Propagation of radiation in time-dependent three-dimensional random media

Mark J. Beran*, Shimshon Frankenthal, Venkatesh Deshmukh, Alan M. Whitman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


In Ref. [1] (Appendix A) we derived equations governing the frequency and spatial spectrum of radiation propagating in three-dimensional time-dependent random media with randomly varying sound speed c (x, t). From the spectral equations we determine equations for the energy flux in both the forward and backward directions. We consider media that are spatially homogeneous and isotropic and stationary in time. In order to allow an independence assumption the analysis is restricted to fluctuations that satisfy the conditions τμ ≫ Lz/c0 and τμ ≪ LFS/ c0 where τμ is the characteristic time of the fluctuations, k0 is the mean radiation wavenumber, Lz is the characteristic correlation length of the random fluctuations in the mean propagation direction and LFS is a mean scattering length. We consider various values of γ = (k0 Lz)2/2. When γ ≪ 1 we find the usual radiation transfer equations. When γ ≫ 1, but back-scattering can be neglected, we find the forward-scattering equations. We also consider γ ≫ 1, when back-scattering cannot be neglected. We consider as initial boundary conditions a plane wave and an infinite incoherent source. We present numerical solutions for γ ≪ 1, γ = O (1) and γ ≫ 1 using a simple Gaussian form for the fluctuation correlation function.

Original languageEnglish
Pages (from-to)435-460
Number of pages26
JournalWaves in Random and Complex Media
Issue number3
StatePublished - Aug 2008


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