Equilibrium conditions for curved shape bays with application to an ancient coast

The seaward concave shape of beaches located between two headlands and exposed to a predominant direction of wave attack has been assimilated previously by a logarithmic spiral.In this study, a similar mathematical concept is applied to the Galé coast (Portugal) and an ancient coast located around 50 m deep on the continental shelf.The shape of the present-day coastline corresponds to a long-term equilibrium form reached almost one century ago. Application of such a model to the ancient coast, parallel to this coastline, suggests that the swell direction likely has not changed during the last 10,000 to 11,000 years.