Skip to main content Accessibility help

Determining the relative stability of leading-edge vortices on nominally two-dimensional flapping profiles

  • Jaime G. Wong (a1) and David E. Rival (a1)


It is hypothesized that the relative stability of leading-edge vortices (LEVs) on flapping profiles can be improved by moderating LEV growth through spanwise vorticity convection and vortex stretching. Moreover, it is hypothesized that the reduced frequency $k$ and profile sweep ${\it\Lambda}$ are critical in predicting relative LEV stability as determined by the aforementioned effects. These hypotheses are then confirmed experimentally with phase-averaged particle image velocimetry (PIV) and three-dimensional particle tracking velocimetry. In particular, more stable LEVs are observed at higher reduced frequencies, which is argued to represent the ratio between the limiting vortex size and the rate of vorticity feeding. The introduction of profile sweep increased both relative LEV stability and spanwise vorticity transport. It is thought that spanwise vorticity transport improved LEV stability by acting as a sink for vorticity generated in the leading-edge shear layer.


Corresponding author

Email address for correspondence:


Hide All
Baik, Y., Bernal, L., Granlund, K. & Ol, M. 2012 Unsteady force generation and vortex dynamics of pitching and plunging aerofoils. J. Fluid Mech. 709, 3768.
Beem, H., Rival, D. E. & Triantafyllou, M. S. 2012 On the stabilization of leading-edge vortices with spanwise flow. Exp. Fluids 51, 511517.
Birch, J. M. & Dickinson, M. H. 2001 Spanwise flow and the attachment of the leading-edge vortex on insect wings. Nature 412, 729733.
Cheng, B., Sane, S. P., Barbera, G., Troolin, D. R., Strand, T. & Deng, X. 2013 Three-dimensional flow visualization and vorticity dynamics in revolving wings. Exp. Fluids 54 (1), 112.
Didden, N. 1979 On the formation of vortex rings: rolling-up and production of circulation. Z. Angew. Math. Phys. 30, 101116.
Ellington, C. P., van den Berg, C., Willmott, A. P. & Thomas, A. L. R. 1996 Leading-edge vortices in insect flight. Nature 384 (6610), 626630.
Garmann, D. J., Visbal, M. & Orkwis, P. D. 2013 Three-dimensional flow structure and aerodynamic loading on a revolving wing. Phys. Fluids 25, 034101.
Graftieaux, L., Michard, M. & Grosjean, N. 2001 Combining PIV, POD and vortex identification algorithms for the study of turbulent swirling flows. Meas. Sci. Technol. 12, 14221429.
Harbig, R. R., Sheridan, J. & Thompson, M. C. 2013 Reynolds number and aspect ratio effects on the leading-edge vortex for rotating insect wing planforms. J. Fluid Mech. 717, 166192.
Hartloper, C., Kinzel, M. & Rival, D. E. 2013 On the competition between leading-edge and tip-vortex growth for a pitching plate. Exp. Fluids 54, 1447.
Jones, A. R., Ford, C. W. P. & Babinsky, H. 2012 Three-dimensional effects on sliding and waving wings. J. Aircraft 48 (2), 633643.
Lentink, D. & Dickinson, M. H. 2009 Rotational accelerations stabilize leading edge vortices on revolving fly wings. J. Expl Biol. 212, 27052719.
Levy, Y., Degani, D. & Arnan, S. 1990 Graphical visualization of vortical flows by means of helicity. AIAA J. 28 (8), 13471352.
Ozen, C. & Rockwell, D. 2012 Three-dimensional vortex structure on a rotating wing. J. Fluid Mech. 707, 541550.
Pitt Ford, C. W. & Babinsky, H. 2013 Lift and the leading edge vortex. J. Fluid Mech. 720, 280313.
Rival, D. E., Kriegseis, J., Schaub, P., Widmann, A. & Tropea, C. 2014 Characteristic length scales for vortex detachment on plunging profiles with varying leading-edge geometry. Exp. Fluids 55 (1), 18.
Rival, D. & Tropea, C. 2010 Characteristics of pitching and plunging airfoils under dynamic-stall conditions. J. Aircraft 47, 8086.
Taylor, G. K., Nudds, R. L. & Thomas, A. 2003 Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency. Nature 425, 707710.
Wojcik, C. J. & Buchholz, J. H. J. 2014 Vorticity transport in the leading-edge vortex on a rotating blade. J. Fluid Mech. 743, 249261.
Wong, J. G., Kriegseis, J. & Rival, D. E. 2013 An investigation into vortex growth and stabilization for two-dimensional plunging and flapping plates with varying sweep. J. Fluids Struct. 43, 231243.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Related content

Powered by UNSILO

Determining the relative stability of leading-edge vortices on nominally two-dimensional flapping profiles

  • Jaime G. Wong (a1) and David E. Rival (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.