R. H. Mellen
I. A. Leykin
Marine Sci. Inst., Univ. of Connecticut, Groton, CT 06340
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(approximately equal to)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.