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.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Rayleigh, Lord . On the instability of jets. Proc. Lond. Math. Soc. X, 4–13 (1879).
Prandtl, L. Essentials of Fluid Mechanics (Hafner, New York, 1952 ).
Couder, Y., Chomaz, J. M. & Rabaud, M. On the hydrodynamics of soap films. Physica D 37, 384–405 ( 1989).
Gharib, M. & Derango, P. A liquid-film (soap film) tunnel to study two-dimensional laminar and turbulent shear flows. Physica D 37, 406–416 ( 1989).
Martin, B. K. & Wu, X.-L. Shear flow in a two-dimensional Couette cell: A technique for measuring the viscosity of free-standing liquid films. Rev. Sci. Instrum. 66, 5603– 5608 (1995).
Rutgers, M. A., Wu, X.-L., Bhagavatula, R., Petersen, A. A. & Goldburg, W. I. Two-dimensional velocity profiles and laminar boundary layers in flowing soap films. Phys. Fluids 8, 2847–2854 ( 1996).
Kellay, H., Wu, X-L. & Goldburg, W. I. Experiments with turbulent soap film. Phys. Rev. Lett. 74, 3975–3978 (1995).
Tritton, D. J. Physical Fluid Dynamics 2nd edn (Oxford Univ. Press, New York, 1988).
Bénard, H. Formation de centres de giration à l'arriére d'un obstacle en mouvement. C. R. Acad. Sci. Paris 147, 839 –842 (1908).
Thorpe, S. A. Experiments on the instability of stratified shear flows: miscible fluids. J. Fluid Mech. 46, 299– 319 (1971).
Triantafyllou, M. S. & Triantafyllou, G. S. An efficient swimming machine. Sci. Am. 272, 64– 70 (1995).
Anderson, J. M., Streitlien, K., Barrett, D. S. & Triantafyllou, M. S. Oscillating foils of high propulsive efficiency. J. Fluid Mech. 360, 41–72 ( 1998).
Drazin, P. G. & Reid, W. H. Hydrodynamic Stability 374–375 (Cambridge Univ. Press, Cambridge, 1981).
Pedley, T. J. The Fluid Mechanics of the Large Blood Vessels (Cambridge Univ. Press, Cambridge, 1979).
Scanlan, R. H. Introduction to the Study of Aircraft Vibration and Flutter (McMillan, New York, 1951).
Paı ¨doussis, M. P. Fluid–Structure Interaction Vol. I (Academic, San Diego, 1998).
Fitt, A. D. & Pope, M. P. The unsteady motion of a two-dimensional flag with bending stiffness. J. Eng. Sci. (submitted).
Chomaz, J. M. & Cathalau, B. Soap films as two-dimensional classical fluids. Phys. Rev. A 41, 2243– 2245 (1990).
Lopez-Ruiz, R. & Pomeau, Y. Transition between two oscillation modes. Phys. Rev. E 55, R3820–R3823 (1997).
Peschard, I. & Le Gal, P. Coupled wakes of cylinders. Phys. Rev. Lett. 77, 3122–3125 (1996).
Peschard, I., Le Gal, P. & Takeda, Y. On the spatio-temporal structure of cylinder wakes. Exp. Fluids 26, 188–196 (1999).
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1038/35048530
This article is cited by
-
Physical models and vortex dynamics of swimming and flying: a review
Acta Mechanica (2022)
-
Influence of geometrical parameters on the hysteresis of flutter onset in confined configurations
Experiments in Fluids (2022)
-
Effect of leading-edge serration on the flow-structure interactions of an inverted flag
Experiments in Fluids (2022)
-
On flowing soap films as experimental models of 2D Navier–Stokes flows
Experiments in Fluids (2021)
-
Numerical simulation on a limit cycle oscillation of a rectangular sheet in three-dimensional flow: influence of vortex element model on post-critical behavior
Nonlinear Dynamics (2021)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.