Modeling the Coherent Vortices in Breaking Waves

Breaking water waves at the shoreline create a wide range of turbulent structures in the water column. Plunging waves are particularly interesting as the plunging tip of the wave impacts into the toe of the wave, often creating a tube or barrel of air that surfers enjoy. As a result, the turbulence left after the passage of the wave consists, in part, of coherent horseshoe (hairpin) vortices that sink deeper into the water column with time. Nadaoka et al. (1989) identified the legs of the horseshoe (hairpin) vortices as obliquely descending eddies; here we show they are just part of the horseshoes (hairpins). We also provide an argument for the creation of these hairpin vortices (Farahani et al., 2014b), based on an analogy with turbulent boundary layers.