### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 5aEA2. Two-sound-pressures theorem for aerodynamic sound from
two-dimensional flows.

**Brenda Henderson
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*Dept. of Mech. Eng., Univ. of Houston, Houston, TX 77204-4792
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The three-sound-pressures theorem [A. Powell, J. Acoust. Soc. Am. 34,
902--906 (1962)] applies to sound generated by inviscid, incompressible, free
flows when the source region is acoustically compact and shows that the
acoustic far field must be reducible to lateral quadrupole radiation only. In
two dimensions, the source region is not compact in the third dimension so it
is not obvious that the three-sound-pressures theorem directly applies in this
case. The two-sound-pressures theorem is developed by integrating Lighthill's
source term over the ``third'' dimension and is shown to be satisfied by
two-dimensional lateral quadrupole radiation. In all known two-dimensional
situations, the two-sound-pressures theorem is satisfied. A simple
two-dimensional line vortex problem involving the collision of four rectilinear
vortices is presented as an illustration.