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A hybrid numerical model for the collective motion of fish groups

Published online by Cambridge University Press:  14 April 2025

Xuewei Mao ,
Jiadong Wang ,
Xingyuan Mao  and
Jian Deng Open the ORCID record for Jian Deng [Opens in a new window]
Xuewei Mao
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Mechanics, Zhejiang University, Hangzhou 310027, PR China
Jiadong Wang
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Mechanics, Zhejiang University, Hangzhou 310027, PR China
Xingyuan Mao
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Mechanics, Zhejiang University, Hangzhou 310027, PR China
Jian Deng*
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Mechanics, Zhejiang University, Hangzhou 310027, PR China
*
Corresponding author: Jian Deng, zjudengjian@zju.edu.cn
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Abstract

We propose a hybrid numerical model for the collective motion of fish groups, which integrates an agent-based model with a computational fluid dynamics (CFD)-based model. In the agent-based model, the fish group is represented by self-propelled particles (SPPs), incorporating social forces with local interactive rules. The CFD-based model treats the fish body with an undulated filament that responds to the hydrodynamic forces imposed by the surrounding fluid flow. These two models are coupled using a central pattern generator controller. We test this hybrid model with groups of 30–50 individuals. The results show that the group exhibits various collective behaviours, including tight schooling, sparse schooling and milling patterns, by adjusting the coefficients in the SPP model. Due to the hydrodynamic interactions, particularly with the obstacle avoidance model, both the individuals’ and the group’s mean speed fluctuate, differentiating it from traditional SPP models that typically consider volumeless particles. More interestingly, our findings indicate that fish benefit from collective motion in terms of energetic consumption in both schooling and milling patterns. It is important to note that the swimming fish are actuated using a very simple mechanism without any optimisation strategy. An additional study investigates the effects of the Reynolds number, demonstrating the capability of the current hybrid model to account for fish groups of varying body lengths or swimming speeds. Future applications of this model are promising, offering potential insights into the energetic advantages of collective motion in large-scale fish groups.

JFM classification

Biological Fluid Dynamics: Collective behaviour Biological Fluid Dynamics: Swimming/flying Biological Fluid Dynamics: Propulsion

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JFM Papers
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Journal of Fluid Mechanics , Volume 1009 , 10 May 2025 , A26
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© The Author(s), 2025. Published by Cambridge University Press

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Supplementary material: File

Mao et al. supplementary material movie 1

S0 Dynamic evolution of mode S0.
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S1 Dynamic evolution of mode S1.
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Mao et al. supplementary material movie 3

S2 Dynamic evolution of mode S2.
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Mao et al. supplementary material movie 4

M1 Dynamic evolution of mode M1.
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