209 1998 Bernhard Muller bernd@tdb.uu.se On sound generation by the Kirchhoff vortex Abstract A 2D test case for low Mach number computational aeroacoustics is provided. The Kirchhoff vortex is an elliptical patch of constant vorticity rotating with constant angular frequency in irrotational flow. This 2D flow field constitutes an exact solution of the 2D incompressible Euler equations. Due to its unsteadiness in the inertial frame of reference, the Kirchhoff vortex generates sound. Here, the exact incompressible velocity and pressure distributions and a low Mach number approximation of the farfield acoustic pressure are stated. Moreover, the Helmholtz equation is exactly solved to yield the complete acoustic pressure field of an almost circular Kirchhoff vortex.