High Range Resolution Radar Measurements of the Speed Distribution of Breaking Events in Wind-Generated Ocean Waves: Surface Impulse and Wave Energy Dissipation Rates

Abstract

A set of X-band radar measurements, backscattered from the sea surface at near grazing incidence with very high spatial and temporal resolution (30 cm in range and 2000-Hz pulse repetition frequency) in moderate wind conditions, are dominated by moving discrete events (sea spikes). They have radar cross sections of up to about 1 m2 and are found to possess the characteristics of breaking wave fronts. Contributions from Bragg backscattering appear to be at least two orders of magnitude smaller. The number of events detected per unit area per unit time was of the same order as found by Ding and Farmer at almost the same wind speed, but the distribution of event speeds was narrower?the fastest breaking wave events observed had line-of-sight speeds of about 0.6 of the dominant wave speed. The measured histograms of number of events versus event speed c suggested that the smaller events with c < 3 m s?1 were only incompletely counted so that the characteristics of only the faster events (3?6 m s?1) were analyzed in detail. With the use of independent data on the average shape of broken areas, for the first time the form of the function ?(c), the distribution with respect to speed of the length of breaking front per unit area of surface and c?(c), and the fraction of surface turned over per unit time per speed increment were determined. These were found to decrease monotonically with increasing event speed, indicating that these quantities are dominated by the smaller, more frequent breaking events. By making use of the Duncan?Melville expression for the dissipation rate per unit length of a breaking front, the distributions of wave energy dissipation by breaking and of momentum flux to the water by breaking wave impulses are also found for the first time. These were found to be broadband over the whole range of breaker speeds that could be measured reliably, that is, those corresponding to scales of 50%?20% of the dominant wavelength. These results offer no support to 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 small scales. The measurements indicate that, in contrast, dissipation is significant at the largest scales of wave breaking and is distributed widely across that spectrum. If the results are interpreted in terms of equilibrium range wave theory, a value for the numerical constant in the Duncan?Melville expression is inferred that is smaller than the range given by Melville, but a simple expression for the total rate of energy loss from the wind-driven waves is quantitatively consistent with results of upper-ocean turbulence dissipation measurements reported by Terray et al.