Reciprocity and energy theorems for waves in a compressible inhomogeneous moving fluid

Abstract A flow reversal theorem (FRT) is established in this paper for sound and acoustic-gravity waves in an arbitrary inhomogeneous moving steady ideal fluid. The theorem is an extension for moving fluid of the reciprocity principle valid in quiescent media. The FRT states symmetry of some wave field quantity with respect to interchange of the source and receiver positions and the simultaneous reversal of the ambient flow. A simple but rather general proof of the FRT becomes possible due to a particular choice of a mixed Eulerian-Lagrangian description of fluid motion. Relation between the FRT proved and a number of known FRTs established earlier for various specific cases is analyzed. 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 discused. Some possible applications of the FRT and the conservation laws in the investigation of sound generation and propagation in a moving medium are considered.

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