Saturation effects associated with sound propagation in a turbulent medium

A theoretical analysis of the acoustic wave field radiated by a time-harmonic point source in a homogeneous, isotropic turbulent medium is presented. The smoothing method is used to study the incoherent, or randomly fluctuating, component of the wave field. The analysis considers the effect on the wave of the velocity fluctuations, as well as the index-of-refraction fluctuations, of the medium. An approximate expression for the second moment of the incoherent wave is obtained for the case in which the wavelenght is much less than the minimum correlation length of the medium. This expression shows that the fluctuations of the wave increase initially in proportion to the propagation distance, but that at larger distances they tend to a limiting, or saturation, value. These results agree with observations of waves propagating in real media. It is also found that the mean square of the total (i.e., coherent plus incoherent) acoustic pressure is unaffected by the randomness of the medium.