Adjoint-based analysis of jet-in-crossflow linear instability

Experiments and direct numerical simulations have demonstrated that the jet-in-crossflow (JICF) features coherent upstream shear layer oscillations in a manner consistent with linear stability analyses, where the shear layer is convectively unstable at relatively large jet-to-crossflow velocity ratios R and absolutely unstable at low R. Small perturbations applied near the jet exit, through either passive or active means, are known to affect these shear layer instabilities, in addition to affecting jet structure and mixing. This work investigates the effect of base flow deviations, such as those created by such perturbations, on JICF linear stability characteristics. The continuous 1D linear stability analysis of Alves, et al., JFM 2008 is extended to an adjoint-leveraged 2D stability analysis to (i) determine the dominant spatial growth rates for the convectively unstable JICF more accurately, (ii) establish the onset of absolute instability for different flow conditions and downstream locations, and (iii) determine the sensitivity of spatial growth rates and onset of absolute instability to base flow modifications.