Skip to main content

A bug on a raft: recoil locomotion in a viscous fluid


The locomotion of a body through an inviscid incompressible fluid, such that the flow remains irrotational everywhere, is known to depend on inertial forces and on both the shape and the mass distribution of the body. In this paper we consider the influence of fluid viscosity on such inertial modes of locomotion. In particular we consider a free body of variable shape and study the centre-of-mass and centre-of-volume variations caused by a shifting mass distribution. We call this recoil locomotion. Numerical solutions of a finite body indicate that the mechanism is ineffective in Stokes flow but that viscosity can significantly increase the swimming speed above the inviscid value once Reynolds numbers are in the intermediate range 50–300. To study the problem analytically, a model which is an analogue of Taylor's swimming sheet is introduced. The model admits analysis at fixed, arbitrarily large Reynolds number for deformations of sufficiently small amplitude. The analysis confirms the significant increase of swimming velocity above the inviscid value at intermediate Reynolds numbers.

Corresponding author
Email address for correspondence:
Hide All
Alben S. 2008 An implicit method for coupled flow-body dynamics. J. Comput. Phys. 227, 49124933.
Braza M., Chassaing P. & Ha Minh H. 1986 Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder. J. Fluid Mech. 165, 79130.
Bush J. W. M. & Hu D. L. 2006 Walking on water: biolocomotion at the interface. Annu. Rev. Fluid Mech. 38, 339369.
Childress S. 1981 Mechanics of Swimming and Flying. Cambridge.
Childress S. 2008 Inertial swimming as a singular perturbation. In Proceedings of the ASME 2008 Dynamic Systems and Control Conference, Ann Arbor, MI. Available at:
Childress S. 2010 Walking on water. J. Fluid Mech. 644, 14.
Daniel T. L. 1983 Mechanics and energetics of medusan jet propulsion. Can. J. Zool. 61, 14061420.
Daniel T. L. 1984 Unsteady aspects of aquatic locomotion. Amer. Zool. 24, 121134.
E W. & Liu J. G. 1996 Essentially compact schemes for unsteady viscous incompressible flows. J. Comput. Phys. 126, 122138.
Eldredge J. D. 2006 Numerical simulations of undulatory swimming at moderate Reynolds number. Bioinsp. Biomim. 1, S19S24.
Elston J. R., Blackburn H. M. & Sheridan J. 2006 The primary and secondary instabilities of flow generated by an oscillating circular cylinder. J. Fluid Mech. 550, 359389.
Kanso E., Marsden J. E., Rowley C. W. & Melli-Huber J. 2005 Locomotion of articulated bodies in a perfect fluid. J. Nonlinear Sci. 15, 255289.
Lighthill J. 1991 Hydrodynamic far fields. In Mathematical Approaches in Hydrodynamics (ed. Miloh T.), pp. 320. Society of Industrial and Applied Mathematics.
Roshko A. 1961 Experiments on the flow past a circular cylinder at very high Reynolds number. J. Fluid Mech. 10, 345356.
Saffman P. G. 1967 Self-propulsion of a deformable body in a perfect fluid. J. Fluid Mech. 28, 385389.
Simon M. A., Woods W. A. Jr, Serebrenik Y. V., Simon S. M., van Griethuijsen L. I., Socha J. J., Lee W-K. & Trimmer B. A. 2010 Visceral-locomotory pistoning in crawling caterpillars. Curr. Biol. 20, 16.
Spagnolie S. E. & Shelley M. J. 2009 Shape-changing bodies in fluid: hovering, ratcheting, and bursting. Phys. Fluids 21, 013103.
Tatsuno M. & Bearman P. W. 1990 A visual study of the flow around an oscillating circular cylinder at low Keulegan–Carpenter numbers and low Stokes numbers. J. Fluid Mech. 211, 157182.
Taylor G. I. 1951 Analysis of the swimming of microscopic organisms. Proc. R. Soc. Lond. A 209, 447461.
Tuck E. O. 1968 A note on the swimming problem. J. Fluid Mech. 31, 305308.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 34 *
Loading metrics...

Abstract views

Total abstract views: 242 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 20th November 2017. This data will be updated every 24 hours.