Citation

Bonneton P, Bruneau N, Castelle B, Marche F. Discrete Contin. Dyn. Syst., Ser. B 2010; 13(4): 729-738.

Copyright

(Copyright © 2010)

DOI

10.3934/dcdsb.2010.13.729

PMID

unavailable

Abstract

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, 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 'macrovortices') 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.

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, we obtain a vorticity forcing term related to differential broken-wave energy dissipation. Then, we derive a new equation for the mean current vorticity, from the nonlinear shallow water shock-wave theory. Both approaches are consistent, under the shallow water assumption, but the later gives explicitly the generation term of vorticity, without any ad-hoc parametrization of the broken-wave energy dissipation.

Keywords: Drowning; Drowning Prevention; Water Safety

Language: 1531-3492