Absolute and convective instabilities in free shear layers

The absolute or convective character of inviscid instabilities in parallel shear flows can be determined by examining the branch-point singularities of the dispersion relation for complex frequencies and wavenumbers. According to a criterion developed in the study of plasma instabilities, a flow is convectively unstable when the branch-point singularities are in the lower half complex-frequency plane. These concepts are applied to a family of free shear layers with varying velocity ratio R = U/2U, where Δ U is the velocity difference between the two streams and U their average velocity. It is demonstrated that spatially growing waves can only be observed if the mixing layer is convectively unstable, i. e. when the velocity ratio is smaller than R t = 1. 315. When the velocity ratio is larger than R t, the instability develops temporally. Finally, the implications of these concepts are discussed also for wakes and hot jets.