On the influence of internal density variations on the linear stability characteristics of planar shear layers

Abstract

Planar shear layers are known to be sensitive to density variation within the vorticity region. The current study will expand on the available literature on the stability characteristics of shear layers with density variation through consideration of new regimes in terms of the velocity and density profiles. Both spatial and spatio-temporal linear analyses were considered. In addition to the maximum density change within the shear layer, the effect of density to vorticity thickness ratio, and transverse shifting of the density profile relative to the velocity profile were considered. For a shear layer experiencing combustion, these effects relate to the relative position and thickness of the flame in the shear layer. Thick density profiles have a stabilizing affect that imposes essentially a low-pass attenuator modulation on the spatial stability. The shear layer is destabilized through the presence of an intense yet thin density reduction that overlaps with the peak vorticity profile, a condition that may be present near the shear layer origination point. The velocity ratio at which the flow transitions between absolute and convective instability is dependent on the magnitude of the density reduction in the shear layer as well as the relative density profile thickness and transverse location. The results generally indicate that the instability of the planar shear layer is strongly influenced by the characteristics of the density-weighted vorticity distribution within the shear layer.