Absolute and convective instability study of weakly compressible mixing layers

Abstract

This is an analysis of stability study of weakly compressible mixing layers under non-homentropic flow conditions. The condition of non-zero group velocity required for convective instability analysis was seen to give new findings as stated below. Also, the dispersion relationships are functions of the cross-stream derivatives, Mach number and chemical reaction parameters. Three modes of oscillations for developing mixing layer were chosen based on previous findings of the author and later in this work their possible validity were confirmed as follows. Jet mode (Mode I), mixed mode (Mode II) and fully developed mixing layer mode (Mode III) oscillations for developing mixing layers are considered in this study. Using impulse response technique it is seen that for symmetric temperature profile, Mode I is absolutely unstable, Mode II is both convectively and absolutely unstable, partially each, an Mode III is dominantly convectively unstable with pockets of absolute instability. For the asymmetric temperature profile of <i>T</i>= 1+ λ tanh (<i>y</i>), Mode I is weakly convectively unstable. Mode II is weakly absolutely unstable and Mode III is convectively unstable for major regions of the flow.