Coherent locomotion as an attracting state for a free flapping body
Open accessAbstract
A recent experiment [Vandenberghe, N., Zhang, J. & Childress, S. (2004) J. Fluid Mech. 506, 147-155] has shown that an axle-mounted blade can spontaneously rotate when oscillated (or "flapped") above a critical frequency in a fluid. To understand the nature of flapping locomotion we study numerically the dynamics of a simple body, flapped up and down within a viscous fluid and free to move horizontally. We show here that, at sufficiently large "frequency Reynolds number," unidirectional locomotion emerges as an attracting state for an initially nonlocomoting body. Locomotion is generated in two stages: first, the fluid field loses symmetry by an instability similar to the classical von Kármán instability; and second, precipitous interactions with previously shed vortical structures "push" the body into locomotion. Body mass and slenderness play central and unexpected roles in each stage. Conceptually, this work demonstrates how locomotion can be transduced from the simple oscillations of a body through an interaction with its fluid environment.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Flapping fins and undulatory swimming do not appear for Re_m < 10.
“Flapping fins and undulatory swimming do not appear for Re m < 10 [2, 5, 38].”
From Reynolds number limits for jet propulsion: a numerical study of simplified jellyfish (2011) · cites this paper as [2]
These vortical structures push the body into motion.
“These vortical structures push the body into motion.”
From Reynolds number limits for jet propulsion: a numerical study of simplified jellyfish (2011) · cites this paper as [2]
The fluid field loses symmetry when vortices formed behind the plate are alternately shed from each side.
“The fluid field loses symmetry when vortices formed behind the plate are alternately shed from each side.”
From Reynolds number limits for jet propulsion: a numerical study of simplified jellyfish (2011) · cites this paper as [2]
The transition from flapping to no flapping is connected to a change in the behavior of the vortex wake behind the flapping plate or appendage.
“Alben and Shelley [2] connect this transition to a change in the behavior of the vortex wake behind the flapping plate or appendage.”
From Reynolds number limits for jet propulsion: a numerical study of simplified jellyfish (2011) · cites this paper as [2]
Cites
Vortex Dynamics in the Cylinder Wake
WILLIAMSON, C. H. K. (1996) · Annual Review of Fluid Mechanics · doi:10.1146/annurev.fl.28.010196.002401 · Cited by 3,552 · see citing works
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 · see citing works
WILLIAMSON, C. H. K., & Govardhan, R. N. (2003) · Annual Review of Fluid Mechanics · doi:10.1146/annurev.fluid.36.050802.122128 · Cited by 2,507 · see citing works
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 · see citing works
Vogel, S. K. (1983) · Princeton University Press eBooks · doi:10.1515/9780691212975 · Cited by 1,120 · see citing works
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 · see citing works
Hydrodynamics of Fishlike Swimming
Triantafyllou, M. S., Triantafyllou, G. S., & Yue, D. K. P. (2000) · Annual Review of Fluid Mechanics · doi:10.1146/annurev.fluid.32.1.33 · Cited by 978 · see citing works
Wang, Z. J., Birch, J. M., & Dickinson, M. H. (2003) · Journal of Experimental Biology · doi:10.1242/jeb.00739 · Cited by 510 · see citing works
Vortex shedding and frequency selection in flapping flight
Wang, Z. J. (2000) · Journal of Fluid Mechanics · doi:10.1017/s0022112099008071 · Cited by 426 · see citing works
Modelling thrust generation of a two-dimensional heaving airfoil in a viscous flow
Lewin, G. C., & Haj‐Hariri, H. (2003) · Journal of Fluid Mechanics · doi:10.1017/s0022112003005743 · Cited by 371 · see citing works
Symmetry breaking leads to forward flapping flight
VANDENBERGHE, N., ZHANG, J., & CHILDRESS, S. (2004) · Journal of Fluid Mechanics · doi:10.1017/s0022112004008468 · Cited by 202 · see citing works
Falling Paper: Navier-Stokes Solutions, Model of Fluid Forces, and Center of Mass Elevation
Pesavento, U., & Wang, Z. J. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.144501 · Cited by 189 · see citing works
When vortices stick: an aerodynamic transition in tiny insect flight
Miller, L. A., & Peskin, C. S. (2004) · Journal of Experimental Biology · doi:10.1242/jeb.01138 · Cited by 169 · see citing works
Essentially Compact Schemes for Unsteady Viscous Incompressible Flows
Weinan, E., & Liu, J. (1996) · Journal of Computational Physics · doi:10.1006/jcph.1996.0125 · Cited by 147 · see citing works
CHILDRESS, S., & DUDLEY, R. (2004) · Journal of Fluid Mechanics · doi:10.1017/s002211200300689x · Cited by 95 · see citing works
Nonvertical ascension or fall of a free sphere in a Newtonian fluid
Jenny, M., Bouchet, G., & Dušek, J. (2002) · Physics of Fluids · doi:10.1063/1.1529179 · Cited by 53 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Reynolds number limits for jet propulsion: a numerical study of simplified jellyfish
Herschlag, G., & Miller, L. (2011) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2011.05.035 · Cited by 79 · see citing works
- Authors
- Alben, S., & Shelley, M.
- Affiliations
- Harvard University (US)
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 2005-07-29
- Volume
- 102
- Issue
- 32
- Pages
- 11163-11166
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC1183592
- OpenAlex
- W2020779850
- Cited by
- 179
- References
- 16
- Citations by year
- 2026: 6 · 2025: 8 · 2024: 8 · 2023: 5 · 2022: 8 · 2021: 11 · 2020: 10 · 2019: 10 · 2018: 11 · 2017: 10 · 2016: 9 · 2015: 18 · 2014: 12 · 2013: 8 · 2012: 11
- FWCI
- 9.26
- Type
- journal article
- Language
- en
- Open access
- green
- europepmc.org
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- 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 locomotion, spontaneous rotation, blade vibration, vortex structures, body mass, viscous fluid
- MeSH terms
- Animals, Biomechanical Phenomena, Computer Simulation, Flight, Animal, Models, Theoretical, Rheology
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
