Excitation of instability waves in free shear layers. Part 1. Theory

Abstract

The generation of instability waves in free shear layers is investigated theoretically. The model assumes an infinitesimally thin shear layer shed from a semi-infinite plate which is exposed to sound excitation. For this model the forced instability waves are calculated. The shear-layer excitation by a source farther away from the plate edge in the downstream direction is very weak while upstream from the plate edge the excitation is relatively efficient. A special solution is given for the source at the plate edge. Any type of source farther away from the plate edge produces a parabolic pressure field near the edge. For this latter, fairly general case, a reference quantity is found for the magnitude of the excited instability waves. The theory is then extended to two streams, one on each side of the shear layer, having different velocities and densities. Furthermore, the excitation of a shear layer in a channel is calculated. The limitations to the theory and some aspects related to experiments are discussed. In particular, for a comparison with measurements, numerical computations of the velocity field outside the shear layer have been carried out.