The DOI matches its Crossref record; 21 of the 21 references it cites were found in a registry or an index.
Symmetry breaking leads to forward flapping flight
Abstract
Flapping flight is ubiquitous in Nature, yet cilia and flagella, not wings, prevail in the world of micro-organisms. This paper addresses this dichotomy. We investigate experimentally the dynamics of a wing, flapped up and down and free to move horizontally. The wing begins to move forward spontaneously as a critical frequency is exceeded, indicating that ‘flapping flight’ occurs as a symmetry-breaking bifurcation from a pure flapping state with no horizontal motion. A dimensionless parameter, the Reynolds number based on the flapping frequency, characterizes the point of bifurcation. Above this bifurcation, we observe that the forward speed increases linearly with the flapping frequency. Visualization of the flow field around the heaving and plunging foil shows a symmetric pattern below transition. Above threshold, an inverted von Kármán vortex street is observed in the wake of the wing. The results of our model experiment, namely the critical Reynolds number and the behaviour above threshold, are consistent with observations of the flapping-based locomotion of swimming and flying animals.
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“Due to the conservation of total vorticity [39], oppositely signed vorticity is generated during bell expansion, but coherent stopping vortex structures do not form.”
From Reynolds number limits for jet propulsion: a numerical study of simplified jellyfish (2011) · cites this paper as [39]
Citations
Cites
Purcell, E. M. (1977) · American Journal of Physics · doi:10.1119/1.10903 · Cited by 4,360
Wing Rotation and the Aerodynamic Basis of Insect Flight
Dickinson, M. H., Lehmann, F., & Sane, S. P. (1999) · Science · doi:10.1126/science.284.5422.1954 · Cited by 2,669
Oscillating foils of high propulsive efficiency
Anderson, J. M., Streitlien, K., Barrett, D. S., & Triantafyllou, M. S. (1998) · Journal of Fluid Mechanics · doi:10.1017/s0022112097008392 · Cited by 1,296
Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency
Taylor, G. K., Nudds, R. L., & Thomas, A. L. R. (2003) · Nature · doi:10.1038/nature02000 · Cited by 994
Optimal Thrust Development in Oscillating Foils with Application to Fish Propulsion
Triantafyllou, G. S., Triantafyllou, M. S., & Grosenbaugh, M. A. (1993) · Journal of Fluids and Structures · doi:10.1006/jfls.1993.1012 · Cited by 887
The Speed of Swimming of Fish as Related to Size and to the Frequency and Amplitude of the Tail Beat
Bainbridge, R. (1958) · Journal of Experimental Biology · doi:10.1242/jeb.35.1.109 · Cited by 776
Experimental and Computational Investigation of the Knoller-Betz Effect
Jones, K., Dohring, C. M., & Platzer, M. F. (1998) · AIAA Journal · doi:10.2514/2.505 · Cited by 408
Mechanics of Swimming and Flying
Craik, A. D. D., & Childress, S. (1982) · Biometrics · doi:10.2307/2530474 · Cited by 389
Two Dimensional Mechanism for Insect Hovering
Wang, Z. J. (2000) · Physical Review Letters · doi:10.1103/physrevlett.85.2216 · Cited by 361
Propulsion of a flapping and oscillating airfoil
Garrick, I. E. (1936) · NASA Technical Reports Server (NASA) · Cited by 358
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Items 201–201 of 201
Trimming and Dynamic Stability of a Flapping Rotary Wing in Forward Flight
Xinyi, W., Jianghao, W., Peng, T., Zhang, Y., & Zhou, C. (2026) · Aerospace Science and Technology · doi:10.1016/j.ast.2026.114130
Metadata
- Authors
- VANDENBERGHE, N., ZHANG, J., & CHILDRESS, S.
- Affiliations
- Courant Institute of Mathematical Sciences (US)
- Venue
- Journal of Fluid Mechanics
- Publisher
- Cambridge University Press (CUP)
- Published
- 2004-04-28
- Volume
- 506
- Pages
- 147-155
- ISSN
- 0022-1120 (ISSN-L)
- 1469-7645
- OpenAlex
- W2056318256
- Cited by
- 202
- References
- 21
- Citations by year
- 2026: 12 · 2025: 3 · 2024: 14 · 2023: 6 · 2022: 9 · 2021: 10 · 2020: 6 · 2019: 6 · 2018: 17 · 2017: 8 · 2016: 11 · 2015: 12 · 2014: 11 · 2013: 13 · 2012: 7
- FWCI
- 9.95
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Fluid Mechanics (publishedVersion)
- HAL (submittedVersion)
- Topics
- Physical Sciences › Engineering › Aerospace Engineering › Biomimetic flight and propulsion mechanisms
- Physical Sciences › Engineering › Computational Mechanics › Fluid Dynamics and Vibration Analysis
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Micro and Nano Robotics
- Keywords
- flapping flight, symmetry breaking, bifurcation, critical Reynolds number, Karman vortex street, cilia and flagella, flapping locomotion
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