Flapping hydrodynamics and efficiency in a pteropod: A computational study of lift-based swimming

Zongze Li; David Murphy; Wenbin Mao

doi:10.1063/5.0313164

journal article Mar 01, 2026

Flapping hydrodynamics and efficiency in a pteropod: A computational study of lift-based swimming

Zongze Li

David Murphy

Wenbin Mao

Physics of Fluids Vol. 38 No. 3 · AIP Publishing

View at Publisher Save 10.1063/5.0313164

Abstract

The flapping of wings is a common locomotion strategy for small organisms in both aerial and aquatic environments. Cuvierina atlantica, a marine pteropod, employs a distinctive “overlap-and-fling” motion to propel itself underwater. To examine the hydrodynamics underlying this behavior, we perform high-resolution fluid–structure interaction simulations using the lattice Boltzmann method coupled with the immersed boundary method. The body geometry and wing kinematics are accurately reconstructed from high-speed experimental videos and validated through direct overlay comparisons. The simulations show that C. atlantica relies primarily on lift-based propulsion, with both leading-edge and trailing-edge vortices contributing to thrust generation. The overlap-and-fling motion enhances circulation, promoting the development of strong vortices and sustained low-pressure regions along the wing edges, while wing–wing interaction increases vertical lift by more than 20%. Parametric analyses demonstrate that higher fluid viscosity elevates total hydrodynamic force but markedly reduces the lift-to-drag ratio and overall propulsion efficiency due to stronger viscous effects. Increasing flapping frequency boosts force production but leads to saturation in lift-to-drag and pressure-to-shear ratios, associated with increasingly chaotic wake structures. When interpreted using the Strouhal number, efficiency in the neutrally buoyant case exhibits an optimal value near 0.6. However, under gravity, this relationship breaks down, as weight-induced posture adjustments modify pitching dynamics and alter the phase relation between force generation and wake evolution. Across all conditions, higher chordwise Reynolds numbers generate numerous small vortices that enhance energy dissipation and reduce swimming efficiency.

Topics

No keywords indexed for this article. Browse by subject →

References

93

[1]

"Unsteady aerodynamic performance of model wings at low Reynolds numbers" J. Exp. Biol. (1993) 10.1242/jeb.174.1.45

[2]

"Predictions of vortex-lift characteristics by a leading-edge suctionanalogy" J. Aircraft (1971) 10.2514/3.44254

[3]

"Bat flight: Aerodynamics, kinematics and flight morphology" J. Exp. Biol. (2015) 10.1242/jeb.031203

[4]

S. Kumar , J.-H.Seo, and R.Mittal, “Computational modeling and analysis of the coupled aero structural dynamics in bat inspired wings,” arXiv:2501.02034 (2025). 10.1017/jfm.2025.356

[5]

"Immersed boundary methods for simulations of biological flows in swimming and flying bio-locomotion: A review" Appl. Sci. (2023) 10.3390/app13074208

[6]

"Vortex dynamics and hydrodynamic performance enhancement mechanism in batoid fish oscillatory swimming" J. Fluid Mech. (2022) 10.1017/jfm.2021.917

[7]

"Bio-inspired propulsion: Towards understanding the role of pectoral fin kinematics in manta-like swimming" Biomimetics (2022) 10.3390/biomimetics7020045

[8]

"Hydrodynamic performance of aquatic flapping: Efficiency of underwater flight in the manta" Aerospace (2016) 10.3390/aerospace3030020

[9]

"The aerodynamic effects of wing rotation and a revised quasi-steady model of flapping flight" J. Exp. Biol. (2002) 10.1242/jeb.205.8.1087

[10]

"Spanwise flow and the attachment of the leading-edge vortex on insect wings" Nature (2001) 10.1038/35089071

[11]

Wing Rotation and the Aerodynamic Basis of Insect Flight

Michael H. Dickinson, Fritz-Olaf Lehmann, Sanjay P. Sane

Science 1999 10.1126/science.284.5422.1954

[12]

"Experiments on the Weis-Fogh mechanism of lift generation by insects in hovering flight. Part 1. Dynamics of the ‘fling’" J. Fluid Mech. (1979) 10.1017/s0022112079001774

[13]

"The mechanics of flight in the hawkmoth Manduca sexta I. Kinematics of hovering and forward flight" J. Exp. Biol. (1997) 10.1242/jeb.200.21.2705

[14]

"Recent developments in the study of insect flight" Can. J. Zool. (2015) 10.1139/cjz-2013-0196

[15]

"The aerodynamics of hovering insect flight. IV. Aerodynamic mechanisms" Philos. Trans. R. Soc. London (1984) 10.1098/rstb.1984.0052

[16]

"Coriolis effect and the attachment of the leading edge vortex" J. Fluid Mech. (2017) 10.1017/jfm.2017.222

[17]

"Unsteady bio-fluid dynamics in flying and swimming" Acta Mech. Sin. (2017) 10.1007/s10409-017-0677-4

[18]

(2025)

[19]

"Flapping-mode changes and aerodynamic mechanisms in miniature insects" Phys. Rev. E (2019) 10.1103/physreve.99.012419

[20]

"When vortices stick: An aerodynamic transition in tiny insect flight" J. Exp. Biol. (2004) 10.1242/jeb.01138

[21]

"Weis-Fogh clap and fling mechanism in Locusta" Nature (1977) 10.1038/269053a0

[22]

"Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production" J. Exp. Biol. (1973) 10.1242/jeb.59.1.169

[23]

"The aerodynamic effects of wing–wing interaction in flapping insect wings" J. Exp. Biol. (2005) 10.1242/jeb.01744

[24]

"Flexible clap and fling in tiny insect flight" J. Exp. Biol. (2009) 10.1242/jeb.028662

[25]

"Wing-kinematics measurement and aerodynamics in a small insect in hovering flight" Sci. Rep. (2016) 10.1038/srep25706

[26]

"Aerodynamic interaction of bristled wing pairs in fling" Phys. Fluids (2021) 10.1063/5.0036018

[27]

"A computational fluid dynamics of clap and fling' in the smallest insects" J. Exp. Biol. (2005) 10.1242/jeb.01376

[28]

"Über die entstehung des dynamischen auftriebes von tragflügeln" Z. Angew. Math. Mech. (1924) 10.1002/zamm.19250050103

[29]

"Aquatic wing flapping at low Reynolds numbers: Swimming kinematics of the Antarctic pteropod, Clione antarctica" J. Exp. Biol. (2005) 10.1242/jeb.01733

[30]

"Swimming in the intermediate Reynolds range: Kinematics of the Pteropod Limacina helicina" Integr. Comp. Biol. (2012) 10.1093/icb/ics113

[31]

"Underwater flight by the planktonic sea butterfly" J. Exp. Biol. (2016) 10.1242/jeb.129205

[32]

"Portable tomographic PIV measurements of swimming shelled Antarctic pteropods" Exp. Fluids (2016) 10.1007/s00348-016-2269-7

[33]

"Swimming and sinking behavior of warm water pelagic snails" Front. Mar. Sci. (2020) 10.3389/fmars.2020.556239

[34]

"Very small insects use novel wing flapping and drag principle to generate the weight-supporting vertical force" J. Fluid Mech. (2018) 10.1017/jfm.2018.668

[35]

"Novel flight style and light wings boost flight performance of tiny beetles" Nature (2022) 10.1038/s41586-021-04303-7

[36]

"Flows around two airfoils performing fling and subsequent translation and translation and subsequent clap" Acta Mech. Sin. (2003) 10.1007/bf02487671

[37]

"Two-and three-dimensional numerical simulations of the clap–fling–sweep of hovering insects" J. Fluids Struct. (2011) 10.1016/j.jfluidstructs.2011.05.002

[38]

"Clap and fling mechanism with interacting porous wings in tiny insect flight" J. Exp. Biol. (2014) 10.1242/jeb.084897

[39]

"A novel cylindrical overlap-and-fling mechanism used by sea butterflies" J. Exp. Biol. (2020) 10.1242/jeb.221499

[40]

"Lattice Boltzmann method for fluid flows" Annu. Rev. Fluid Mech. (1998) 10.1146/annurev.fluid.30.1.329

[41]

Lattice-Boltzmann Method for Complex Flows

Cyrus K. Aidun, Jonathan R. Clausen

Annual Review of Fluid Mechanics 2010 10.1146/annurev-fluid-121108-145519

[42]

"Palabos: Parallel lattice Boltzmann solver" Comput. Math. Appl. (2021) 10.1016/j.camwa.2020.03.022

[43]

"A fast approach to estimating Windkessel model parameters for patient-specific multi-scale CFD simulations of aortic flow" Comput. Fluids (2023) 10.1016/j.compfluid.2023.105894

[44]

"Generalized three-dimensional lattice Boltzmann color-gradient method for immiscible two-phase pore-scale imbibition and drainage in porous media" Phys. Rev. E (2017) 10.1103/physreve.95.033306

[45]

(2017)

[46]

"Effect of internal mass in the simulation of a moving body by the immersed boundary method" Comput. Fluids (2011) 10.1016/j.compfluid.2011.05.011

[47]

"Flow patterns around heart valves: A numerical method" J. Comput. Phys. (1972) 10.1016/0021-9991(72)90065-4

[48]

"Numerical analysis of blood flow in the heart" J. Comput. Phys. (1977) 10.1016/0021-9991(77)90100-0

[49]

"The immersed boundary method" Acta Numer. (2002) 10.1017/s0962492902000077

[50]

"The immersed boundary-lattice Boltzmann method for solving fluid–particles interaction problems" J. Comput. Phys. (2004) 10.1016/j.jcp.2003.10.013

Showing 50 of 93 references

Metrics

0

Citations

93

References

Details

Published: Mar 01, 2026
Vol/Issue: 38(3)

Authors

Z

Zongze Li

Department of Mechanical and Aerospace Engineering, University of South Florida , 4202 E. Fowler Avenue, ENG 030, Tampa, Florida 33620,

D

David Murphy

Department of Mechanical and Aerospace Engineering, University of South Florida , 4202 E. Fowler Avenue, ENG 030, Tampa, Florida 33620,

W

Wenbin Mao

Department of Mechanical and Aerospace Engineering, University of South Florida , 4202 E. Fowler Avenue, ENG 030, Tampa, Florida 33620,

Cite This Article

Zongze Li, David Murphy, Wenbin Mao (2026). Flapping hydrodynamics and efficiency in a pteropod: A computational study of lift-based swimming. Physics of Fluids, 38(3). https://doi.org/10.1063/5.0313164

Flapping hydrodynamics and efficiency in a pteropod: A computational study of lift-based swimming

You May Also Like