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Published August 15, 2009 | Published + Supplemental Material
Journal Article Open

Rotational accelerations stabilize leading edge vortices on revolving fly wings


The aerodynamic performance of hovering insects is largely explained by the presence of a stably attached leading edge vortex (LEV) on top of their wings. Although LEVs have been visualized on real, physically modeled, and simulated insects, the physical mechanisms responsible for their stability are poorly understood. To gain fundamental insight into LEV stability on flapping fly wings we expressed the Navier–Stokes equations in a rotating frame of reference attached to the wing's surface. Using these equations we show that LEV dynamics on flapping wings are governed by three terms: angular, centripetal and Coriolis acceleration. Our analysis for hovering conditions shows that angular acceleration is proportional to the inverse of dimensionless stroke amplitude, whereas Coriolis and centripetal acceleration are proportional to the inverse of the Rossby number. Using a dynamically scaled robot model of a flapping fruit fly wing to systematically vary these dimensionless numbers, we determined which of the three accelerations mediate LEV stability. Our force measurements and flow visualizations indicate that the LEV is stabilized by the `quasi-steady' centripetal and Coriolis accelerations that are present at low Rossby number and result from the propeller-like sweep of the wing. In contrast, the unsteady angular acceleration that results from the back and forth motion of a flapping wing does not appear to play a role in the stable attachment of the LEV. Angular acceleration is, however, critical for LEV integrity as we found it can mediate LEV spiral bursting, a high Reynolds number effect. Our analysis and experiments further suggest that the mechanism responsible for LEV stability is not dependent on Reynolds number, at least over the range most relevant for insect flight (100

Additional Information

© The Company of Biologists Ltd 2009. Accepted 19 April 2009. First published online July 31, 2009. Supplementary material available online at http://jeb.biologists.org/cgi/content/full/212/16/2705/DC1 We gratefully acknowledge Will Dickson for help with the experimental setup, valuable suggestions and proof reading the manuscript, and Andrew Straw for helping with the video set-up. We also thank Douglas Althshuler for valuable comments and lending his waterproof force sensor. And we thank Ulrike Müller, Jim Usherwood, Mees Muller, John Dabiri and GertJan van Heijst for valuable comments. We acknowledge Koert Lindenburg for proof reading the manuscript and mathematical derivations. We thank Johan van Leeuwen for hearty support, encouragement and proof reading of the various versions of the manuscript. Finally D.L. wishes to thank Peter Bakker, Hester Bijl and Bas van Oudheusden for helping him obtain travel bursaries for this research. This research is supported by travel bursaries of the Netherlands Organization for Scientific Research, the Journal of Experimental Biology and the J. M. Burgerscentrum for fluid dynamic research and NWO-ALW grant 817.02.012 to D.L. and a Grant from the National Science Foundation (IBN-0217229) and Packard Foundation (2001-17741A) to M.H.D.

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August 20, 2023
August 20, 2023