A Structured Input-Output Framework for Robust Stability Analysis of Compressible Flows

In this work, we propose a structured input-output (I/O) framework for conducting robust stability analysis of compressible flows. This is based on the notion of structured singular value (SSV) from the robust controls literature. The approach accounts for the structure of the nonlinear terms in the governing equations to improve the stability analysis relative to linear approaches. Here, we make use of an exact quadratic representation of the compressible Navier-Stokes equations to efficiently model the nonlinear terms within the structured I/O framework. Moreover, we propose efficient numerical algorithms that exploit additional structure in this representation and refine upper-bound calculations of the SSV. We demonstrate the structured I/O framework on a compressible plane Couette flow over a range of subsonic and supersonic conditions. Results are compared with those obtained from resolvent analysis and unstructured I/O analysis. Our findings show that accounting for the structure of the nonlinearity reveals different instability mechanisms than these other analysis tools.