Analytical Development of a One-Line Model for the Analysis of Shoreline Change by Wind Generated Waves

This paper deals with an analytical solution of the shoreline evolution due to random sea waves. The phenomenon of the shoreline change is modeled by means of a one-line theory. The solution is based on the hypotheses that thedeviation of the shoreline planform from the general shoreline alignment (x-axis) approaches zero and that a particular relationshipbetween higher order derivatives of the shoreline holds. It is proved that the shoreline evolution is described by a diffusion equation, in which the diffusivity G1R is a function of the sea state and the sediment characteristics. Next, particularattention is dedicated to the longshore diffusivity. Its behaviour is analysed and effects of different spectral shapes and of different breaking depths are investigated. It is shown that the diffusivity assumes both positive and negative values.