Abstract
The previous results of Blokhintzev and of Bretherton and Garrett [Proc R. Soc. (1968)] concerning wave action conservation in slowly varying moving inhomogeneous fluids are shown to also apply when the ambient state is time dependent. Also, a simple consistent set of approximate fluid dynamic equations is derived which implicitly contains all geometrical acoustics theory but which also governs diffraction phenomena (e.g., caustics). Möhring's [AIAA paper (1977)] energy conservation explanation of S. Davis's (J. Acoust. Soc. Am. 59, 264–266 (1976) reciprocity theorem is reinterpreted in terms of wave action. If an acoustic wave is transmitted through a narrow tube with variable cross-section transition carrying an inhomogeneous flow, the sum, wave action transmitted plus reflected, is equal to wave action incident. The fractions reflected and transmitted are independent of direction of incoming wave.
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