The dissipation range of wind-wave spectra observed on a lake

Abstract

Based on an interpretation of a field experiment it is argued that, due to breaking of wind waves in deep water, the dissipation of energy is restricted to a range of frequencies "SUB g" much higher than the frequency "SUB m" of the dominant waves. In this dissipation range the spectrum has the form S = betag "SUP 2-5" where g is the acceleration due to gravity and beta = 0.025. For spectral wave components at l or = "SUB g" , only a local balance between energy input from the wind and the weak, third-order, nonlinear interaction is important. Asymptotically as mmt "SUB m" the wind input becomes unimportant, and the wave spectrum has the Kitaigorodskii form of a Kolgomorov analog S= 2a epsilon "SUB o" "SUP 1/3" g "SUP 4/3 -4" where epsilon "SUB o" is a constant flow of mean energy per unit surface area through the spectrum dissipated at high frequencies (when multiplied by g and water density "SUB w" ). From a method of M.S. Longuet-Higgins the magnitude of the dissipation (due to wave breaking) is estimated and Kolmogorov constant is found to be a approx0.6. When a model, explained by Phillips, for wind energy input to the wave spectrum is applied to a simplified spectral model prescribing the scales of dissipation and growth of spectral wave components, good agreement is found with measurements by Donelan et al. of the coefficient 2a epsilon "SUB o" "SUP 1/3" and its dependence on the frequency omega "SUB m" of the dominant waves at the spectral peak. (A)