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 ? > ?g, much higher than the frequency ?m of the dominant waves. In this dissipation range the spectrum has the form S(?) = ?g2??5 where g is the acceleration due to gravity and ? = 0.025. For spectral wave components at ? ≤ ?g, only a local balance between energy input from the wind and the weak, third-order, nonlinear interaction is important. Asymptotically as ? ? ?m the wind input becomes unimportant, and the wave spectrum has the Kitaigorodskii form of a Kolgomorov analog S(?) = 2a?0? g4/3 ??4 where ?0 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 ?w). From a method of M. S. Longuet-Higgins we estimate the magnitude of the dissipation (due to wave breaking) and find the Kolmogorov constant to be a ≈ 0.6. 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?0? and its dependence on the frequency ?m of the dominant waves at the spectral peak.