Parametric solutions for breaking waves

Abstract

Time-dependent flows such as occur in breaking surface waves are often most con- veniently described in parametric form, with the coordinate z and velocity potential χ each expressed in terms of a third complex variable ω and the time t.In this paper we discuss some interesting flows given in terms of elementary functions of ω and t. Included are the Stokes 120° corner flow, the 45° rotor or rotating wedge, and a decelerated upwelling flow, with an exactly plane surface.Lastly it is shown that a class of cubic flows, which are related to the plane upwelling flow just mentioned, has a free surface that corresponds with remarkable accuracy to the forward face of an overturning, or plunging, breaker.