Decomposition of the forcing to the compressible resolvent operator for laminar and turbulent boundary layers

Recent work by Bae et al. (J. Fluid Mech., vol. 883, 2020, pp. 336–382, pp. A29) used the resolvent analysis framework of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to show that, within the regime of compressible turbulent boundary layer flows, the linearized Navier-Stokes equations capture two distinct sets of modes: the relatively subsonic modes that have an equivalent in the incompressible flow regime, and the relatively supersonic modes. In the current work we aim to analyze if the forcing to this compressible resolvent operator for boundary layers can be appropriately decomposed so as to isolate these relatively subsonic and relatively supersonic modes. We verify this decomposition of the forcing in laminar and turbulent boundary layers, with and without wall cooling. Implications for low-order modeling and connections with the incompressible resolvent operator will be briefly described.