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Two-dimensional hydrodynamic schooling of two flapping swimmers initially in tandem formation

Published online by Cambridge University Press:  27 April 2022

Xingjian Lin ,
Jie Wu Open the ORCID record for Jie Wu [Opens in a new window] ,
Liming Yang  and
Hao Dong
Xingjian Lin
Affiliation:
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu 210016, PR China Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu 210016, 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, Jiangsu 210016, PR China School of Mechanical Engineering, Nanjing Institute of Technology, Nanjing, Jiangsu 211167, 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, Jiangsu 210016, PR China Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu 210016, 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, Jiangsu 210016, PR China
Liming Yang
Affiliation:
Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu 210016, 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, Jiangsu 210016, PR China
Hao Dong
Affiliation:
Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu 210016, 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, Jiangsu 210016, PR China
*
†Email address for correspondence: wuj@nuaa.edu.cn
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Abstract

The effect of hydrodynamic interactions on the collective locomotion of fish schools is still poorly understood. In this paper, the flow-mediated organization of two tandem flapping foils, which are free in both the longitudinal and lateral directions, is numerically studied. It is found that the tandem formation is unstable for two foils when they can self-propel in both the longitudinal and lateral directions. Three types of resultant regular formations are observed, i.e. semi-tandem formation, staggered formation and transitional formation. Which type of regular formation occurs depends on the flapping parameters and the initial longitudinal distance between the two foils. Moreover, there is a threshold value of the cycle-averaged longitudinal distance (which is approximately 0.55) below which both velocity enhancement and efficiency augmentation can be achieved by two foils in regular formations. The results obtained here may shed some light on understanding the emergence of regular formations of fish schools.

JFM classification

Biological Fluid Dynamics: Swimming/flying Biological Fluid Dynamics: Propulsion
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 941 , 25 June 2022 , A29
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Lin et al. supplementary movie 1

The propulsion of two flapping swimmers in the semi-tandem formation.

Download Lin et al. supplementary movie 1(Video)
Video 2.6 MB

Lin et al. supplementary movie 2

The propulsion of two flapping swimmers in the staggered formation.

Download Lin et al. supplementary movie 2(Video)
Video 697.5 KB

Lin et al. supplementary movie 3

The propulsion of two flapping swimmers in the transitional formation.

Download Lin et al. supplementary movie 3(Video)
Video 4 MB