## 2aPAb9. The Kirchhoff--Helmholtz integral theorem and related identities for waves in an inhomogeneous moving fluid.

### Session: Tuesday Morning, May 14

### Time: 10:45

**Author: Oleg A. Godin**

**Location: School of Earth and Ocean Sciences, Univ. of Victoria, P.O. Box 1700, Victoria, BC V8W 2Y2, Canada**

**Abstract:**

The Kirchhoff--Helmholtz integral theorem (KHT), which expresses the wave
field in a volume inside (or outside) a given surface in terms of the field's
value on the surface, is well known and widely used in acoustics of motionless
media. In this paper, an extension of the theorem to acoustic-gravity waves in
an arbitrary inhomogeneous moving fluid is obtained as a corollary of the
reciprocity-type relations constituting the recently established flow reversal
theorem (FRT) [O. A. Godin, J. Acoust. Soc. Am. 97, 3396(A) (1995); 98, 2866(A)
(1995)]. The KHT takes a concise form when stated in terms of acoustic pressure
and oscillatory displacement of fluid particles. The KHT is applied to study
uniqueness of solutions to acoustic boundary value problems in moving media and
to establish unitarity and other general properties of the scattering matrix for
surface and volume scattering as well as in an irregular (range-dependent)
waveguide with flow. Relation of the scattering matrix properties to the FRT and
to wave-action conservation is discussed. [Work supported by NSERC.]

from ASA 131st Meeting, Indianapolis, May 1996