### ASA 125th Meeting Ottawa 1993 May

## 5aPA7. Sound propagation through atmospheric turbulence: Multifractal
phase fluctuations.

**R. H. Mellen
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G. Siling
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*Marine Sci. Inst., Univ. of Connecticut, Groton, CT 06340
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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.