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Impulsive fluid forcing and water strider locomotion

Published online by Cambridge University Press:  05 February 2007

OLIVER BÜHLER
OLIVER BÜHLER*
Affiliation:
Center for Atmosphere Ocean Science at the Courant Institute of Mathematical SciencesNew York University, New York, NY 10012, USA
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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
Information
Journal of Fluid Mechanics , Volume 573 , February 2007 , pp. 211 - 236
Copyright
Copyright © Cambridge University Press 2007

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