Finestructure of Wind Waves Analyzed with Wavelet Transform

One central problem in the study of wind-generated gravity waves is the energy balancing process in the equilibrium spectral subrange. In considering the predicted equilibrium spectral forms from physical models proposed by Kitaigorodskii, other investigators accepted that the statistical equilibrium state is effectively characterized by the wave action conservation law: δE/δt+C⃗g·∇E = 0, where E is the wave energy spectrum and C⃗g = ∇kω(k) is the group velocity. Here the continuous wavelet transform is used to analyze typical sets of wind-generated gravity wave data obtained both in the ocean and in a wind-wave channel. This "space scale" analysis is shown to provide the first visual evidence that when the fetch is not very short, the wave action conservation law mentioned above is not convenient to describe the dynamics of the wave components in the equilibrium range estimated from its energy spectrum.