Energy and momentum dissipation through wave breaking

Abstract

Wave breaking plays an important role in air‐sea interaction. Laboratory and field measurements suggest that the wave field dissipation can be significantly enhanced by wave breaking and acts as a source of energy for generating current and entraining air against the effect of buoyancy forces. In the present study, a breaking wave model is formulated by taking the acceleration threshold value of − g /2 as breaking criterion, and the statistics of breaking waves, such as breaking wave coverage per unit time, and the volume of breaking water per unit area of wave surface per unit time are estimated. Statistical models are also developed to assess energy and momentum dissipation through wave breaking. It is found that the energy and momentum dissipation rates decay as k −3 and k −2.5 , respectively. The energy loss is mainly due to wave components at frequencies higher than the spectral peak frequency. Though energy loss due to wave components at frequencies lower than the spectral peak frequency is found, these wave components do not significantly lose energy after the breaking. The energy loss, when expressed as phase speed c b of breaking waves, is mainly in the range 0.20 c p < c b < 0.90 c p , where c p is the dominant wave phase speed, and the energy dissipation rate falls off rapidly toward shorter scales. This offers no support for the hypothesis of a “Kolmogorov cascade” in wind‐generated waves analogous to that in turbulence, with energy input from the wind at large scales and dissipation from the waves at the smallest scales. It is also demonstrated that, compared with empirical formula results, our model of energy (or momentum) dissipation rate lies between those models that estimate by empirical formula the rate of energy (or momentum) loss from a breaker with proportional coefficients 0.0085 and 0.0007. In addition, the peak frequency of our model energy (or momentum) dissipation rate downshifts to the lower‐frequency band as wind speed increases, whereas the peak of the empirical formula remains at the same frequency.