Spatio-temporal eigenmodes of plane-Poiseuille flow interacting with a finite compliant panel

Abstract

This paper presents and deploys a hybrid computational and theoretical technique to study the stability of a fluid-structure system that comprises fully developed plane Poiseuille flow at transitional Reynolds numbers over a finite flexible wall of streamwise extent. This builds upon recent work involving a uniform inviscid flow interacting with a flexible plate held at both its ends to include consideration of the full spatio-temporally evolving, rotational flow dynamics. Although presently considering the two-dimensional case the method may be extended to three-dimensions and arbitrary mean-flow fields other than plane Poiseuille.We show how stability diagrams for the fully-coupled finite flow-structure system can be assembled, identifying classes of wall-based or fluid-based and spatio-temporal wave behaviour in the system. In doing so we present a new and versatile approach to the modelling of the fluid-structure interaction (FSI) of a finite flexible wall. The method lies between classical hydrodynamic-stability theory and direct numericalsimulation and enjoys a combination of the benefits of both of these hitherto distinct approaches to FSI problems.