Transition from ciliary to flapping mode in a swimming mollusc: flapping flight as a bifurcation in ${\hbox{\it Re}}_\omega$
Abstract
From observations of swimming of the shell-less pteropod mollusc Clione antarctica we compare swimming velocities achieved by the organism using ciliated surfaces alone with velocities achieved by the same organism using a pair of flapping wings. Flapping dominates locomotion above a swimming Reynolds number ${\it Re}$ in the range 5–20. We test the hypothesis that ${\it Re} \approx$ 5–20 marks the onset of ‘flapping flight’ in these organisms. We consider the proposition that forward, reciprocal flapping flight is impossible for locomoting organisms whose motion is fully determined by a body length $L$ and a frequency $\omega$ below some finite critical value of the Reynolds number ${\it Re}_\omega = \omega L^2/\nu$ . For a self-similar family of body shapes, the critical Reynolds number should depend only upon the geometry of the body and the cyclic movement used to locomote. We give evidence of such a critical Reynolds number in our data, and study the bifurcation in several simplified theoretical models. We argue further that this bifurcation marks the departure of natural locomotion from the low Reynolds number or Stokesian realm and its entry into the high Reynolds number or Eulerian realm. This occurs because the equilibrium swimming or flying speed $U_f$ obtained at the instability is determined by the mechanics of a viscous fluid at a value of ${\it Re}_f=U_f L/\nu$ that is not small.
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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 [5]
Below some critical Re, animals switch from reciprocal methods of locomotion to ciliary and flagellar locomotion.
“Below some critical Re , animals switch from reciprocal methods of locomotion to ciliary and flagellar locomotion.”
From Reynolds number limits for jet propulsion: a numerical study of simplified jellyfish (2011) · cites this paper as [5]
The Antarctic pteropod uses ciliary locomotion at low speeds and flapping locomotion at high speeds.
“Childress and Dudley [5] describe how the Antarctic pteropod uses ciliary locomotion at low speeds and flapping locomotion at high speeds.”
From Reynolds number limits for jet propulsion: a numerical study of simplified jellyfish (2011) · cites this paper as [5]
Below a critical Re, flapping appendages can no longer generate enough thrust to swim or fly efficiently.
“Childress and Dudley [5] suggest that below a critical Re , flapping appendages can no longer generate enough thrust to swim or fly efficiently.”
From Reynolds number limits for jet propulsion: a numerical study of simplified jellyfish (2011) · cites this paper as [5]
Intermediate Re flows define an upper limit to ciliary and flagellar locomotion.
“Intermediate Re fl ows also define an upper limit to ciliary and flagellar locomotion.”
From Reynolds number limits for jet propulsion: a numerical study of simplified jellyfish (2011) · cites this paper as [5]
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- Authors
- CHILDRESS, S., & DUDLEY, R.
- Affiliations
- Courant Institute of Mathematical Sciences (US)
- University of California, Berkeley (US)
- Venue
- Journal of Fluid Mechanics
- Publisher
- Cambridge University Press (CUP)
- Published
- 2004-01-10
- Volume
- 498
- Pages
- 257-288
- ISSN
- 0022-1120 (ISSN-L)
- 1469-7645
- OpenAlex
- W1970874549
- Cited by
- 95
- References
- 0
- Citations by year
- 2026: 1 · 2025: 2 · 2024: 2 · 2023: 1 · 2022: 4 · 2021: 7 · 2020: 6 · 2019: 5 · 2018: 4 · 2017: 2 · 2016: 2 · 2015: 4 · 2014: 4 · 2013: 3 · 2012: 9
- FWCI
- 12.25
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Fluid Mechanics (publishedVersion)
- Topics
- Physical Sciences › Engineering › Aerospace Engineering › Biomimetic flight and propulsion mechanisms
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Micro and Nano Robotics
- Physical Sciences › Engineering › Computational Mechanics › Fluid Dynamics and Turbulent Flows
- Keywords
- pteropods, flapping flight, Reynolds number, bifurcation, viscous flow, swimming speed, fluid-structure interaction
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 ›
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