Sensitivity analysis using adjoint parabolized stability equations for compressible flows

An input/output framework is used to analyze the sensitivity of two- and th ree-dimensional disturbances in a compressible boundary layer for changes i n wall and momentum forcing. The sensitivity is defined as the gradient of the kinetic disturbance energy at a given downstream position with respect to the forcing. The gradients are derived using the parabolized stability e quations (PSE) and their adjoint (APSE). The adjoint equations are derived in a consistent way for a quasi-two-dimensional compressible flow in an ort hogonal curvilinear coordinate system. The input/output framework provides a basis for optimal control studies. Analysis of two-dimensional boundary l ayers for Mach numbers between 0 and 1.2 show that wall and momentum forcin g close to branch I of the neutral stability curve give the maximum magnitu de of the gradient. Forcing at the wall gives the largest magnitude using t he wall normal velocity component. In case of incompressible flow, the two- dimensional disturbances are the most sensitive ones to wall inhomogeneity. For compressible flow, the three-dimensional disturbances are the most sen sitive ones. Further, it is shown that momentum forcing is most effectively done in the vicinity of the critical layer.