R. H. Mellen
Marine Sci. Inst., Univ. of Connecticut, Groton, CT 06340
Measurements of phase fluctuations in sound propagation through turbulent air show frequency spectra that approximate the Kolmogorov (beta)=5/3 scaling law over several decades. This suggests a fractal-like process for which the apparent fractal dimension would be D=(5-(beta))/2(approximately equal to)5/3. However, most natural phenomena are found to be multifractal rather than monofractal. Multifractal theory treats, not only first and second moments of the process, but also the relation between moments (including nonintegral). For monofractals, this relation is simply a linear function of the moment number and a codimension 0(less than or equal to)C[sub 1](less than or equal to)1. The degree of multifractality 0(less than or equal to)(alpha)(less than or equal to)2 is determined from systematic deviations from linearity. The parameters (alpha), (beta), and C[sub 1] are all indicators of the nature of the nonlinear energy cascade. Analysis of experimental data obtained at 5 kHz, range (approximately equal to)4 m and wind speed (approximately equal to)12 m/s is reported here. Results indicate that phase fluctuations are ``hard multifractal'' ((alpha)>1), which is comparable to measures of velocity fluctuations in atmospheric turbulence.