A simple relationship for crenulate-shaped bay in static equilibrium

A crenulate-shaped bay is always formed on a sedimentary coast between headlands. The planform of bays in static equilibrium has received attentions since 1940s. A number of empirical models and formulations have been proposed to describe it. However, many researchers and practitioners commented that inconvenience and uncertainties might be encountered in determining the two parameters of these models, i.e. the control line of bay and the incident wave obliquity. This study shows that the parallel indentation of a crenulate-shaped bay to its upcoast headland could be taken as an intrinsic parameter in the description of the bay planform with a straight downcoast segment. This approach leads to a simple formula of the shape of such bayed beaches. The proposed relationship is verified with the data of bayed beaches in many parts of the world.