Skip to main content Accessibility help

Vortex dynamics of clapping plates

  • Daegyoum Kim (a1), Fazle Hussain (a2) and Morteza Gharib (a1)


Vortex formation and force generation of clapping plates with various aspect ratios ( $AR$ ) and stroke angles were investigated. Experiments were performed with a pair of hinged rectangular plates that were rotated symmetrically in a static fluid, and defocusing digital particle image velocimetry was employed to measure the three-dimensional flow field. Single-plate cases were also studied to compare with clapping plate cases. As $AR$ decreases, both circulation of the tip vortex and area enclosed by the vortex loop increase inversely. An empirical power-law relationship with a negative exponent is found between total impulse and $AR$ for a given stroke angle. The sensitivity of the force generated by the plates to the change of $AR$ is larger at the smaller stroke angle because of faster acceleration and deceleration. The increase in impulse per plate from the single-plate case to the clapping double-plate case is larger for lower $AR$ . These results reveal that low $AR$ wings are more efficient in propulsive force generation in some specific modes of unsteady flapping flight. The evolution of the wake structures is found to depend on $AR$ and stroke angle.


Corresponding author

Email address for correspondence:


Hide All
Betts, C. R. & Wootton, R. J. 1988 Wing shape and flight behavior in butterflies (Lepidoptera, Papilionoidea and Hesperioidea) – a preliminary analysis. J. Expl Biol. 138, 271288.
Brodsky, A. K. 1991 Vortex formation in the tethered flight of the peacock butterfly Inachis io L. (Lepidoptera, Nymphalidae) and some aspects of insect flight evolution. J. Expl Biol. 161, 7795.
Cooter, R. J. & Baker, P. S. 1977 Weis-Fogh clap and fling mechanism in Locusta . Nature 269, 5354.
Dudley, R. 1990 Biomechanics of flight in neotropical butterflies – morphometrics and kinematics. J. Expl Biol. 150, 3753.
Ellington, C. P. 1984a The aerodynamics of hovering insect flight. 3. Kinematics. Phil. Trans. R. Soc. Lond. B 305, 4178.
Ellington, C. P. 1984b The aerodynamics of hovering insect flight. 4. Aerodynamic mechanisms. Phil. Trans. R. Soc. Lond. B 305, 79113.
Gal, J. M. & Blake, R. W. 1988 Biomechanics of frog swimming. 2. Mechanics of the limb-beat cycle in Hymenochirus boettgeri . J. Expl Biol. 138, 413429.
Hussain, F. & Husain, H. S. 1989 Elliptic jets. 1. Characteristics of unexcited and excited jets. J. Fluid Mech. 208, 257320.
Johansson, L. C. & Lauder, G. V. 2004 Hydrodynamics of surface swimming in leopard frogs (Rana pipiens). J. Expl Biol. 207, 39453958.
Kambe, T. & Takao, T. 1971 Motion of distorted vortex rings. J. Phys. Soc. Japan 31, 591599.
Kida, S. & Takaoka, M. 1994 Vortex reconnection. Annu. Rev. Fluid Mech. 26, 169189.
Kim, D. & Gharib, M. 2011 Characteristics of vortex formation and thrust performance in drag-based paddling propulsion. J. Expl Biol. 214, 22832291.
Maxworthy, T. 1979 Experiments on the Weis-Fogh mechanism of lift generation by insects in hovering flight. 1. Dynamics of the fling. J. Fluid Mech. 93, 4763.
Melander, M. V. & Hussain, F. 1989 Cross-linking of two antiparallel vortex tubes. Phys. Fluids A 1, 633636.
Miller, L. A. & Peskin, C. S. 2005 A computational fluid dynamics of ‘clap and fling’ in the smallest insects. J. Expl Biol. 208, 195212.
Pereira, F. & Gharib, M. 2002 Defocusing digital particle image velocimetry and the three-dimensional characterization of two-phase flows. Meas. Sci. Technol. 13, 683694.
Pereira, F., Stuer, H., Graff, E. C. & Gharib, M. 2006 Two-frame 3D particle tracking. Meas. Sci. Technol. 17, 16801692.
Spedding, G. R. & Maxworthy, T. 1986 The generation of circulation and lift in a rigid two-dimensional fling. J. Fluid Mech. 165, 247272.
Stamhuis, E. J. & Nauwelaerts, S. 2005 Propulsive force calculations in swimming frogs. II. Application of a vortex ring model to DPIV data. J. Expl Biol. 208, 14451451.
Sun, M. & Yu, X. 2003 Flows around two airfoils performing fling and subsequent translation and translation and subsequent clap. Acta Mechanica Sin. 19, 103117.
Weis-Fogh, T. 1973 Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production. J. Expl Biol. 59, 169230.
Willert, C. & Gharib, M. 1992 Three-dimensional particle imaging with a single camera. Exp. Fluids 12, 353358.
Wu, J. C. 1981 Theory for aerodynamic force and moment in viscous flows. AIAA J. 19, 432441.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Related content

Powered by UNSILO

Vortex dynamics of clapping plates

  • Daegyoum Kim (a1), Fazle Hussain (a2) and Morteza Gharib (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.