An analytical model of crenulate shaped beaches

An analytical model for the development of crenulate shaped beaches is constructed. It is assumed that the shape of the crenulate shaped beach remains constant with time and expands with a rate according to a time function. Based upon a sediment balance, a simplified model of wave diffraction and refraction and a nearshore current model an expression for the shape function and the time function of crenulate shaped beaches is derived. It is shown that in the diffraction zone the time function should follow a t1/3 law, while for the refraction zone the well known t1/2 law is found. This implies that the evolution of a crenulate beach in the diffraction zone should initially be faster and on the long term slower than is found in refraction zones. The hypothesis is verified using available data. The resulting shape function of crenulate shaped beaches is expressed in terms of the diffracted wave field.