Stability and coupled dynamics of three-dimensional dual inverted flags

Abstract

Fluid–structure interaction of an inverted flag, which has a free leading edge and a clamped trailing edge, has drawn attention recently because of its novel properties such as divergence stability, a low stability threshold, and large-amplitude flapping motion. In this study, the stability and flapping behaviors of dual inverted flags with finite height are investigated for a side-by-side arrangement, and their noticeable characteristics are compared to those of dual conventional flags. The critical velocity at which the inverted flags break the equilibrium of a straight configuration reduces monotonically when a gap distance between the two flags becomes smaller and an aspect ratio becomes larger, which is also predicted by our linear stability analysis using simple theoretical models of two-dimensional flags and slender flags. After bifurcation, in addition to the synchronized in-phase and out-of-phase modes commonly observed in dual conventional flags, a novel attached mode appears which is mainly observed for small gap distance and small aspect ratio. In this non-linear mode, the leading edges of the two inverted flags touch each other on a midline, and the deformed inverted flags maintain static equilibrium. In a non-linear flapping regime, a new mechanism of a mode transition from an out-of-phase mode to an in-phase mode is identified, which is allowed by the collision of the two flags flapping with large amplitude.