### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 4pSA4. Waves in random media: Coherent and fluctuating parts, energy
distribution.

**Samuil A. Rybak
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*N. N. Andreyev Acoustics Inst., 117036 Shvernik Str. 4, Moscow, Russia
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Waves in media with fluctuating parameters are described with the help of a
Green's function method. For the average field, the integral Dyson equation is
formulated and its solution is obtained by means of the Bourret approximation.
The average field (coherent part) decays exponentially with distance from the
point source while the fluctuations grow. The Bethe--Salpeter equations are
formulated for the average energy distribution. The ``ladder'' approximation
then gives a system of transport integral equations which resemble heat
transport equations. For the validity of the theory some threshold level of
dissipation in the medium is necessary. The distribution of the fluctuations of
the parameters is taken to be Gaussian. The solutions for energy distribution
have an exponential decay with the index proportional to the root of the
dissipation coefficient of the medium. In waveguides with fluctuating parameters
the wave modes are coupled and both the coherent parts of these modes and the
energy distributions are not independent. The energy fluxes become equal for
traveling normal waves. Elastic plates with fluctuating parameters are examples
of such waveguides for coupled longitudinal and flexural waves. Verification of
the theory was made with the help of direct calculations for some simple models.