Non viscous sensitivity analysis of noise generation mechanism in a low Mach number jet

The first step of the sensitivity analysis of some quadratic quantity related to acoustic waves with respect to any flow or wall disturbance is proposed in the configuration of subsonic jet flow. The generation of noise has been demonstrated to originate from convective instabilities that amplify in the jet stream. Several authors have investigated them through the Parabolized Stability Equations approach (PSE). The present work aims to develop the adjoint of the PSE to extract from a mathematically well posed problem the sensitivity coefficients which can be understood as gradient. The final objective is to propose some path of possible actuations in order to decrease noise emission in some jet flows. To date some trend can be given. The shape and the location of the maximum of sensitivity are strongly related to the radial and streamwise variation of the base flow. In particular the maximum of sensitivity is located along the border of the potential cone and seems to be well correlated with the location of the sound generation mechanism. In addition the sensitivity to axial momentum forcing is higher than to a radial momentum forcing. Finally the sensitivity increases when the perturbation is near to the exit of the nozzle