with the numerical solution of the coupled equations demonstrate model performance, with one test exploring beach and dune response to potential increase in storm-wave height with global warming. Finally, the numerical model is applied to examine the consequences of groin shortening at Westhampton Beach, Long Island, New York, as an alternative for providing a sand supply to the down-drift beach. Results indicate that the sand will be released over several decades as the shoreline and dune move landward in adjustment to the new equilibrium condition with the shortened groins.