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Hydrodynamic schooling of multiple self-propelled flapping plates

Published online by Cambridge University Press:  29 August 2018

Ze-Rui Peng ,
Haibo Huang Open the ORCID record for Haibo Huang [Opens in a new window]  and
Xi-Yun Lu Open the ORCID record for Xi-Yun Lu [Opens in a new window]
Ze-Rui Peng
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Haibo Huang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Xi-Yun Lu*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
*
†Email address for correspondence: [email protected]
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Abstract

While hydrodynamic interactions for aggregates of swimmers have received significant attention in the low Reynolds number realm ($Re\ll 1$), there has been far less work at higher Reynolds numbers, in which fluid and body inertia are involved. Here we study the collective behaviour of multiple self-propelled plates in tandem configurations, which are driven by harmonic flapping motions of identical frequency and amplitude. Both fast modes with compact configurations and slow modes with sparse configurations were observed. The Lighthill conjecture that orderly configurations may emerge passively from hydrodynamic interactions was verified on a larger scale with up to eight plates. The whole group may consist of subgroups and individuals with regular separations. Hydrodynamic forces experienced by the plates near their multiple equilibrium locations are all springlike restoring forces, which stabilize the orderly formation and maintain group cohesion. For the cruising speed of the whole group, the leading subgroup or individual plays the role of ‘leading goose’.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Propulsion Biological Fluid Dynamics: Swimming/flying
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 853 , 25 October 2018 , pp. 587 - 600
Copyright
© 2018 Cambridge University Press 

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References

Alben, S. 2009 Wake-mediated synchronization and drafting in coupled flags. J. Fluid Mech. 641, 489–496.Google Scholar
Alben, S. & Shelley, M. J. 2005 Coherent locomotion as an attracting state for a free flapping body. Proc. Natl Acad. Sci. USA 102, 11163–11166.Google Scholar
Becker, A. D., Masoud, H., Newbolt, J. W., Shelley, M. & Ristroph, L. 2015 Hydrodynamic schooling of flapping swimmers. Nat. Commun. 6, 8514.Google Scholar
Boschitsch, B. M., Dewey, P. A. & Smits, A. J. 2014 Propulsive performance of unsteady tandem hydrofoils in an in-line configuration. Phys. Fluids 26, 051901.Google Scholar
Chen, S. & Doolen, G. D. 1998 Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329–364.Google Scholar
Couzin, I. D., Krause, J., Franks, N. R. & Levin, S. A. 2005 Effective leadership and decision-making in animal groups on the move. Nature 433 (7025), 513–516.Google Scholar
Doyle, J. F. 2001 Nonlinear Analysis of Thin-Walled Structures: Statics, Dynamics, and Stability. Springer.Google Scholar
Godoy-Diana, R., Marais, C., Aider, J.-L. & Wesfreid, J.-E. 2009 A model for the symmetry breaking of the reverse Bénard–von Kármán vortex street produced by a flapping foil. J. Fluid Mech. 622, 23–32.Google Scholar
Hua, R.-N., Zhu, L. & Lu, X.-Y. 2013 Locomotion of a flapping flexible plate. Phys. Fluids 25, 121901.Google Scholar
Hua, R.-N., Zhu, L. & Lu, X.-Y. 2014 Dynamics of fluid flow over a circular flexible plate. J. Fluid Mech. 759, 56–72.Google Scholar
Kelley, D. H. & Ouellette, N. T. 2013 Emergent dynamics of laboratory insect swarms. Sci. Rep. 3, 1073.Google Scholar
Lauga, E. & Powers, T. R. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72 (9), 096601.Google Scholar
Lighthill, M. J. 1975 Mathematical Biofluiddynamics. SIAM.Google Scholar
Mittal, R. & Iaccarino, G. 2005 Immersed boundary methods. Annu. Rev. Fluid Mech. 37, 239–261.Google Scholar
Parrish, J. K. & Edelstein-Keshet, L. 1999 Complexity, pattern, and evolutionary trade-offs in animal aggregation. Science 284, 99–101.Google Scholar
Peskin, C. S. 2002 The immersed boundary method. Acta Numerica 11, 479–517.Google Scholar
Portugal, S. J., Hubel, T. Y., Fritz, J., Heese, S., Trobe, D., Voelkl, B., Hailes, S., Wilson, A. M. & Usherwood, J. R. 2014 Upwash exploitation and downwash avoidance by flap phasing in ibis formation flight. Nature 505 (7483), 399–402.Google Scholar
Ramananarivo, S., Fang, F., Oza, A., Zhang, J. & Ristroph, L. 2016 Flow interactions lead to orderly formations of flapping wings in forward flight. Phys. Rev. Fluids 1 (7), 071201.Google Scholar
Ristroph, L. & Zhang, J. 2008 Anomalous hydrodynamic drafting of interacting flapping flags. Phys. Rev. Lett. 101 (19), 194502.Google Scholar
Rosellini, L. & Zhang, J.2007 The effect of geometry on the flapping flight of a simple wing. http://www.physics.nyu.edu/jz11/publications/LT10521stop.pdf.Google Scholar
Saintillan, D. & Shelley, M. J. 2008 Instabilities and pattern formation in active particle suspensions: kinetic theory and continuum simulations. Phys. Rev. Lett. 100, 178103.Google Scholar
Tytell, E. D., Hsu, C.-Y., Williams, T. L., Cohen, A. H. & Fauci, L. J. 2010 Interactions between internal forces, body stiffness, and fluid environment in a neuromechanical model of lamprey swimming. Proc. Natl Acad. Sci. USA 107 (46), 19832–19837.Google Scholar
Uddin, E., Huang, W.-X. & Sung, H. J. 2015 Actively flapping tandem flexible flags in a viscous flow. J. Fluid Mech. 780, 120–142.Google Scholar
Vicsek, T. & Zafeiris, A. 2012 Collective motion. Phys. Rep. 517 (3), 71–140.Google Scholar
Weihs, D. 1973 Hydromechanics of fish schooling. Nature 241, 290–291.Google Scholar
Wu, T. Y. & Chwang, A. T. 1975 Extraction of flow energy by fish and birds in a wavy stream. In Swimming and Flying in Nature, pp. 687–702. Springer.Google Scholar
Zhang, H.-P., Beer, A., Florin, E.-L. & Swinney, H. 2010 Collective motion and density fluctuations in bacterial colonies. Proc. Natl Acad. Sci. USA 107, 13626–13630.Google Scholar
Zhu, X., He, G. & Zhang, X. 2014 Flow-mediated interactions between two self-propelled flapping filaments in tandem configuration. Phys. Rev. Lett. 113, 238105.Google Scholar
Zou, Q. & He, X. 1997 On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys. Fluids 9 (6), 1591–1598.Google Scholar

Peng et al. supplementary movie 1

Dynamics of the orderly formation (Fast Mode "C3+1"). The initial gap spacing is G0=1. At the equilibrium state, the whole group with N=4 consists of a compact subgroup “C3” and an individual "1" following the subgroup.

Download Peng et al. supplementary movie 1(Video)
Video 7.1 MB

Peng et al. supplementary movie 2

Equilibrium state of the orderly formation (Fast Mode "C3+C2+1"). The initial gap spacing is G0=1. The whole group with N=6 consists of two compact subgroups “C3”, “C2” and an individual "1" following the subgroups.

Download Peng et al. supplementary movie 2(Video)
Video 6.7 MB

Peng et al. supplementary movie 3

Dynamics of the orderly formation (Slow Mode "S4"). The initial gap spacing is G0=3. At the equilibrium state, the sparse configuration emerges and the four plates are equally spaced with normalized gap spacing G/λ=1.

Download Peng et al. supplementary movie 3(Video)
Video 5.2 MB

Peng et al. supplementary movie 4

Equilibrium state of the orderly formation (Slow Mode "S6+S2"). The initial gap spacing is G0=3. The whole group with N=8 consists of two sparse subgroups “S6” and “S2”.

Download Peng et al. supplementary movie 4(Video)
Video 5.9 MB

Peng et al. supplementary movie 5

Equilibrium state of the orderly formation (Slow Mode "S6+S2"). The initial gap spacing is G0=3. The whole group with N=8 consists of two sparse subgroups “S6” and “S2”.

Download Peng et al. supplementary movie 5(Video)
Video 3.3 MB

Peng et al. supplementary movie 6

Equilibrium state of the orderly formation (Slow Mode "S8"). The initial gap spacing is G0=5. In the sparse configuration, the eight plates are equally spaced with normalized gap spacing G/λ =1.

Download Peng et al. supplementary movie 6(Video)
Video 4.3 MB