Air bubble entrainment by breaking waves and estimation of the related statistical quantities

Based on the experiments, the energy loss from wave breaking epsilon(ed), the bubble plume penetration depth z(b) I the rate of air entrainment Q(z), and the turbulent kinetic energy dissipation rate epsilon(T)(z) are estimated in this study. As a consequence, a simple bubble size spectrum model N(a, z) is proposed and the rate of energy dissipation due to air bubble entrainment and bubble fragment Hinze scale and bubble size spectrum are investigated under different sea states. It is indicated that the rate of energy dissipation due to air bubble entrainment ranges from 0.1 to 0.6 in low and moderate sea states, but may be negligible in the high sea state. Bubble fragment Hinze scale downshifts to the lower-frequency band as wind speed increases. Bubble size spectrum not only depends on the rate of air entrainment, the breaking rate, and the turbulent kinetic energy dissipation rate, but also strongly on the wind and sea state.