Oleg A. Godin
NOAA/Atlantic Oceanogr. and Meteorol. Lab., 4301 Rickenbacker Cswy., Miami, FL 33149
The reciprocity principle is known to be invalid for acoustic waves in a moving fluid due to differences in up- and down-flow wave propagation velocities. A variation of the reciprocity principle, a flow reversal theorem (FRT), which states symmetry of some field quantity with respect to interchange of the source and receiver positions and the simultaneous reversal of flow, was considered by many authors during the last four decades. It was proven under that or other specific assumptions about fluid parameters and/or flow velocity space dependence or in a framework of some asymptotic representations of the acoustic field. A simple but rather general proof of the FRT will be presented which is valid for sound as well as acoustic-gravity waves in an arbitrary three-dimensional inhomogeneous moving fluid with time-independent parameters provided divergence of the flow velocity is zero. The fluid may be unbounded or have pressure-release, rigid, or impedance boundaries. The key point in the approach is the choice of a set of dependent variables in hydrodynamic equations for describing the wave field. An implication of the FRT on wave action conservation for cw sound in moving fluid is considered. Some possible FRT applications are indicated. [Work supported by NRC.]