The European Physical Journal Special Topics

, Volume 224, Issue 17–18, pp 3185–3197 | Cite as

Self-propulsion of free solid bodies with internal rotors via localized singular vortex shedding in planar ideal fluids

  • P. Tallapragada
  • S.D. KellyEmail author
Regular Article Physics of Locomotion
Part of the following topical collections:
  1. Dynamics of Animal Systems


Diverse mechanisms for animal locomotion in fluids rely on vortex shedding to generate propulsive forces. This is a complex phenomenon that depends essentially on fluid viscosity, but its influence can be modeled in an inviscid setting by introducing localized velocity constraints to systems comprising solid bodies interacting with ideal fluids. In the present paper, we invoke an unsteady version of the Kutta condition from inviscid airfoil theory and a more primitive stagnation condition to model vortex shedding from a geometrically contrasting pair of free planar bodies representing idealizations of swimming animals or robotic vehicles. We demonstrate with simulations that these constraints are sufficient to enable both bodies to propel themselves with very limited actuation. The solitary actuator in each case is a momentum wheel internal to the body, underscoring the symmetry-breaking role played by vortex shedding in converting periodic variations in a generic swimmer’s angular momentum to forward locomotion. The velocity constraints are imposed discretely in time, resulting in the shedding of discrete vortices; we observe the roll-up of these vortices into distinctive wake structures observed in viscous models and physical experiments.


Vortex Vorticity Internal Rotor European Physical Journal Special Topic Point Vortex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    T. Sarpkaya, J. Fluid Mech. 68, 109 (1975)ADSCrossRefGoogle Scholar
  2. 2.
    P.G. Saffman, J.C. Schatzman, J. Fluid Mech. 122, 467 (1982)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    K. Streitlien, Ph.D. thesis, Massachusetts Institute of Technology, 1994Google Scholar
  4. 4.
    R.J. Mason, J.W. Burdick, Proc. IEEE Int. Conf. Robot. Autom., 1999Google Scholar
  5. 5.
    R.J. Mason, Ph.D. thesis, California Institute of Techn., 2002Google Scholar
  6. 6.
    M.A. Jones, M.J. Shelley, J. Fluid Mech. 540, 393 (2005)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    S. Alben, M.J. Shelley, Phys. Rev. Lett. 100, 074301 (2008)ADSCrossRefGoogle Scholar
  8. 8.
    S. Michelin, S.G.L. Smith, Theor. Comput. Fluid Dyn. 23, 127 (2009)CrossRefGoogle Scholar
  9. 9.
    S. Michelin, S.G.L. Smith, Theor. Comput. Fluid Dyn. 24, 195 (2010)CrossRefGoogle Scholar
  10. 10.
    A. Ysasi, E. Kanso, P.K. Newton, Phys. D 240, 1574 (2010)CrossRefGoogle Scholar
  11. 11.
    J. Koiller, Phys. Lett. A 120, 391 (1987)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    J. Roenby, H. Aref, Proc. Royal Soc. London A 466, 1871 (2010)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    S. Alben, J. Fluid Mech. 635, 27 (2009)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    J. Vankerschaver, E. Kanso, J.E. Marsden, J. Geom. Mech. 1, 227 (2009)MathSciNetGoogle Scholar
  15. 15.
    J. Vankerschaver, E. Kanso, J.E. Marsden, Regular and Chaotic Dyn. 15, 606 (2010)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    E. Kanso, Theor. Comput. Fluid Dyn. 24, 201 (2010)CrossRefGoogle Scholar
  17. 17.
    J. Roenby, H. Aref, J. Fluids Struct. 27, 768 (2011)ADSCrossRefGoogle Scholar
  18. 18.
    B.N. Shashikanth, J.E. Marsden, J.W. Burdick, S.D. Kelly, Phys. Fluids 14, 1214 (2002)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    A.V. Borisov, I.S. Mamaev, S.M. Ramodanov, Regular Chaotic Dyn. 8, 449 (2003)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    B.N. Shashikanth, Regular Chaotic Dyn. 10, 1 (2005)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    B.N. Shashikanth, A. Sheshmani, S.D. Kelly, J.E. Marsden, Theor. Comput. Fluid Dyn. 22, 37 (2008)CrossRefGoogle Scholar
  22. 22.
    H. Xiong, Ph.D. thesis, University of Illinois at Urbana-Champaign, 2007Google Scholar
  23. 23.
    S.D. Kelly, H. Xiong, Theor. Comput. Fluid Dyn. 24, 45 (2010)CrossRefGoogle Scholar
  24. 24.
    P. Tallapragada, S.D. Kelly, Regular Chaotic Dyn. 18, 21 (2013)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    M.J. Fairchild, P.M. Hassing, S.D. Kelly, P. Pujari, P. Tallapragada, Proc. ASME Dyn. Syst. Control Conf. (2011)Google Scholar
  26. 26.
    S.D. Kelly, M.J. Fairchild, P.M. Hassing, P. Tallapragada, Proc. Amer. Control Conf. (2012)Google Scholar
  27. 27.
    S.H. Lamb, Hydrodyn. (Dover, 1945)Google Scholar
  28. 28.
    L.M. Milne-Thomson, Theor. Hydrodyn. (Dover, 1996)Google Scholar
  29. 29.
    J.E. Marsden, T.S. Ratiu, Introduction to Mechanics and Symmetry, 2nd edn. (Springer-Verlag, 1999)Google Scholar
  30. 30.
    R. Krasny, J. Fluid Mech. 184, 123 (1987)ADSCrossRefGoogle Scholar
  31. 31.
    R. Krasny, Fluid Dyn. Res. 3, 93 (1988)ADSCrossRefGoogle Scholar
  32. 32.
    D. Crowdy, Theor. Comput. Fluid Dyn. 24, 9 (2010)CrossRefGoogle Scholar
  33. 33.
    M.S. Triantafyllou, G.S. Triantafyllou, Sci. Amer. 272, 64 (1995)CrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2015

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringClemson UniversityClemsonUSA
  2. 2.Department of Mechanical Engineering and Engineering ScienceUniversity of North Carolina at CharlotteCharlotteUSA

Personalised recommendations