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Flow-mediated organization of two freely flapping swimmers

Published online by Cambridge University Press:  15 February 2021

Xingjian Lin ,
Jie Wu Open the ORCID record for Jie Wu [Opens in a new window] ,
Tongwei Zhang  and
Liming Yang
Xingjian Lin
Affiliation:
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu210016, PR China Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu210016, PR China
Jie Wu*
Affiliation:
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu210016, PR China Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu210016, PR China Key Laboratory of Unsteady Aerodynamics and Flow Control, Ministry of Industry and Information Technology, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu210016, PR China
Tongwei Zhang
Affiliation:
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu210016, PR China Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu210016, PR China
Liming Yang
Affiliation:
Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu210016, PR China Key Laboratory of Unsteady Aerodynamics and Flow Control, Ministry of Industry and Information Technology, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu210016, PR China Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore119260, Republic of Singapore
*
†Email address for correspondence: [email protected]
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Abstract

Fish schools and bird flocks, which involve a variety of orderly formations, have fascinated people for a long time. The collective performance of two flapping foils in parallel, which can self-propel in both lateral and longitudinal directions, is numerically studied through two-dimensional simulations in this paper. For the first time it is numerically confirmed that two flapping swimmers can simultaneously converge to equilibrium distances in both lateral and longitudinal directions. Two types of stable formations have been observed and which type occurs depends on the phase difference between two foils. The staggered formation appears in the in-phase scenario, and the side-by-side formation occurs in the anti-phase scenario. Moreover, both types of the stable formations strongly depend on the flapping frequency and amplitude, but are independent of the perturbation of the initial distance between the two foils when the perturbation is small. In addition, considerable velocity enhancement can be achieved by two foils in all of the stable formations, as compared with that of a single foil. Moreover, the velocity of the two-foil system can be couched as a specific scaling law, which is determined by the type of the stable formations. Finally, the mechanism behind the stable formations has been analysed. The results obtained here may shed some light on the understanding of collective behaviour of fish schools and bird flocks.

JFM classification

Biological Fluid Dynamics: Swimming/flying Biological Fluid Dynamics: Propulsion
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 912 , 10 April 2021 , A37
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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