Dependence of whitecap coverage on wind and wind-wave properties

Abstract

Using Phillips equilibrium range theory and observational data, we show first that the total rates of wave energy dissipation estimated by the Hasselmann and Phillips dissipation models are substantially consistent with each other, though their original forms are different. Both are proportional to the cube of air friction velocity, u*3, with a weak dependence on wave age. As a direct manifestation of the wave energy dissipation processes, we reanalyze previous observational data of whitecap coverage and find that it has greater correlation with the wind speed or friction velocity than the wave period or wave age. However, the data scatter decreases remarkably when the breaking-wave parameter RB= u*2/νωp is used, where ν is the kinematic viscosity of air, and ωp, the wind-wave spectral peak frequency. Physical interpretation of RB with some related issues, and a discussion of the probability models of whitecap coverage in terms of a threshold mechanism, are also presented. We conclude that RB is a good parameter to effectively express the overall wave breaking behavior for the case of wind-waves in local equilibrium with the wind. Since RB can be expressed as the product of u*3 and the wave age, this result demonstrates a stronger dependence of whitecap coverage on wave age than expected by the previous description by power-laws of u* and by the two theoretical models. Our conclusion suggests that current dissipation models should also be modified to represent full properties of wind-wave breaking.