a1 Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA
a2 Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA
a3 Trinity Hall, Cambridge CB2 1TJ, UK
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.
(Received March 13 2010)
(Revised September 30 2010)
(Accepted September 30 2010)
(Online publication January 12 2011)