Symmetry breaking leads to forward flapping flight

VANDENBERGHE, NICOLAS; ZHANG, JUN; CHILDRESS, STEPHEN

doi:10.1017/s0022112004008468

Cited by 202Biomimetic flight and propulsion mechanismsFluid Dynamics and Vibration AnalysisMicro and Nano Robotics

Symmetry breaking leads to forward flapping flight

VANDENBERGHE, NICOLAS, ZHANG, JUN, CHILDRESS, STEPHEN·2004·Journal of Fluid Mechanics

DOI 10.1017/s0022112004008468

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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, oppositely signed vorticity is generated during bell expansion, but coherent stopping vortex structures do not form.
“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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Authors: VANDENBERGHE, N., ZHANG, J., & CHILDRESS, S.
Affiliations: Courant Institute of Mathematical Sciences (US)
ORCID: VANDENBERGHE, NICOLAS
CHILDRESS, STEPHEN
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
DOI: 10.1017/s0022112004008468
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
Licence: www.cambridge.org/core/terms (unspecified)
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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Symmetry breaking leads to forward flapping flight

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