Intensity fluctuations in a quadratic channel

Using previously developed two-scale solutions [S. Frankenthal et al., J. Acoust. Soc. Am. 71, 1124-1130 (1982); B. J. Uscinski, Proc. R. Soc. London Ser. A 380, 137-169 (1982); C. Macaskill, ibid. 386, 461-474 (1983); S. Frankenthal et al., J. Opt. Soc. Am. A 1, 585-597 (1984); A. M. Whitman and M. J. Beran, ibid. 2, 2133-2143 (1985)], the scintillation of acoustic radiation in a random medium with a vertical quadratic mean sound-speed profile is considered. It is assumed that the statistics of the random medium are sufficiently anisotropic that fluctuations in the cross horizontal direction may be neglected. A point source is used as a boundary condition. Numerical calculations are performed for Gaussian and exponential correlation functions. Results are compared to those obtained in the absence of a channel. When the focusing length of the channel is small compared to the distance at which saturation would occur in the absence of a channel, the scintillation index is dramatically affected by the presence of the channel.