A Variational Principle for Wave Propagation in Random Media

Details A Variational Principle for Wave Propagation in Random Media A Variational Principle for Wave Propagation in Random Media

Feb 1972

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1972ap%26ss..15..206l&link_type=abstract

Astrophysics and Space Science, Volume 15, Issue 2, pp.206-213

Astronomy and Astrophysics

Astrophysics

Scientific paper

We set up a variational integral appropriate for discussing the ‘eigenvalues’ of theexact probability equation describing wave propagation in a turbulent medium. We demonstrate that:
(i)
Extremal variations of the integral with respect to an adjoint probability field gives the probability equation (which is not self-adjoint) relevant to wave propagation in the random medium.
(ii)
Extremal variations of the integral with respect to the probability field gives the adjoint probability equations.
(iii)
Extremal variations of the integral with respect to trial functions for both the probability field and its adjoint gives a variational principle for calculating the normal mode eigenvalues describing wave propagation in the turbulent medium. We illustrate the power, and accuracy, of the variational approach by several illustrative examples.

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