Absolute and convective instabilities in free shear layers

TLDR

In parallel shear flows, the absolute or convective nature of inviscid instabilities is identified by the location of branch‑point singularities in the complex‑frequency plane, with convective instability occurring when these singularities lie in the lower half‑plane. The authors apply this criterion to free shear layers whose velocity ratio varies relative to the mean flow. They find that spatially growing waves occur only when the velocity ratio is below Rt = 1.315, while above this threshold the instability is temporal, and they discuss the implications for wakes and hot jets.

Abstract

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 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 Rt = 1.315. When the velocity ratio is larger than Rt, the instability develops temporally. Finally, the implications of these concepts are discussed also for wakes and hot jets.