Asymptotic forms for jets from standing waves

Standing gravity waves forced beyond the maximum height for perfect periodicity can produce vertical jets with sharp-pointed tips. In this paper, canonical forms for the wave crests are derived which display sharp cusps in the limit as the time t tends to infinity. The theoretical profile is in general quartic in the space coordinates, and can describe the smooth transition of a fairly low wave crest to a cusped form. There is no singularity as the surface slope passes through 45°.