A KINETIC EQUATION FOR WAVE PROPAGATION IN RANDOM MEDIA

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Abstract
This paper discusses the multiple scattering of waves in randomly inhomogeneous media. An asymptotic, multiple-scales analysis is presented which leads to a kinetic equation describing the evolution in space and time of wave energy in wave-number space. A wide class of scalar wave propagation problems is considered by means of an approach based on the use of a Lagrangian density. The analysis confirms the results of heuristic arguments presented in a companion paper. The example of nondispersive waves propagating in a medium in which the refractive index is a random function of position is used to demonstrate that the theory recovers well-known results of single scattering theory and geometrical optics (ray theory) in the respective opposite asymptotic extremes of wavelength long and short compared to the correlation scale of the inhomogeneities. This, it is argued, gives confidence in the ability of the theory to make predictions at intermediate wavelengths which cannot be treated by classical methods.

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