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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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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