The interaction of a hollow vortex with an inclined plane and the acousticradiation produced

A hollow vortex of circulation Gamma and core radius a is created above a r igid infinite plane which is inclined at angle 1/2 pi - alpha to the undist urbed vortex lines, where alpha is small. The fluid is assumed to be invisc id and slightly compressible. The deformation of the filament is a source o f acoustic radiation, which is calculated on the assumption that the source is compact, which will be true if the time since the creation of the filam ent is not too large. The acoustic pressure field at a large distance R fro m the region of interaction is of order of magnitude alpha rho(0)Gamma(2)M/aR and has a strong directionality, which is calculated. Here, rho(0) is the a mbient density and ni is the Mach number based on the circumferential speed of fluid particles in the hollow vortex boundary. Insertion of values of t he constants for the vortex sized from a helicopter rotor blade suggest tha t the interaction might be a significant noise source.