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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

Information

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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References

Ashraf, I., Godoy-Diana, R., Halloy, J., Collignon, B. & Thiria, B. 2016 Synchronization and collective swimming patterns in fish (Hemigrammus bleheri). J. R. Soc. Interface 13, 20160734.CrossRefGoogle Scholar
Becker, A.D., Masoud, H., Newbolt, J.W., Shelley, M. & Ristroph, L. 2015 Hydrodynamic schooling of flapping swimmers. Nat. Commun. 6, 8514.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Cleaver, D.J., Wang, Z. & Gursul, I. 2012 Bifurcating flows of plunging aerofoils at high Strouhal numbers. J. Fluid Mech. 708, 349–376.CrossRefGoogle Scholar
Dai, L., He, G., Zhang, X. & Zhang, X. 2018 Stable formations of self-propelled fish-like swimmers induced by hydrodynamic interactions. J. R. Soc. Interface 15, 20180490.CrossRefGoogle ScholarPubMed
Dewey, P.A., Quinn, D.B., Boschitsch, B.M. & Smits, A.J. 2014 Propulsive performance of unsteady tandem hydrofoils in a side-by-side configuration. Phys. Fluids 26, 041903.CrossRefGoogle Scholar
Dong, G.-J. & Lu, X.-Y. 2007 Characteristics of flow over traveling wavy foils in a side-by-side arrangement. Phys. Fluids 19, 057107.CrossRefGoogle Scholar
Fukuda, H., Torisawa, S., Sawada, Y. & Takagi, T. 2010 Ontogenetic changes in schooling behaviour during larval and early juvenile stages of Pacific bluefin tuna Thunnus orientalis. J. Fish Biol. 76, 1841–1847.CrossRefGoogle ScholarPubMed
Gazzola, M., Hejazi, B. & Koumoutsakos, P. 2014 Reinforcement learning and wavelet adapted vortex methods for simulations of self-propelled swimmers. SIAM J. Sci. Comput. 36, 622–639.CrossRefGoogle Scholar
Gungor, A. & Hemmati, A. 2020 Wake symmetry impacts the performance of tandem hydrofoils during in-phase and out-of-phase oscillations differently. Phys. Rev. E 102, 043104.CrossRefGoogle ScholarPubMed
Khalid, M.S.U., Akhtar, I. & Dong, H. 2016 Hydrodynamics of a tandem fish school with asynchronous undulation of individuals. J. Fluid Struct. 66, 19–35.CrossRefGoogle Scholar
Krebs, J. 1976 Fish schooling. Nature 264, 701.CrossRefGoogle Scholar
Kurt, M. & Moored, K.W. 2018 Flow interactions of two- and three-dimensional networked bio-inspired control elements in an in-line arrangement. Bioinspir. Biomim. 13, 045002.CrossRefGoogle Scholar
Lagopoulos, N.S., Weymouth, G.D. & Ganapathisubramani, B. 2020 Deflected wake interaction of tandem flapping foils. J. Fluid Mech. 903, A9.CrossRefGoogle Scholar
Larsson, M. 2012 Why do fish school? Curr. Zool. 58, 116–128.CrossRefGoogle Scholar
Liao, J.C., Beal, D.N., Lauder, G.V. & Triantafyllou, M.S. 2003 Fish exploiting vortices decrease muscle activity. Science 302, 1566–1569.CrossRefGoogle ScholarPubMed
Lighthill, M. 1975 Mathematical Biofluiddynamics. SIAM.CrossRefGoogle Scholar
Lin, X., He, G., He, X. & Wang, Q. 2018 Dynamic response of a semi-free flexible filament in the wake of a flapping foil. J. Fluid Struct. 83, 40–53.CrossRefGoogle Scholar
Lin, X., Wu, J. & Zhang, T. 2019 a Performance investigation of a self-propelled foil with combined oscillating motion in stationary fluid. Ocean Engng 175, 33–49.CrossRefGoogle Scholar
Lin, X., Wu, J. & Zhang, T. 2020 Self-directed propulsion of an unconstrained flapping swimmer at low Reynolds number: hydrodynamic behaviour and scaling laws. J. Fluid Mech. 907, R3.CrossRefGoogle Scholar
Lin, X., Wu, J., Zhang, T. & Yang, L. 2019 b Phase difference effect on collective locomotion of two tandem autopropelled flapping foils. Phys. Rev. Fluids 4, 054101.CrossRefGoogle Scholar
Lin, X., Wu, J., Zhang, T. & Yang, L. 2019 c Self-organization of multiple self-propelling flapping foils: energy saving and increased speed. J. Fluid Mech. 884, R1.CrossRefGoogle Scholar
Lin, X., Wu, J., Zhang, T. & Yang, L. 2021 Flow-mediated organization of two freely flapping swimmers. J. Fluid Mech. 912, A37.CrossRefGoogle Scholar
Lopez, U., Gautrais, J., Couzin, I.D. & Theraulaz, G. 2012 From behavioural analyses to models of collective motion in fish schools. Interface Focus 2, 693–707.CrossRefGoogle ScholarPubMed
Maertens, A.P., Gao, A. & Triantafyllou, M.S. 2017 Optimal undulatory swimming for a single fish-like body and for a pair of interacting swimmers. J. Fluid Mech. 813, 301–345.CrossRefGoogle Scholar
Marras, S., Killen, S.S., Lindstrom, J., Mckenzie, D.J., Steffensen, J.F. & Domenici, P. 2015 Fish swimming in schools save energy regardless of their spatial position. Behav. Ecol. Sociobiol. 69, 219–226.CrossRefGoogle ScholarPubMed
Marras, S. & Porfiri, M. 2012 Fish and robots swimming together: attraction towards the robot demands biomimetic locomotion. J. R. Soc. Interface 9, 1856–1868.CrossRefGoogle ScholarPubMed
Muscutt, L.E., Weymouth, G.D. & Ganapathisubramani, B. 2017 Performance augmentation mechanism of in-line tandem flapping foils. J. Fluid Mech. 827, 484–505.CrossRefGoogle Scholar
Park, S.G. & Sung, H.J. 2018 Hydrodynamics of flexible fins propelled in tandem, diagonal, triangular and diamond configurations. J. Fluid Mech. 840, 154–189.CrossRefGoogle Scholar
Peng, Z.-R., Huang, H. & Lu, X.-Y. 2018 Collective locomotion of two closely spaced self-propelled flapping plates. J. Fluid Mech. 849, 1068–1095.CrossRefGoogle 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, 071201.CrossRefGoogle Scholar
Rohr, J.J. & Fish, F.E. 2004 Strouhal numbers and optimization of swimming by odontocete cetaceans. J. Exp. Biol. 207, 1633–1642.CrossRefGoogle ScholarPubMed
Romanczuk, P., Couzin, I.D. & Schimansky-Geier, L. 2009 Collective motion due to individual escape and pursuit response. Phys. Rev. Lett. 102, 010602.CrossRefGoogle ScholarPubMed
Ryu, J., Yang, J., Park, S.G. & Sung, H.J. 2020 Phase-mediated locomotion of two self-propelled flexible plates in a tandem arrangement. Phys. Fluids 32, 041901.Google Scholar
Saadat, M., Berlinger, F., Sheshmani, A., Nagpal, R., Lauder, G.V. & Haj-Hariri, H. 2021 Hydrodynamic advantages of in-line schooling. Bioinspir. Biomim. 16, 046002.CrossRefGoogle ScholarPubMed
Verma, S., Novati, G. & Koumoutsakos, P. 2018 Efficient collective swimming by harnessing vortices through deep reinforcement learning. PNAS 115, 5849–5854.CrossRefGoogle ScholarPubMed
Weihs, D. 1973 Hydromechanics of fish schooling. Nature 241, 290–291.CrossRefGoogle Scholar
Wu, J. & Shu, C. 2009 Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications. J. Comput. Phys. 228, 1963–1979.CrossRefGoogle Scholar
Xu, G.D., Duan, W.Y. & Xu, W.H. 2017 The propulsion of two flapping foils with tandem configuration and vortex interactions. Phys. Fluids 29, 097102.CrossRefGoogle Scholar
Yang, L.M., Shu, C., Yang, W.M. & Wang, Y. 2017 A simplified circular function-based gas kinetic scheme for simulation of incompressible flows. Intl J. Numer. Meth. Fluids 85, 583–598.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed

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