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Intermittent swimmers optimize energy expenditure with flick-to-flick motor control

Published online by Cambridge University Press:  10 March 2025

Yi Zhu ,
Linlin Kang Open the ORCID record for Linlin Kang [Opens in a new window] ,
Xinyu Tong ,
Jingtao Ma ,
Fangbao Tian Open the ORCID record for Fangbao Tian [Opens in a new window]  and
Dixia Fan Open the ORCID record for Dixia Fan [Opens in a new window]
Yi Zhu
Affiliation:
Key Laboratory of Coastal Environment and Resources of Zhejiang Province, School of Engineering, Westlake University, Hangzhou, Zhejiang 310030, PR China
Linlin Kang*
Affiliation:
Key Laboratory of Coastal Environment and Resources of Zhejiang Province, School of Engineering, Westlake University, Hangzhou, Zhejiang 310030, PR China
Xinyu Tong
Affiliation:
Key Laboratory of Coastal Environment and Resources of Zhejiang Province, School of Engineering, Westlake University, Hangzhou, Zhejiang 310030, PR China
Jingtao Ma
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, M2P2, Marseille, France School of Engineering and Information Technology, University of New South Wales, Canberra, ACT 2600, Australia
Fangbao Tian*
Affiliation:
School of Engineering and Information Technology, University of New South Wales, Canberra, ACT 2600, Australia
Dixia Fan*
Affiliation:
Key Laboratory of Coastal Environment and Resources of Zhejiang Province, School of Engineering, Westlake University, Hangzhou, Zhejiang 310030, PR China
*
Corresponding authors: Linlin Kang, [email protected]; Fangbao Tian, [email protected]; Dixia Fan, [email protected]
Corresponding authors: Linlin Kang, [email protected]; Fangbao Tian, [email protected]; Dixia Fan, [email protected]
Corresponding authors: Linlin Kang, [email protected]; Fangbao Tian, [email protected]; Dixia Fan, [email protected]
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Abstract

Intermittent swimming behaviour is commonly observed in larval zebrafish, often attributed to energy-saving mechanisms. In this study, we utilize a hybrid approach combining deep reinforcement learning and the immersed boundary–lattice Boltzmann method to train a larval zebrafish-like swimmer to reach a target with minimized energy expenditure. We find that when the tail-beat period is fixed, continuous swimming emerges as the optimal strategy. However, when the tail-beat period is allowed to vary, intermittent swimming proves superior in energy performance, achieved through reductions in tail-beat amplitude and frequency. Our detailed analysis reveals that intermittent swimmers employ rapid backward tail flicks to attain high speeds, coupled with slower forward tail flicks and coasting phases to conserve energy. Furthermore, we derive scaling laws governing the swimming performance of trained fish. These results offer valuable insights into the intermittent swimming patterns of fish, with implications for understanding bio-inspired locomotion and informing the design of energy-efficient aquatic systems.

JFM classification

Biological Fluid Dynamics: Swimming/flying Biological Fluid Dynamics: Propulsion
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1006 , 10 March 2025 , A27
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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Footnotes

†

Y. Zhu and L. Kang contributed equally to this work and should be considered co-first authors.

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