Free-surface flows related to breaking waves

Abstract

Using the semiLagrangian approach of John (1953), both Longuet-Higgins (1982) and New (1983) have proposed simple analytical models of the underside or loop of a plunging breaking wave. Although New's ellipse model appears to be remarkably accurate both in profile and free-surface particle dynamics for a limited region of the loop, both of the loop models are shown to be deficient because neither correctly accounts for the rest of the wave. On the other hand, Longuet-Higgins (1983) gives a semiLagrangian representation of the Dirichlet hyperbola, previously shown to be relevant to the jet of fluid ejected from the top of a breaking wave (see Longuet-Higgins 1980). We show that both this jet flow and the ellipse model of New describing the loop are, for large time, complementary solutions of the same free surface equation. This in turn suggests solutions which combine both the jet and the loop, to give a much more complete model of the entire overturning region not too far from the wave crest, and which has approximately correct free-surface particle velocities and accelerations.