On the overturning of gravity waves

It is shown that an approximation to the initial stages of overturning in an irrotational gravity wave is given by the potential function X = 2/3ig½z3/2 + 2Az½, where g denotes acceleration due to gravity, z is a complex coordinate in the plane of motion, and A is a linear function of the time t. By adding to the above expression a third term, linear in z, an expression is obtained which can describe the development of sharp corners or cusps in the free surface.