Sensitivity and uncertainty quantifications for jet stability analysis

The paper is twofold. It aims first to validate and compare adjoint-based sensitivity and other sensitivity methods and their possible relation to Uncertainty Quantification analysis. These methods, illustrated on a simple toy-models can be a lower cost tool for mathematical analysis of complex problems of industrial interests. The second objective is to propose an Uncertainty Quantification of the compressible single stream jet stability subjected to frequency variation. The governing equations are the low cost model called Parabolized Stability Equations. This objective is strongly related to the noise sensitivity and control studies since it has been demonstrated that noise is originated from K-H instability in such a flow. Later, the adjoint PSE approach will be used, to make the link between sensitivity and UQ analysis as this quantification for Large Eddy Simulations or Reynolds Average Navier-Stokes simulations can be considerably expensive. Envelope curves of the standard deviation are determined and compared with good agreement for small variations of the input parameters in the first toy model. For the jet stability, it has been found that the growth rate is almost insensitive to small frequency variations and, on the other hand, the phases of the amplitude functions of the disturbance are extremely sensitive to frequency