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Model Problems for Fish Schooling

  • Silas AlbenEmail author
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 155)

Abstract

We review recent work on model systems for body-vortex and body-body interactions in a fluid, related to fish schooling. The studies show a variety of structured and disordered dynamics which can occur when vortices interact with passive and actively-driven deformable bodies. The energy savings due to body-vortex interactions depend strongly on the geometric arrangement of multiple bodies and/or ambient vortices, the phases of the bodies’ motions relative to those of the vortices and other bodies, and the rigidity of flexible appendages.

Key words

Flexible vorticity coupled flow-body 

References

  1. [1].
    Koehl MAR (2003) Physical modelling in biomechanics. Philos Trans R Soc Lond Ser B Biol Sci 358(1437):1589CrossRefGoogle Scholar
  2. [2].
    Liao JC, Beal DN, Lauder GV, Triantafyllou MS (2003) Fish exploiting vortices decrease muscle activity. Science 302(5650):1566–1569CrossRefGoogle Scholar
  3. [3].
    Liao JC (2007) A review of fish swimming mechanics and behaviour in altered flows. Philos Trans R Soc B Biol Sci 362(1487):1973CrossRefGoogle Scholar
  4. [4].
    Newman JN (1975) Swimming of slender fish in a non-uniform velocity field. ANZIAM J 19(1):95–111zbMATHCrossRefGoogle Scholar
  5. [5].
    Dabiri JO (2007) Renewable fluid dynamic energy derived from aquatic animal locomotion. Bioinspiration Biomim 2:L1CrossRefGoogle Scholar
  6. [6].
    Streitlien K, Triantafyllou GS, Triantafyllou MS (1996) Efficient foil propulsion through vortex control. AIAA J 34(11):2315–2319zbMATHCrossRefGoogle Scholar
  7. [7].
    Doligalski TL, Smith CR, Walker JDA (1994) Vortex interactions with walls. Annu Rev Fluid Mech 26(1):573–616MathSciNetCrossRefGoogle Scholar
  8. [8].
    Alben S (2009) On the swimming of a flexible body in a vortex street. J Fluid Mech 635:27–45MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9].
    Taylor G (1951) Analysis of the swimming of microscopic organisms. Proc R Soc Lond Ser A Math Phys Sci 209(1099):447–461zbMATHCrossRefGoogle Scholar
  10. [10].
    Alben S (2009) Passive and active bodies in vortex-street wakes. J Fluid Mech 642:95–125MathSciNetCrossRefGoogle Scholar
  11. [11].
    Eldredge JD, Pisani D (2008) Passive locomotion of a simple articulated fish-like system in the wake of an obstacle. J Fluid Mech 607:279–288zbMATHCrossRefGoogle Scholar
  12. [12].
    Manela A, Howe MS (2009) The forced motion of a flag. J Fluid Mech 635:439–454MathSciNetzbMATHCrossRefGoogle Scholar
  13. [13].
    Alben S (2011) Interactions between vortices and flexible walls. Int J Non-Linear Mech 46:586–591CrossRefGoogle Scholar
  14. [14].
    Rockwell D (1998) Vortex-body interactions. Ann Rev Fluid Mech 30(1):199–229MathSciNetCrossRefGoogle Scholar
  15. [15].
    Dong GJ, Lu XY (2007) Characteristics of flow over traveling wavy foils in a side-by-side arrangement. Phys Fluids 19:057107CrossRefGoogle Scholar
  16. [16].
    Wang ZJ, Russell D (2007) Effect of forewing and hindwing interactions on aerodynamic forces and power in hovering dragonfly flight. Phys Rev Lett 99(14):148101CrossRefGoogle Scholar
  17. [17].
    Zhu L, Peskin CS (2003) Interaction of two flapping filaments in a flowing soap film. Phys Fluids 15:1954–1960MathSciNetCrossRefGoogle Scholar
  18. [18].
    Zhang J, Childress S, Libchaber A, Shelley M (2000) Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature 408(6814):835–839CrossRefGoogle Scholar
  19. [19].
    Shelley MJ, Zhang J (2011) Flapping and bending bodies interacting with fluid flows. Annu Rev Fluid Mech 43(1):449MathSciNetCrossRefGoogle Scholar
  20. [20].
    Farnell DJJ, David T, Barton DC (2004) Coupled states of flapping flags. J Fluid Struct 19(1):29–36CrossRefGoogle Scholar
  21. [21].
    Jia L-B, Li F, Yin X-Z, Yin X-Y (2007) Coupling modes between two flapping filaments. J Fluid Mech 581:199–220MathSciNetzbMATHCrossRefGoogle Scholar
  22. [22].
    Drucker EG, Lauder GV (2001) Locomotor function of the dorsal fin in teleost fishes: experimental analysis of wake forces in sunfish. J Exp Biol 204(17):2943–2958Google Scholar
  23. [23].
    Ristroph L, Zhang J (2008) Anomalous hydrodynamic drafting of interacting flapping flags. Phys Rev Lett 101(19):194502CrossRefGoogle Scholar
  24. [24].
    Alben S (2009) Wake-mediated synchronization and drafting in coupled flags. J Fluid Mech 641:489–496MathSciNetzbMATHCrossRefGoogle Scholar
  25. [25].
    Schouveiler L, Eloy C (2009) Coupled flutter of parallel plates. Phys Fluids 21:081703CrossRefGoogle Scholar
  26. [26].
    Michelin S, Llewellyn Smith SG (2009) Linear stability analysis of coupled parallel flexible plates in an axial flow. J Fluids Struct 25(7):1136–1157CrossRefGoogle Scholar
  27. [27].
    Zhu L (2009) Interaction of two tandem deformable bodies in a viscous incompressible flow. J Fluid Mech 635:455–475MathSciNetzbMATHCrossRefGoogle Scholar
  28. [28].
    Kim S, Huang W, Sung HJ (2010) Constructive and destructive interaction modes between two tandem flexible flags in viscous flow. J Fluid Mech 661:511–521zbMATHCrossRefGoogle Scholar
  29. [29].
    Weihs D (1973) Hydromechanics of fish schooling. Nature 241(5387):290–291CrossRefGoogle Scholar
  30. [30].
    Kanso E, Marsden JE, Rowley CW, Melli-Huber JB (2005) Locomotion of articulated bodies in a perfect fluid. J Nonlinear Sci 15(4):255–289MathSciNetzbMATHCrossRefGoogle Scholar
  31. [31].
    Kelly SD, Xiong H (2006) Controlled hydrodynamic interactions in schooling aquatic locomotion. In: Decision and control, 2005 and 2005 European control conference. CDC-ECC’05. 44th IEEE conference on, Seville. IEEE, pp 3904–3910Google Scholar
  32. [32].
    Nair S, Kanso E (2007) Hydrodynamically coupled rigid bodies. J Fluid Mech 592:393–411MathSciNetzbMATHCrossRefGoogle Scholar
  33. [33].
    Partridge BL, Pitcher TJ (1979) Evidence against a hydrodynamic function for fish schools. Nature 279(5712):418CrossRefGoogle Scholar
  34. [34].
    Fauci LJ (1990) Interaction of oscillating filaments: a computational study. J Comput Phys 86(2):294–313MathSciNetzbMATHCrossRefGoogle Scholar
  35. [35].
    Fish FE (1995) Kinematics of ducklings swimming in formation: consequences of position. J Exp Zool 273(1):1–11MathSciNetCrossRefGoogle Scholar
  36. [36].
    Saintillan D, Shelley MJ (2007) Orientational order and instabilities in suspensions of self-locomoting rods. Phys Rev Lett 99(5):58102CrossRefGoogle Scholar
  37. [37].
    Ishikawa T, Pedley TJ (2008) Coherent structures in monolayers of swimming particles. Phys Rev Lett 100(8):88103CrossRefGoogle Scholar
  38. [38].
    Saintillan D, Shelley MJ (2008) Instabilities and pattern formation in active particle suspensions: kinetic theory and continuum simulations. Phys Rev Lett 100(17):178103CrossRefGoogle Scholar
  39. [39].
    Pedley TJ (2010) Collective behaviour of swimming micro-organisms. Exp Mech 50(9):1293–1301CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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