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]
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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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