Stochastic Model for Embayed Beaches

Abstract

Equilibrium models for beach morphology can be a useful engineering tool. In practice, conditions are rarely such that true equilibrium is reached or maintained. Nevertheless, equilibrium models have been used successfully in coastal studies, and extended in their application to describe quasi-equilibrium situations where, for example, wave conditions are relatively persistent over considerable periods of time. This paper describes a simple but efficient statistical method to estimate the mean and variance of crenuate shaped bays from the (long term or static) equilibrium according to the measured wave directions. The technique relies on the concept of ensemble averaging. The theoretical development is carried out by considering a sequence of problems of successive generality. Analytical solutions are first tested against results from a numerical Monte Carlo simulation which demonstrates the importance of the shape of the wave direction distribution in defining the variability of the beach position. The analytical solutions are then applied to the embayed beach at Christchurch Bay on the south coast of the United Kingdom. Hindcast wave conditions and a set of beach profile measurements covering a period of approximately