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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.

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S. Alben 2008 An implicit method for coupled flow-body dynamics. J. Comput. Phys. 227, 49124933.

J. W. M. Bush & D. L. Hu 2006 Walking on water: biolocomotion at the interface. Annu. Rev. Fluid Mech. 38, 339369.

S. Childress 2008 Inertial swimming as a singular perturbation. In Proceedings of the ASME 2008 Dynamic Systems and Control Conference, Ann Arbor, MI. Available at:

T. L. Daniel 1983 Mechanics and energetics of medusan jet propulsion. Can. J. Zool. 61, 14061420.

T. L. Daniel 1984 Unsteady aspects of aquatic locomotion. Amer. Zool. 24, 121134.

W. E & J. G. Liu 1996 Essentially compact schemes for unsteady viscous incompressible flows. J. Comput. Phys. 126, 122138.

J. D. Eldredge 2006 Numerical simulations of undulatory swimming at moderate Reynolds number. Bioinsp. Biomim. 1, S19S24.

E. Kanso , J. E. Marsden , C. W. Rowley & J. Melli-Huber 2005 Locomotion of articulated bodies in a perfect fluid. J. Nonlinear Sci. 15, 255289.

M. A. Simon , W. A. Woods Jr, Y. V. Serebrenik , S. M. Simon , L. I. van Griethuijsen , J. J. Socha , W-K. Lee & B. A. Trimmer 2010 Visceral-locomotory pistoning in crawling caterpillars. Curr. Biol. 20, 16.

S. E. Spagnolie & M. J. Shelley 2009 Shape-changing bodies in fluid: hovering, ratcheting, and bursting. Phys. Fluids 21, 013103.

G. I. Taylor 1951 Analysis of the swimming of microscopic organisms. Proc. R. Soc. Lond. A 209, 447461.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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