Emendation of the Brown & Michael equation, with application to sound generation by vortex motion near a half-plane

(Received 24 February 1996 and in revised form 11 July 1996) A reappraisal is made of the Brown & Michael (1954, 1955) equation that is widely used to model high-Reynolds-number vortex shedding in two dimensions by rectilinear vortices of time-dependent circulations. It is concluded that the equation introduces an unbalanced and unacceptable surface force that can significantly influence predicted flow characteristics. A corrected equation is derived which removes this force, and is applied to determine the sound generated at low Mach numbers when a line vortex translates around the edge of a rigid half-plane. The solution of this problem in the absence of vortex shedding (Crighton 1972) is extended by permitting shedding to occur at the edge in accordance with the unsteady Kutta condition. The shed vorticity is assumed to roll-up into a concentrated core whose motion is calculated by both the emended and original Brown & Michael equations. The two models exhibit large qualitative differences in the predicted wake flow near the edge ; both predict significant reductions in the radiated sound, but the reduction is smaller by about 4 dB for the emended Brown & Michael equation.