Large-scale vorticity generation due to dissipating waves in the surf zone

In this paper, we investigate the mechanisms which control the generation of wave-induced mean current vorticity in the surf zone. From the vertically-integrated and time-averaged momentum equations given recently by Smith (21), we obtain a vorticity forcing term related to differential broken-wave energy dissipation. Then, we derive a new equation for the mean current vor- ticity, from the nonlinear shallow water shock-wave theory. Both approaches are consistent, under the shallow water assumption, but the later gives explic- itly the generation term of vorticity, without any ad-hoc parametrization of the broken-wave energy dissipation. 1. Introduction. In the nearshore, alongshore variations in waves and wave-induced currents are ubiquitous. These variations can be due to alongshore inhomogeneities in the incident wave field or in the local bathymetry. As shown theoretically by Peregrine (18), non-uniformities along the breaking-wave crest drive vertical vorticity. The vorticity that is being discussed here is not the small scale vorticity caused directly by wave breaking and subsequent turbulent motions, but the vorticity in the form of quasi two-dimensional eddies (usually called 'macrovor- tices') with horizontal scales larger than the local water depth. The most frequently observed nearshore macrovortices are rip current circulations. Rip currents are shore-normal, narrow, seaward-flowing intense currents that originate within surf zone, extend seaward of the breaking region, and are associated with horizontal eddies. These macrovortices play a major role in circulation and mixing processes in the nearshore. Studies described in Peregrine (18) and Brocchini et al. (4) draw attention to the way in which non-uniformities along the bore crests lead to generation of vertical vorticity. They proceeded to a direct analysis of vorticity, at the wave's time scale, modeling the breaking event as the development of a surface and current discontinu- ity in the non-linear shallow water equations (also called Saint Venant equations). These breaking wave processes induce wave-averaged current and mean vorticity. The aim of the present paper is to investigate wave-averagedmean flow vorticity due to differential wave breaking in the surf zone. Mean vertical vorticity equations are