A reduced resolvent model of linear amplification mechanisms in channel flow

The linearized Navier-Stokes (LNS) equations are employed in channel flow to study linear amplification mechanisms. We examine wave-number regions corresponding to streamwise streaks, oblique waves and Tollmien-Schlichting waves, linking these mechanisms back to the linearized Navier-Stokes equations. In particular, we examine the Orr-Sommerfeld and Squire (OSS) equations from an input-output point of view, considering the full LNS system, and a reduced model in which the OSS equations are considered separately as subsystems. This approach enables individual analysis of the Orr-Sommerfeld and Squire systems, revealing the relationship between linear amplification and the linear mechanisms from which it arises. In order to accomplish this, we use a Reynolds number scaling argument to justify the simplification of pathways in the linear model. Results indicate that the Orr-Sommerfeld system contains amplified regions for all three flow features, while the Squire system only amplifies streamwise streaks and oblique waves. Analysis is performed for laminar Poiseuille flow, laminar Couette flow, and turbulent Poiseuille flow using an eddy-viscosity model. Additionally we compare modal structures between the full and reduced models using singular value decomposition.