On the influence of density-weighted vorticity on the linear stability characteristics of planar shear layers
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The objective of this research is to investigate the stability characteristics of planar shear layers with density variation. It is well known that variation in the mean density profile through the shear zone, induced through compressibility and/or heat release effects, has a strong influence on the characteristics of a planar shear layer. 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 field. Both spatial and Spatio-temporal linear analyses are considered. The approach is based on the solution of the eigenvalue problem corresponding to normal mode decomposition of the linearized governing equations. Due to the complexity of the problem, numerical procedures are used to determine the eigenvalue and the eigenfunctions. In addition to the density ratio (max/min shear layer density to the freestream density), the effect of density to vorticity thickness ratio, and transverse shifting of the density profile relative to the velocity profile are considered. For a shear layer experiencing combustion, these effects relate to the position and thickness of the flame in the shear layer. It was found that the relative thickness of the density profile plays a key factor in the conditions under which a reacting planar shear layer transitions between convective and absolute instability. It is anticipated that the results will shed insight on understanding a broad range of reacting shear layers, and how these flows can be controlled through manipulation of the convective/absolute stability nature of the flow.