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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 flap1,2. 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.

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Figure 1: Experimental set-up.
Figure 2: The two stable states of the filament.
Figure 3: The flapping frequency and amplitude of the filament as functions of L, the filament length.
Figure 4: Dual filaments of the same length oscillating at the same frequency, when L = 3.5 cm and U = 220 cm s-1.

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Acknowledgements

We thank L. Becker, A. Belmonte, F. Hayot and C. Wiggins for helpful discussions. We thank D. Havir for assistance with the LDV measurements. This work was supported in part by the National Science Foundation and by the Department of Energy.

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Correspondence to Jun Zhang.

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Zhang, J., Childress, S., Libchaber, A. et al. Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature 408, 835–839 (2000). https://doi.org/10.1038/35048530

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