A model of the intensity probability distribution for wave propagation in random media

Ewart and Percival [J. Acoust. Soc. Am. 80, 1745 (1986)] have shown that the generalized gamma distribution effectively models intensity probability distributions of temporal fluctuations observed in a field experiment and transverse spatial fluctuations simulated in numerical experiments. In both cases the fluctuations are due to wave propagation through a medium with a random index of refraction. Here, the transverse spatial intensity fluctuations of a wave propagating through a medium with a power‐law autocorrelation function of wave speed are modeled over a regime that spans 10⁸ in scattering strength and 10⁶ in scaled range (range divided by the Fresnel length). This scattering parameter regime transforms to ranges between 100 m and 100 km and to frequencies between 100 Hz and 100 kHz when normalizations typical of observed ocean internal wave fluctuations are used. Contour plots of the variance, skewness, and kurtosis of the intensity distribution are presented for the range/frequency plane. It is shown that the region of saturation, i.e., exponential intensity distribution, cannot be attained except for very large source strengths. Also, the lognormal intensity distribution, which is assumed for scintillation indices near zero, can be applied only in the region of vanishingly small intensity fluctuations. This work, while based on plane‐wave propagation and a fourth‐order power‐law transverse spectrum of the medium, retains the essential character of the intensity fluctuations and provides a prescription for modeling the intensity distribution for any medium where the random index of refraction process can be assumed stationary.