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.]