Semianalytical Solutions of Shoreline Response to Time-Varying Wave Conditions

Abstract

Analytical solutions to an extended version of the one-line model for shoreline change are derived in this paper for two cases: (1) shoreline change when the evolution of an alongshore position is a known function of time; and (2) shoreline change within a groyne compartment. The solutions extend existing analytic approaches by accounting for arbitrarily time-varying wave conditions. Explicit solutions are obtained by means of integral transform techniques. The generalized expressions can account for time-varying wave conditions, for an initial beach shape which is an arbitrary function of position, and for sources/sinks of sediment that are a known function of time and space. Example applications are described and the impact that a time-varying wave forcing can have on beach development is investigated. In contrast to previous analytic work, changes in shoreline evolution rate in response to the continuously changing wave conditions in a time series are revealed. Apart from being a more realistic tool for a fast preliminary estimation of long-term shoreline change, the new solutions are also a valuable independent means for validating numerical one-line models.