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Reciprocity and energy theorems for waves in compressible inhomogeneous moving fluid. (English) Zbl 0930.76080
Summary: We establish a flow reversal theorem (FRT) for sound and acoustic-gravity waves in an arbitrary inhomogeneous moving steady ideal fluid. The theorem is an extension to moving fluid of the reciprocity principle valid in quiescent media. The FRT states symmetry of some wave field quantity with respect to interchange of source and receiver positions, and to the simultaneous reversal of the ambient flow. A proof of the FRT becomes possible due to a particular choice of a mixed Eulerian-Lagrangian description of fluid motion. We also discuss relations between the FRT proved and a number of known FRTs estabilshed earlier for various particular cases. Wave quasi-energy and wave-action conservation laws, related to the FRT, are proved for linear waves in an inhomogeneous moving steady compressible fluid. Validity domains of the FRT and the conservation laws are outlined, and some applications of the FRT and conservation laws to the investigation of sound generation and propagation in a moving medium are considered.

MSC:
76Q05 Hydro- and aero-acoustics
76N15 Gas dynamics (general theory)
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