Mechanisms of non-modal energy amplification in channel flow between compliant walls

The mechanisms leading to large transient growth of disturbances for the flow in a channel with compliant walls are investigated. The walls are modelled as thin spring-backed plates, and the flow dynamics is modelled using the Navier-Stokes equations linearized round the Poiseuille profile. Analysis for streamwise invariant perturbations show that this fluid-structure system can sustain oscillatory energy evolution of large amplitude, in the form of spanwise standing waves. Such waves are related to the travelling waves which a free wall can support, modified to account for an 'added mass' effect. Simple scaling arguments are found to provide results in excellent agreement with computations of optimal disturbances, for low-to-moderate values of the stiffness parameter characterizing the compliant surface.