Scaling of vortex generation by breaking surface gravity 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. In this study, we consider the relationship between a breaking wave and an impulsively forced fluid, allowing us to build upon the classical work on vortex ring phenomena to quantify the circulation generated by a breaking wave. From this we find that the circulation Γ = \chi c^3/g, where \chi is a proportionality factor, c is the phase speed of the wave and g is the acceleration due to gravity. Using a scaling argument, we show that \chi= α (hk)^(3)/(2), where hk is a breaking slope parameter and α is a constant. This formula then allows us to find a direct relationship between the circulation and the wave energy dissipation rate due to breaking, ɛ . We find agreement between our model and the limited available experimental data. An application of this theory to ocean surface processes will be discussed.