Breaking of surface gravity waves and air-sea momentum flux

Recently we have developed a model for the equilibrium range of the spectrum of wind-forced ocean surface waves that satisfies conservation of total momentum (Hara and Belcher, 2000). The new feature of the study is the model for the wind forcing of waves. Long wavelength waves exert a drag on the air flow so that they support a fraction of the applied wind stress, which thus leaves a smaller turbulent stress near the surface to force growth of shorter wavelength waves.

In this study the result of the equilibrium spectrum is used to estimate the statistical distribution of breaking wave crests. The distribution function of breaking wave crest is obtained with the assumptions that energy dissipation is entirely due to wave breaking, and that the energy dissipation rate is related to the total length of breaking wave crests per unit surface area. The result of the distribution function has very different wavenumber dependence depending on the range of the wavenumber. In the limit of low wavenumber or low wind it approaches the result by Phillips (1985). On the other hand, at high wavenumbers and high winds it approaches the form predicted by Belcher and Vassilicos (1997) and its magnitude becomes almost independent of the total wind stress. These new theoretical findings are compared to recent spatial measurements of surface waves both over the open ocean and in a laboratory wind wave tank. Finally, the enhanced air-sea momentum flux due to breaking gravity waves are estimated.