Shoreline change at an infinite jetty for wave time series

Future shoreline changes on a sandy beach with a structure such as a jetty or groin can be estimated when wave time series is known (i.e. sequence of wave height, period, and direction). This paper presents an extension of an existing solution (Pelnard-Considere, 1956) for the linearized partial differential equation for shoreline change at an infinite jetty where waves are time varying and when the angle of the shoreline is small with respect to the waves breaking at the shoreline. The novel solution provided in this paper allows the previous constant wave condition solution to be extended to the case where wave properties (i.e. wave direction, wave height, and wave period) are time varying. Example usage of the method presented shows that shorelines may be of different final plan form shape for time varying wave conditions even though the sediment transport along adjacent beaches is not spatially varying (i.e. spatially constant) from time step to time step. Although this difference in shape may have been known previously using numerical models, it could not be proved analytically. Reversals of wave height, period, and direction time series are shown to provide different final shoreline shapes even though the time series consists of the same waves although in different ordered time. The solution provided will allow one line numerical shoreline models to be tested using an analytic solution.