Dept. of Mech. Eng., Univ. of Houston, Houston, TX 77204-4792
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.