Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind

Abstract

The dynamics of swimming fish and flapping flags involves a complicated interaction of their deformable shapes with the surrounding fluid flow. Even in the passive case of a flag, the flag exerts forces on the fluid through its own inertia and elastic responses, and is likewise acted on by hydrodynamic pressure and drag. But such couplings are not well understood. Here we study these interactions experimentally, using an analogous system of flexible filaments in flowing soap films. We find that, for a single filament (or 'flag') held at its upstream end and otherwise unconstrained, there are two distinct, stable dynamical states. The first is a stretched-straight state: the filament is immobile and aligned in the flow direction. The existence of this state seems to refute the common belief that a flag is always unstable and will flap. The second is a flapping state: the filament executes a sinuous motion in a manner akin to the flapping of a flag in the wind. We study further the hydrodynamically coupled interaction between two such filaments, and demonstrate the existence of four different dynamical states.

The origin of hysteresis in the flag instability

“…The present stiffening scenario might not be the only cause of hysteresis: in particular, it cannot explain the bistability observed in the soap film experiments of Zhang et al (2000). However, the alternative explanations found in the literature are ruled out by the present set of experiments: both blockage and damping effects would not lead to poor repeatability of U * c and a drastic increase of U * c when curvature is introduced.…”

“…Since the pioneering study of Taneda (1968), different groups have performed experiments on the flag instability either for small aspect ratios (Datta & Gottenberg 1975;Lemaitre et al 2005) or for moderate to large aspect ratios (Zhang et al 2000;Tang et al 2003;Eloy et al 2008, among others). In this latter case, a large hysteresis is always observed at threshold or, said differently, the motionless state and the flapping state coexist and are both stable over a large range of airflow velocities.…”

Flutter-driven triboelectrification for harvesting wind energy

“…The first experimental study on fluttering behaviour was performed by Taneda 27 with a flag made of various fabrics and shapes, to find a variety of flapping modes (for example, nodeless, one-node, imperfect-node and two-node flutters). In addition, using one-dimensional filaments, the distinct dynamic states (for example, a stretchedstraight state and a flapping state) and the coupled interaction between the states were observed through a flowing soap film experiment 28 . On the other hand, the interaction of the flag and a counter rigid plate hitherto has received scant attention, although their coupled dynamics can be a very powerful vibration source for triboelectric generator due to its self-sustained nature.…”

Response of a flexible filament in a flowing soap film subject to a forced vibration

“…The interactions between a flexible plate and its ambient fluid are common phenomena in our daily life and industry, such as a flag flapping in the wind, 1 snoring caused by the soft palate in human airway, 2 and the flutter of a newspaper during its printing process. 3 These phenomena occur when a flexible plate structure loses its instability in flow.…”