Vortex generation by deep-water breaking waves

The connection between wave dissipation by breaking deep-water surface gravity waves and the resulting turbulence and mixing is crucial for an improved understanding of air-sea interaction processes. Starting with the ensemble-averaged Euler equations, governing the evolution of the mean flow, we model the forcing, associated with the breaking-induced Reynolds shear stresses, as a body force describing the bulk scale effects of a breaking deep-water surface gravity wave on the water column. From this, we derive an equation describing the generation of circulation, Gamma of the ensemble-average velocity field, due to the body force. By examining the relationship between a breaking wave and an impulsively forced fluid, we propose a functional form for the body force, allowing us to build upon the classical work on vortex ring phenomena to both quantify the circulation generated by a breaking wave and describe the vortex structure of the induced motion. Using scaling arguments, we show that Gamma = alpha(hk)(3/2)c(3)/g, where (c, h, k) represent a characteristic speed, height and wavenumber of the breaking wave, respectively, g is the acceleration due to gravity and alpha is a constant. This then allows us to find a direct relationship between the circulation and the wave energy dissipation rate per unit crest length due to breaking, epsilon(l). Finally, we compare our model and the available experimental data.