Skip to main content
SpringerLink
Log in

The three-dimensional hydrodynamics of tadpole model’s solitary swimming and parallel schooling

  • Articles
  • Published:
Journal of Hydrodynamics Aims and scope Submit manuscript

Abstract

Tadpole swimming, including a solitary tadpole swimming and schooling side-by-side in an in-phase mode, is investigated numerically in the present paper. The three-dimensional Navier-Stokes equations for the unsteady incompressible viscous flow are solved. A dynamic mesh fitting the tadpole’s deforming body surface is adopted. The results showed that for a solitary tadpole swimming, two vortex rings are shed in each undulating period. However, as the resultant force on the tadpole is drag, the vortex rings are obviously asymmetric, shaped like “C”. When the resultant force in the swimming direction approaches zero, the axes of the vortex rings are nearly vertical to the swimming direction. Distorted vortex rings are found when the resultant force on the tadpole is thrust. When the tadpole model obtains the optimum propulsive efficiency, its swimming speed and undulating frequency are close to the values observed in nature. For tadpoles swimming side-by-side in an in-phase mode, the vortex structures in the wake may merge, split and recombine. Compared with a solitary tadpole swimming, only a small hydrodynamic advantage occur with schooling in parallel, which may be one of the reasons why tadpoles rarely, if ever swim, side by side for any amount of time or distance in nature. The effect of the undulating frequency on the tadpoles schooling is similar to that on a solitary tadpole. In addition, with an increase in the Reynolds number, the thrust force and the propulsive efficiency both increase, while the power consumption decreases. We also found that the tadpole benefits from the vortex pair shedding from its blunt snout, which can strengthen the vortex intensity in the wake and improve the pressure distribution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Videler J J. Fish swimming [M]. Springer Science & Business Media, 2012.

    Google Scholar 

  2. Wassersug R J, Hoff K. The kinematics of swimming in anuran larvae [J]. Journal of Experimental Biology, 1985, 119(1): 1–30.

    Google Scholar 

  3. Azizi E, Landberg T, Wassersug R J. Vertebral function during tadpole locomotion [J]. Zoology, 2007, 110(4): 290–297.

    Article  Google Scholar 

  4. Olson R S, Hintze A, Dyer F C, et al. Predator confusion is sufficient to evolve swarming behaviour [J]. Journal of the Royal Society Interface, 2013, 10(85):20130305.

    Article  Google Scholar 

  5. Humston R, Ault J S, Lutcavage M and Olson D B. Schooling and migration of large pelagic fishes relative to environmental cues [J]. Fisheries Oceanography, 2010, 9(2):136–146.

    Article  Google Scholar 

  6. Sung G P, Sung H J. Hydrodynamics of flexible fins propelled in tandem, diagonal, triangular and diamond configurations [J]. Journal of Fluid Mechanics, 2018, 840:154–189.

    Article  MathSciNet  Google Scholar 

  7. Lin X, He G, He X, Wang Q, Chen L. Numerical study of the hydrodynamic performance of two wiggling hydrofoils in diagonal arrangement [J]. Journal of Applied Mathematics & Physics, 2017, 05(1):31–38.

    Article  Google Scholar 

  8. Maertens A P, Gao A, Triantafyllou M S. Optimal undulatory swimming for a single fish-like body and for a pair of interacting swimmers [J]. Journal of Fluid Mechanics, 2017, 813:301–345.

    Article  MathSciNet  Google Scholar 

  9. Mohsen Daghooghi, Iman Borazjani. The hydrodynamic advantages of synchronized swimming in a rectangular pattern [J]. Bioinspiration & Biomimetics, 2015, 10(5):056018.

    Article  Google Scholar 

  10. Deng J, Shao X M, Yu Z S. Hydrodynamic studies on twotravelling wavy foils in tandem arrangement [J]. Physics of Fluids, 2007, 19(11):305–371.

    Article  Google Scholar 

  11. Dong G J, Lu X Y. Characteristics of flow over travelling wavy foils in a side-by-side arrangement [J]. Physics of Fluids, 2007, 19(5):057107.

    Article  Google Scholar 

  12. Wang L, Wang M, Fu Q, Miao R D. Numerical simulation of two self-propelled fish swimming in a side-by-side arrangement[J].Chinese Journal of Computational Mechanics, 2014,31(1):103–109.

    Google Scholar 

  13. Caldwell, J P. Structure and behaviour of Hyla geographica tadpole schools, with comments on classification of group behaviour in tadpoles [J]. Copeia, 1989, 4:938–950.

    Article  Google Scholar 

  14. Heursel, A D, Celio Haddad F B. Schooling and swimming behaviors of Hyla semilineata tadpoles (anura,hylidae) [J]. Iheringia, Sér. Zool., Porto Alegre, 2002, 92(1):99–104.

    Article  Google Scholar 

  15. Breden F, Lum A, Wassersug R J. Body size and orientation in aggregates of toad tadpoles Bufo woodhousei [J]. Copeia, 1982, 3:672–680.

    Article  Google Scholar 

  16. Wassersug R J, Lum A M, Potel M J. An analysis of school structure for tadpoles (Anura: Amphibia) [J]. Behavioral Ecology and Sociobiology, 1981, 9:15–22.

    Article  Google Scholar 

  17. Chen X Y, Hu W R. Numerical investigation of tadpole models swimming in side-by-side arrangement [J]. Journal of Hydrodynamics, Ser.A, 2017, 32(2):133–140.

    Google Scholar 

  18. Handrigan G R, Wassersug R J. The anuran Bauplan: A review of the adaptive, developmental, and genetic underpinnings of frog and tadpole morphology [J]. Biological Reviews, 2007, 82(1):1–25.

    Article  Google Scholar 

  19. Köhler G, Lehr E, McCranie J R. The tadpole of the Central American toad Bufo luetkenii Boulenger [J]. Journal of Herpetology, 2000: 303–306.

    Google Scholar 

  20. Yuan H T, Hu W R. A numerical study on tadpole swimming in the wake of a D-section cylinder [J]. Journal of hydrodynamics, Ser. B, 2017, 29(6):1044–1053.

    Article  Google Scholar 

  21. Hoff K, Wassersug R J. Tadpole locomotion: axial movement and tail functions in a largely vertebraeless vertebrate [J]. American Zoologist, 2000, 40(1):62–076.

    Google Scholar 

  22. Lu X Y, Yang J M, Yin X Z. Propulsive performance and vortex shedding of a foil in flapping flight [J]. Acta Mechanica, 2003, 165(3–4): 189–206.

    Article  Google Scholar 

  23. Martinat G, Braza M, Hoarau Y, Harran G. Turbulence modelling of the flow past a pitching NACA0012 airfoil at 105 and 106 Reynolds numbers[J]. Journal of Fluids & Structures, 2008, 24(8):1294–1303.

    Article  Google Scholar 

  24. Hu W R, Tong B, Ma H, Liu H. A computational study of a backward swimming hydrodynamics of the eel Anguilla [J]. Journal of Hydrodynamics, 2005, 4(4):438–447.

    MATH  Google Scholar 

  25. Cheng J Y, Zhuang L X, Tong B G. Analysis of swimming three-dimensional waving plates [J].Journal of Fluid Mechanics, 1991, 232(232): 341–355.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai, 200240, China

    Ting-ting Li, Wen-rong Hu & Xu-yang Chen

  2. Shanghai Jiao Tong University and Chiba University International Cooperative Research Center (SJTU-CU-ICRC), Shanghai Jiao Tong University, Shanghai, 200240, China

    Ting-ting Li & Wen-rong Hu

  3. MOE Key Laboratory of Hydrodynamics, Shanghai Jiao Tong University, Shanghai, 200240, China

    Ting-ting Li & Wen-rong Hu

  4. Department of Mechanical Engineering, Tokyo Institute of Technology, Tokyo, 1528550, Japan

    Xu-yang Chen

Authors
  1. Ting-ting Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wen-rong Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xu-yang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wen-rong Hu.

Additional information

Project supported by the National Natural Science Foundation of China (Grant No.11472173).

Biography: Ting-ting Li(1993–), Female, Master

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Tt., Hu, Wr. & Chen, Xy. The three-dimensional hydrodynamics of tadpole model’s solitary swimming and parallel schooling. J Hydrodyn 32, 548–560 (2020). https://doi.org/10.1007/s42241-019-0071-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42241-019-0071-8

Key words

Search

Navigation