TY - JOUR

T1 - Propagation of radiation in time-dependent three-dimensional random media

AU - Beran, Mark J.

AU - Frankenthal, Shimshon

AU - Deshmukh, Venkatesh

AU - Whitman, Alan M.

PY - 2008/8

Y1 - 2008/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=47549119791&partnerID=8YFLogxK

U2 - 10.1080/17455030802078429

DO - 10.1080/17455030802078429

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AN - SCOPUS:47549119791

SN - 1745-5030

VL - 18

SP - 435

EP - 460

JO - Waves in Random and Complex Media

JF - Waves in Random and Complex Media

IS - 3

ER -