Generally speaking, research activities to model and understand morphodynamic processes in the coastal zone are still very active , a diffusion-type equation has been derived applying mass conservation law to the one-line model of coastal profiles.
A high amplitude of the long-shore sand transport rate produces a rapid shoreline response, so that a new state of equilibrium with the incident waves is attained.
Furthermore, a larger “depth of closure” indicates that a larger part of the beach profile participates in the sand movement, leading to a slower shoreline response.
Here, instead of determining the behavior of contour lines, the behavior of bathymetry was considered, by evaluating locally the sediment transport and using sand conservation to obtain the local depth variations.
The diffusion coefficient in the governing equation, having the physical dimension of a square length divided by time, corresponds to the time scale of shoreline change, following a disturbance (a wave action).
One of the final goals is always understanding and predicting the long-term evolution of the plan shape of sandy beaches, as explicitly stated in .