Skip to main content Accessibility help

Global vorticity shedding for a vanishing wing

  • M. S. Wibawa (a1), S. C. Steele (a1), J. M. Dahl (a1), D. E. Rival (a1) (a2), G. D. Weymouth (a3) and M. S. Triantafyllou (a1)...


If a moving body were made to vanish within a fluid, its boundary-layer vorticity would be released into the fluid at all locations simultaneously, a phenomenon we call global vorticity shedding. We approximate this process by studying the related problem of rapid vorticity transfer from the boundary layer of a body undergoing a quick change of cross-sectional and surface area. A surface-piercing foil is first towed through water at constant speed, , and constant angle of attack, then rapidly pulled out of the fluid in the spanwise direction. Viewed within a fixed plane perpendicular to the span, the cross-sectional area of the foil seemingly disappears. The rapid spanwise motion results in the nearly instantaneous shedding of the boundary layer into the surrounding fluid. Particle image velocimetry measurements show that the shed layers quickly transition from free shear layers to form two strong, unequal-strength vortices, formed within non-dimensional time , based on the foil chord and forward velocity. These vortices are connected to, and interact with, the foil’s tip vortex through additional streamwise vorticity formed during the rapid pulling of the foil. Numerical simulations show that two strong spanwise vortices form from the shed vorticity of the boundary layer. The three-dimensional effects of the foil removal process are restricted to the tip of the foil. This method of vorticity transfer may be used for quickly introducing circulation to a fluid to provide forcing for biologically inspired flow control.


Corresponding author

Email address for correspondence:


Hide All
1. Abbott, I. H. & von Doenhoff, A. E. 1959 Theory of Wing Sections. Dover.
2. Alam, Md. M., Zhou, Y., Yang, H. X., Guo, H. & Mi, J. 2010 The ultra-low Reynolds number airfoil wake. Exp. Fluids 48, 81103.
3. Aref, H. 1983 Integrable, chaotic and turbulent vortex motion in two-dimensional flows. Annu. Rev. Fluid Mech. 15, 345389.
4. Betz, A. 1950 Wie Entsteht ein Wirbel in einer Wenig Zähen Flüssigkeit? Die Naturwissenschaft 37, 193196.
5. Birch, D. & Lee, T. 2005 Investigation of the near-field tip vortex behind an oscillating wing. J. Fluid Mech. 544, 201241.
6. Blondeaux, P., Fornarelli, F., Guglielmini, L., Triantafyllou, M. S. & Verzicco, R. 2005 Numerical experiments on flapping foils mimicking fish-like locomotion. Phys. Fluids 17, 113601.
7. Buchholz, J. H. J. & Smits, A. J. 2006 On the evolution of the wake structure produced by a low-aspect-ratio pitching panel. J. Fluid Mech. 546, 433443.
8. Buchholz, J. H. J. & Smits, A. J. 2008 The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel. J. Fluid Mech. 603, 331365.
9. Childress, S., Vandenberghe, N. & Zhang, J. 2006 Hovering of a passive body in an oscillating airflow. Phys. Fluids 18, 117103.
10. Dabiri, J. O. 2009 Optimal vortex formation as a unifying principle in biological propulsion. Annu. Rev. Fluid Mech. 41, 1733.
11. Dickinson, M. 2003 Animal locomotion: how to walk on water. Nature 424, 621622.
12. Dong, H., Bozkurttas, M., Mittal, R., Madden, P. & Lauder, G. V. 2010 Computational modelling and analysis of the hydrodynamics of a highly deformable fish pectoral fin. J. Fluid Mech. 645, 345373.
13. von Ellenrieder, K. D., Parker, K. & Soria, J. 2003 Flow structures behind a heaving and pitching finite-span wing. J. Fluid Mech. 490, 129138.
14. Hsieh, S. T. & Lauder, G. V. 2004 Running on water: three-dimensional force generation by basilisk lizards. Proc. Natl Acad. Sci. USA 101, 16787.
15. Hu, D. L. & Bush, J. W. M. 2010 The hydrodynamics of water-walking arthropods. J. Fluid Mech. 644, 533.
16. Hubel, T. Y., Hristov, N. I., Schwartz, S. M. & Breuer, K. S. 2009 Time-resolved wake structure and kinematics of bat flight. Exp. Fluids 46, 933943.
17. Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.
18. Johansson, L. C. & Norberg, R. A. 2003 Delta-wing function of webbed feet gives hydrodynamic lift for swimming propulsion in birds. Nature 424, 6568.
19. Johansson, L. C. & Norberg, U. M. L. 2001 Lift-based paddling in diving grebe. J. Expl Biol. 204, 16871696.
20. Kaden, H. 1931 Aufwicklung einer unstabilen Unstetigkeitsfläche. Ing.-Arch. 2, 140168.
21. Klein, F. 1910 Über die Bildung von Wirbeln in reibungslosen Flüssigkeiten. Z. Math. Phys. 58, 259262.
22. Lentink, D., Müller, U. K., Stamhuis, E. J., de Kat, R., van Gestel, W., Veldhuis, L. L. M., Henningsson, P., Hedenström, A., Videler, J. J. & van Leeuwen, J. L. 2007 How swifts control their glide performance with morphing wings. Nature 446, 10821085.
23. Margolin, L. G., Rider, W. J. & Grinstein, F. F. 2007 Modelling turbulent flow with implicit LES . J. Turbul. 7, 127.
24. Morton, B. R. 1984 The generation and decay of vorticity. Geophys. Astrophys. Fluid Dyn. 28, 277308.
25. Müller, U. K. & Lentink, D. 2004 Physiology – turning on a dime. Science 306, 18991900.
26. Prandtl, L. 1927 Die Entstehung von Wirbeln in einer Flüssigkeit Kleinster Reibung. Z. Flugtech. Motorluftschiffahrt 18, 489496.
27. Prandtl, L. 1936 Entstehung von Wirbeln bei Wasserströmungen: – 1. Entstehung von Wirbeln und Künstliche Beeinflussung der Wirbelbildung. Institut für Wissenschaftlichen Film (DVD) – Historische Filmaufnahmen.
28. Raffel, M., Willert, C. E., Wereley, S. T. & Kompenhans, J. 2007 Particle Image Velocimetry: A Practical Guide, 2nd edn. Springer.
29. Rockwell, D. 1998 Vortex-body interactions. Annu. Rev. Fluid Mech. 30, 199229.
30. Slaouti, A. & Gerrard, J. H. 1981 An experimental investigation of the end effects on the wake of a circular cylinder towed through water at low Reynolds numbers. J. Fluid Mech. 112, 297314.
31. Spagnolie, S. E. & Shelley, M. J. 2009 Shape-changing bodies in fluid: hovering, ratcheting, and bursting. Phys. Fluids 21, 013103.
32. Taneda, S. 1977 Visual study of unsteady separated flows around bodies. Prog. Aerosp. Sci. 17, 287348.
33. Taylor, G. I. 1953 Formation of a vortex ring by giving an impulse to a circular disk and then dissolving it away. J. Appl. Phys. 24, 104.
34. Wagner, H. 1925 Über die Entstehung des dynamischen Auftriebes an Tragflügeln. Z. Angew. Math. Mech. 5, 1735.
35. Weymouth, G. D., Dommermuth, D. G., Hendrickson, K. & Yue, D. K.-P. 2006 Advancements in Cartesian-grid methods for computational ship hydrodynamics. In 26th Symposium on Naval Hydrodynamics. Office of Naval Research.
36. Weymouth, G. D. & Yue, D. K.-P. 2011 Boundary data immersion method for Cartesian-grid simulations of fluid-body interaction problems. J. Comput. Phys. 230, 62336247.
37. Zdravkovich, M. M. 2003 Flow Around Circular Cylinders, Volume 2: Applications. Oxford University Press.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Related content

Powered by UNSILO

Global vorticity shedding for a vanishing wing

  • M. S. Wibawa (a1), S. C. Steele (a1), J. M. Dahl (a1), D. E. Rival (a1) (a2), G. D. Weymouth (a3) and M. S. Triantafyllou (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.