Nonlinear dynamics of wind waves: Multifractal phase/time effects

Recent analyses of the phase/time behavior of wind waves have shown self‐similarity, the power spectra of the phase fluctuations having no characteristic frequency scale. This has suggested fractal properties and a fractal dimension of D≊1.4 has been estimated from data obtained at sea and in the laboratory [R. Mellen and I. Leykin, J. Acoust. Soc. Am. 91, 2319 (A) (1992)]. However, analyses of a broad range of natural phenomena have demonstrated multifractal properties [S. Lovejoy and D. Schertzer, ‘‘Multifractals in Geophysics,’’ AGU/CGU/MSA, 1992 Spring Meeting]. The theory considers, not simply the second moments, but relations between moments including nonintegral. This provides a quantitative link with the nonlinear dynamics of the process involved. Analysis of laboratory wave data is reported here and the results suggest that the phase fluctuations are ‘‘hard multifractal’’‐like turbulence. Implications for backscattering from ocean waves are considered.