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Swimming in an inviscid fluid

  • Eva KansoEmail author
Original Article

Abstract

We present a set of equations governing the motion of a body due to prescribed shape changes in an inviscid, planar fluid with nonzero vorticity. The derived equations, when neglecting vorticity, reduce to the model developed in Kanso et al. (J Nonlinear Sci 15:255–289, 2005) for swimming in potential flow, and are also consistent with the models developed in Borisov et al. (J Math Phys 48:1–9, 2007), Kanso and Oskouei (J Fluid Mech 800:77–94, 2008), Shasikanth et al. (Phys Fluids 14(3):1214–1227, 2002) for a rigid body interacting dynamically with point vortices. The effects of cyclic shape changes and the presence of vorticity on the locomotion of a submerged body are discussed through examples.

Keywords

Swimming Dynamics Vorticity 

PACS

47 47.10.Fg 47.32.C- 47.63.-b 47.63.mc 

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References

  1. 1.
    Beal D.N., Hover F.S., Triantafyllou M.S., Liao J.C., Lauder G.V.: Passive propulsion in vortex wakes. J. Fluid Mech. 549, 385–402 (2006)CrossRefGoogle Scholar
  2. 2.
    Borisov A.V., Mamaev I.S., Ramodanov S.M.: Dynamic interaction of point vortices and a two-dimensional cylinder. J. Math. Phys. 48, 1–9 (2007)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Jones M.A.: The separated flow of an inviscid fluid around a moving flat plate. J. Fluid Mech. 496, 405–441 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Kanso E., Marsden J.E., Rowley C.W., Melli-Huber J.: Locomotion of articulated bodies in a perfect fluid. J. Nonlinear Sci. 15, 255–289 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Kanso E., Oskouei B.: Stability of a coupled body-vortex system. J. Fluid Mech. 800, 77–94 (2008)MathSciNetGoogle Scholar
  6. 6.
    Kanso, E.: Swimming due to transverse shape deformations. J. Fluid Mech. (2009, in press)Google Scholar
  7. 7.
    Katz J., Plotkin A.: Low-Speed Aerodynamics. Cambridge Aerospace Series, Cambridge (2001)zbMATHGoogle Scholar
  8. 8.
    Kelly, S.D.: The mechanics and control of robotic locomotion with applications to aquatic vehicles. Ph.D. thesis, California Institute of Technology (1998)Google Scholar
  9. 9.
    Lamb H.: Hydrodynamics. Dover, New York (1932)zbMATHGoogle Scholar
  10. 10.
    Lighthill, J.: Mathematical Biofluiddynamics. Society for Industrial and Applied Mathematics. Philadelphia (1975)Google Scholar
  11. 11.
    Miloh T., Galper A.: Self-propulsion of general deformable shapes in a perfect fluid. Proc. R. Soc. Lond. A 442, 273–299 (1993)zbMATHCrossRefGoogle Scholar
  12. 12.
    Montgomery R.: Isoholonomic problems and some applications. Commun. Math. Phys. 128, 565–592 (1990)zbMATHCrossRefGoogle Scholar
  13. 13.
    Radford, J.: Symmetry, Reduction and swimming in a perfect fluid. Ph.D. thesis, California Institute of Technology (2003)Google Scholar
  14. 14.
    Shapere, Wilczek: Self-propulsion at low Reynolds number. Phys. Rev. Lett. 58(2), 2051–2054 (1987)Google Scholar
  15. 15.
    Shashikanth, B.N., Marsden, J.E., Burdick, J.W., Kelly, S.D.: The Hamiltonian structure of a 2D rigid circular cylinder interacting dynamically with N Point vortices. Phys. Fluids 14(3), 1214–1227 (2002) (see also Erratum, Phys. Fluids 14(11), 4099)Google Scholar
  16. 16.
    Shashikanth B.N.: Poisson brackets for the dynamically interacting system of a 2D rigid cylinder and N point vortices: the case of arbitrary smooth cylinder shapes. Reg. Chaos. Dyn. 10(1), 110 (2005)MathSciNetGoogle Scholar
  17. 17.
    Shukla R.K., Eldredge J.E.: An inviscid model for vortex shedding from a deforming body. Theor. Comput. Fluid Dyn. 21(5), 343–368 (2007)CrossRefGoogle Scholar
  18. 18.
    Saffman, P.G.: Vortex dynamics. Cambridge Monographs on Mechanics and Applied Mathematics (1992)Google Scholar
  19. 19.
    Tytell E.D., Lauder G.V.: The hydrodynamics of eel swimming: I. Wake structure. J. Exp. Biol. 207, 1825–1841 (2004)CrossRefGoogle Scholar
  20. 20.
    Wu T.: Hydrodynamics of swimming propulsion. Part 1. Swimming of a two-dimensional flexible plate at variable forward speeds in an inviscid fluid. J. Fluid Mech. 46(2), 337–355 (1971)CrossRefGoogle Scholar
  21. 21.
    Wu T.: Hydrodynamics of swimming propulsion. Part 2. Some optimum shape problems. J. Fluid Mech. 46(3), 521–544 (1971)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.University of Southern CaliforniaLos AngelesUSA

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