Onset of instability of a flag in uniform flow

摘要

This paper numerically and analytically studies the onset of instability of a flag in uniform flow.The three-dimensional(3D) simulation is performed by using an immersed-boundary method coupled with a nonlinear finite element method.The global stability,bistability and instability are identified in the 3D simulations.The Squire's theorem is extended to analyze the stability of the fluid-flag system with 3D initial perturbations.It is found that if a parallel flow around the flag admits an unstable 3D disturbance for a certain value of the flutter speed,then a two-dimensional(2D) disturbance at a lower flutter speed is also admitted.In addition,the growth rate of 2D disturbance is larger than that of the 3D disturbance.