Anti-pseudoresonance and performance bounds for linearized flow over a compliant surface

This work analyzes the properties of a coupled, linearized fluid-structure system consisting of an incompressible wall-bounded flow over a surface that responds dynamically to interfacial forces. We first characterize a phenomenon where a marginally stable eigenmode introduced by a compliant surface can lead to a reduction in amplification of the coupled system at nearby frequencies, when compared with the corresponding rigid-wall case. The emergence of this behavior, which we term anti-pseudoresonance, is enabled by the non-normality of the fluid system. We additionally identify fundamental limitations in the use of compliant surfaces for the suppression amplification within an adjacent fluid flow, through the application of classical results in linear feedback control. Together, these observations highlight the challenges, potential pitfalls, and counterintuitive behavior that can emerge in the design of compliant surfaces for reducing fluctuations in fluid flows featuring broadband receptivity to disturbances.