Global instability in a plane jet with flexible nozzle

The stability of free jets is one of the fundamental problems that has driven the development of new theoretical and numerical methods in fluid mechanics. Extensive research has focused on the convective instabilities that characterise their elusive dynamics. However, in real-world configurations, free jets are often confined by solid walls which may exhibit different degrees of flexibility. The present paper presents, for the first time, evidence that even slightly flexible nozzles can lead to global instabilities. To show it, we adopted the classical tools of linear stability analysis, solving the fluid–structure interaction (FSI) problem by an arbitrary Lagrangian–Eulerian method, formulating a monolithic three-field problem. The investigation of the base flow properties reveals the effect of the Reynolds number, based on the bulk velocity and channel height, in the range $[50,200]$ and of the plate stiffness on the nozzle deformation and on the jet flow development. Exploiting an idea first proposed by Luchini and Charru, we develop an ad hoc quasi-one-dimensional model capable of predicting the displacement of elastic boundaries even for large displacements. The stability and sensitivity analysis shows that the interaction of the flow with the flexible structure leads to two categories of globally unstable modes: sinuous (in-phase) modes and varicose (out-of-phase) modes. All the results presented have been cross-checked with direct numerical simulations of the nonlinear FSI system, revealing that the instabilities correspond to supercritical bifurcations. This work has significant implications for many natural and industrial phenomena where a jet is produced by a compliant nozzle.