Inviscid instability characteristics of free shear layers with non-uniform density

Abstract

The linear spatial instability of two-dimensional two-stream plane mixing layers has been studied extensively in the past. In the case of uniform density, Michalke (1965) investigated the single-stream shear layer and Monkewitz & Huerre (1982) considered the effect of the velocity ratio. Maslowe & Kelly (1971) studied the stratified (non-uniform density) shear layers and showed that density variations can be destabilizing. In all these studies, the mean velocity profile has been assumed to be monotonically increasing from the value on the low-speed stream to that on the high-speed stream and usually the hyperbolic tangent form is used. It should be noted, however, that under experimental conditions the initial mean velocity profile almost always has a wake component due to the boundary layers on the two sides of the splitter plate. The effect of the wake component has only recently come into consideration with the investigations of Miau 1984 and Zhang et al. 1984 for the uniform density case. The purpose of the present work is to study the instability characteristics of both uniform and non-uniform density plane shear layers taking into account the wake component of the initial velocity profile. The inviscid, linear, parallel-flow stability analysis of spatially growing disturbances is utilized to numerically calculate the range of unstable frequencies and wave-numbers.