On the breaking of standing waves by falling jets

By direct numerical time stepping, using two different methods of calculation, we follow the development of a standing gravity wave on the surface of deep water when it is given an initial energy exceeding that of the most energetic periodic wave of the same wavelength. Two aspects of the motion are studied in detail: the sequence of wave profiles close to the instant when the maximum surface slope angle is close to 45° and, second, the conditions under which a sharp cusp is formed at the free surface. When a cusp is formed, it can fall vertically into the wave trough, enclosing “bubbles of air.”