Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T06:23:36.961Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  12 January 2011

STEPHEN CHILDRESS ,
SAVERIO E. SPAGNOLIE  and
TADASHI TOKIEDA
STEPHEN CHILDRESS*
Affiliation:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA
SAVERIO E. SPAGNOLIE
Affiliation:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA
TADASHI TOKIEDA
Affiliation:
Trinity Hall, Cambridge CB2 1TJ, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

JFM classification

Biological Fluid Dynamics: Propulsion Biological Fluid Dynamics: Swimming/flying
Type
Papers
Information
Journal of Fluid Mechanics , Volume 669 , 25 February 2011 , pp. 527 - 556
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Alben, S. 2008 An implicit method for coupled flow-body dynamics. J. Comput. Phys. 227, 4912–4933.CrossRefGoogle Scholar
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, 79–130.CrossRefGoogle Scholar
Bush, J. W. M. & Hu, D. L. 2006 Walking on water: biolocomotion at the interface. Annu. Rev. Fluid Mech. 38, 339–369.CrossRefGoogle Scholar
Childress, S. 1981 Mechanics of Swimming and Flying. Cambridge.CrossRefGoogle Scholar
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: http://www.math.nyu.edu/faculty/childres/preprints.html.Google Scholar
Childress, S. 2010 Walking on water. J. Fluid Mech. 644, 1–4.CrossRefGoogle Scholar
Daniel, T. L. 1983 Mechanics and energetics of medusan jet propulsion. Can. J. Zool. 61, 1406–1420.CrossRefGoogle Scholar
Daniel, T. L. 1984 Unsteady aspects of aquatic locomotion. Amer. Zool. 24, 121–134.CrossRefGoogle Scholar
E, W. & Liu, J. G. 1996 Essentially compact schemes for unsteady viscous incompressible flows. J. Comput. Phys. 126, 122–138.CrossRefGoogle Scholar
Eldredge, J. D. 2006 Numerical simulations of undulatory swimming at moderate Reynolds number. Bioinsp. Biomim. 1, S19–S24.CrossRefGoogle ScholarPubMed
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, 359–389.CrossRefGoogle Scholar
Kanso, E., Marsden, J. E., Rowley, C. W. & Melli-Huber, J. 2005 Locomotion of articulated bodies in a perfect fluid. J. Nonlinear Sci. 15, 255–289.CrossRefGoogle Scholar
Lighthill, J. 1991 Hydrodynamic far fields. In Mathematical Approaches in Hydrodynamics (ed. Miloh, T.), pp. 3–20. Society of Industrial and Applied Mathematics.Google Scholar
Roshko, A. 1961 Experiments on the flow past a circular cylinder at very high Reynolds number. J. Fluid Mech. 10, 345–356.CrossRefGoogle Scholar
Saffman, P. G. 1967 Self-propulsion of a deformable body in a perfect fluid. J. Fluid Mech. 28, 385–389.CrossRefGoogle Scholar
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, 1–6.CrossRefGoogle ScholarPubMed
Spagnolie, S. E. & Shelley, M. J. 2009 Shape-changing bodies in fluid: hovering, ratcheting, and bursting. Phys. Fluids 21, 013103.CrossRefGoogle Scholar
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, 157–182.CrossRefGoogle Scholar
Taylor, G. I. 1951 Analysis of the swimming of microscopic organisms. Proc. R. Soc. Lond. A 209, 447–461.Google Scholar
Tuck, E. O. 1968 A note on the swimming problem. J. Fluid Mech. 31, 305–308.CrossRefGoogle Scholar

Childress et al. supplementary material

Movie 1. The vorticity field generated by recoil locomotion of a finite body is shown. By periodic variations in presented surface area, in conjunction with recoil forcing from the oscillations of an internal mass, the body advances with each period to the right. Here, the Reynolds number based on the frequency of oscillation is 16.

Download Childress et al. supplementary material(Video)
Video 1.5 MB

Childress et al. supplementary material

Movie 2. The same as in Movie 1, but for motion at frequency Reynolds number 256.

Download Childress et al. supplementary material(Video)
Video 1.5 MB