Structured Input-Output Analysis of Compressible Plane Couette Flow

This paper extends the recently introduced structured input-output analysis method for incompressible flows to the compressible regime. The proposed method relies upon an exact quadratic representation of the compressible Navier-Stokes equations that allows for efficient modeling and analysis within the structured singular value framework. Specifically, the compressible plane Couette flow is investigated and the structure of the nonlinear forcing is used to formulate an input-output model suitable for the structured singular value analysis. We have outlined an efficient method to compute upper bounds on the structured singular value, which provide insight into flow instability. Numerical results of the proposed framework are included for subsonic, transonic, and supersonic Mach numbers. These results are compared with those obtained from resolvent gain and unstructured input-output analysis. Our findings show that accounting for the structure of the nonlinearity not only reduces the conservatism in the unstructured gains-thereby increasing the estimated stability margin-but also eliminates some of the instability mechanisms predicted by these other analysis tools. Moreover, the structured input-output results reveal instability mechanisms that are not captured by the resolvent analysis. These contradictory findings between the analysis techniques considered need to be substantiated through experimental and/or computational studies in the future.