The effects of curvature on wake-dominated incompressible free shear layers

Abstract

Instability characteristics of curved incompressible free shear layers, with mean velocity profiles having a wake component, are studied using linear inviscid stability theory in spatial formulation. Both two- and three-dimensional disturbances are considered. The shear layer mode and the wake mode, previously found in a plane shear layer with a wake component in the mean velocity profile, are also found in the corresponding curved shear layer. Results of unstably curved shear layers with a wake component are consistent with those of previous investigations of a curved shear layer without a wake component. Results for a stably curved shear layer with a wake component show that the growth rate of the wake mode increases with increasing shear layer curvature and an oblique wake mode can become dominant compared to its corresponding two-dimensional wake mode. A wake-dominated shear layer, therefore, can become unstable as its curvature increases, regardless of whether the shear layer is stably or unstably curved regarding the corresponding monotonic mixing layer profile. The amplification rates of the shear layer mode and the wake mode could become comparable by varying the free-stream density ratio. For a wake-dominated shear layer under three-dimensional disturbances, the centrifugal modes are found. These modes are developed out of the wake mode for a stably curved shear layer and developed out of the shear layer mode for an unstably curved shear layer. Since the stability behavior is governed by the wake behavior, the wake-dominated shear layer could support the centrifugal instability regardless of the sense of curvature regarding the corresponding monotonic mixing layer profile.