Hostname: page-component-7c8c6479df-xxrs7 Total loading time: 0 Render date: 2024-03-27T02:06:07.772Z Has data issue: false hasContentIssue false

Impulsive fluid forcing and water strider locomotion

Published online by Cambridge University Press:  05 February 2007

OLIVER BÜHLER*
Affiliation:
Center for Atmosphere Ocean Science at the Courant Institute of Mathematical SciencesNew York University, New York, NY 10012, USA

Abstract

This paper presents a study of the global response of a fluid to impulsive and localized forcing; it has been motivated by the recent laboratory experiments on the locomotion of water-walking insects reported in Hu, Chan & Bush (Nature, vol. 424, 2003, p. 663). These insects create both waves and vortices by their rapid leg strokes and it has been a matter of some debate whether either form of motion predominates in the momentum budget. The main result of this paper is to argue that generically both waves and vortices are significant, and that in linear theory they take up the horizontal momentum with share 1/3 and 2/3, respectively.

This generic result, which depends only on the impulsive and localized nature of the forcing, is established using the classical linear impulse theory, with adaptations to weakly compressible flows and flows with a free surface. Additional general comments on experimental techniques for momentum measurement and on the wave emission are given and then the theory is applied in detail to water-walking insects.

Owing to its generality, this kind of result and the methods used to derive it should be applicable to a wider range of wave–vortex problems in the biolocomotion of water-walking animals and elsewhere.

Type
Papers
Copyright
Copyright © Cambridge University Press 2007

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

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Bretherton, F. P. 1969 On the mean motion induced by internal gravity waves. J. Fluid Mech. 36, 785803.CrossRefGoogle Scholar
Bühler, O. & McIntyre, M. E. 2003 Remote recoil: a new wave–mean interaction effect. J. Fluid Mech. 492, 207230.CrossRefGoogle Scholar
Bühler, O. & McIntyre, M. E. 2005 Wave capture and wave–vortex duality. J. Fluid Mech. 534, 6795.CrossRefGoogle Scholar
Bush, J. W. M. & Hu, D. L. 2006 Walking on water: biolocomotion at the interface. Annu. Rev. Fluid Mech. 38, 339369.CrossRefGoogle Scholar
Denny, M. W. 1993 Air and Water: The Biology and Physics of Life's Media. Princeton University Press.CrossRefGoogle Scholar
Drucker, E. G. & Lauder, G. V. 1999 Locomotor forces on a swimming fish: three-dimensional vortex wake dynamics quantified using digital particle image velocimetry. J. Expl Biol. 202, 23932412.Google Scholar
Hu, D. L., Chan, B. & Bush, J. W. M. 2003 The hydrodynamics of water strider locomotion. Nature 424, 663666.CrossRefGoogle ScholarPubMed
Keller, J. B. 1998 Surface tension force on a partly submerged body. Phys. Fluids 10, 30093010.CrossRefGoogle Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.Google Scholar
Longuet-Higgins, M. S. 1977 The mean forces exerted by waves on floating or submerged bodies with applications to sand bars and wave power machines. Proc. R. Soc. Lond. A 352, 463480.Google Scholar
McIntyre, M. E. 1981 On the ‘wave momentum’ myth. J. Fluid Mech. 106, 331347.Google Scholar
Raphael, E. & de Gennes, P.-G. 1996 Capillary gravity waves caused by a moving disturbance; wave resistance. Phys. Rev. E 53, 3448.CrossRefGoogle ScholarPubMed
Sun, S.-M. & Keller, J. B. 2001 Capillary-gravity wave drag. Phys. Fluids 13, 21462151.Google Scholar
Suter, R., Rosenberg, R., Loeb, S., Wildman, H. & Long, J. J. 1997 Locomotion on the water surface: propulsive mechanisms of the fisher spider dolomedes triton. J. Expl Biol. 200, 25232538.CrossRefGoogle Scholar
Theodorsen, T. 1941 Impulse and momentum in an infinite fluid. In Von Karman Anniversary Volume, pp. 49–57. Caltech.Google Scholar