On the Theory of the Equilibrium Range in the Spectrum of Wind-Generated Gravity Waves

Abstract

It is shown that an exact analog of Kolmogoroff's spectrum in a random field of weekly nonlinear surface gravity waves gives a spectral form for frequency spectra S(ω) ∼ ω−4 in close agreement with the results of recent observational studies. The proposed theory also indicates the existence of a “transitional” range of wavenumbers (frequencies) where the deviation from Kolmogoroff's equilibrium is due to gravitational instability (wave breaking). Because of this it is suggested dot the equilibrium form for the spectrum of wind-generated waves has two asymptotic regimes: Kolmogoroff's and Philips' type of equilibrium with a relatively rapid transition from the first to the second. The experiments data favor such an interpretation.