### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

## 5aPA13. Reciprocity-type relations for waves in a moving inhomogeneous
fluid.

**Oleg A. Godin
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*NOAA/Atlantic Oceanogr. and Meteorol. Lab., 4301 Rickenbacker Cswy.,
Miami, FL 33149
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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.]