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

Published online by Cambridge University Press:  12 January 2011

Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA
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
Trinity Hall, Cambridge CB2 1TJ, UK
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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.

Copyright © Cambridge University Press 2011

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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 2 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 2 MB