Sensitivity of wavepackets in subsonic coaxial jets

Coaxial jets are widely applied in Aeronautics and Astronautics. However great limitation generally exists for predicting wavepackets and noise by theoretical models based on linear mechanisms, and the effect of nonlinearity has become a research hotspot recently. The effects of nonlinearity on wavepackets in subsonic coaxial jets with different velocity ratios are studied by adding external harmonic forcing to linear Parabolized Stability Equations (PSE). The present work focuses on investigating wavepacket model of coaxial jets due to the fact that there are two distinct shear layer modes. With the mean flow of coaxial jets, the linear model of wavepackets based on PSE is constructed, while the sensitivity of total disturbance energy with respect to external forcing is obtained by solving the adjoint PSE (APSE). The results show that the sensitivity and flow response reach their maximum around the inner and outer critical layers, both of them turn out to be sensitive to external forcing, while the mutual influence between two instability modes can be identified in the downstream region. Finally, the optimal forcing for the outer mode is obtained using an APSE based optimization methodology, giving rise to more rapid growth of wavepackets.