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Swimming in potential flow

Published online by Cambridge University Press:  01 December 2022

Alec Glisman Open the ORCID record for Alec Glisman [Opens in a new window]  and
John F. Brady Open the ORCID record for John F. Brady [Opens in a new window]
Alec Glisman
Affiliation:
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
John F. Brady*
Affiliation:
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: [email protected]
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Abstract

The well-known self-propulsion, or swimming, of a deformable body in Stokes flow (i.e. at low Reynolds number) can be understood and modelled from the variation in the configuration-dependent hydrodynamic resistance tensor throughout the period of deformation. Remarkably, at the other extreme of high Reynolds number, a deformable body may also self-propel without doing any net work on the fluid in potential flow. As a body deforms, the mass of fluid displaced – the so-called added mass – depends on the instantaneous body configuration, and a net displacement is possible over a period of deformation. This potential swimming takes a form identical to that for Stokes swimmers with the configuration-dependent added mass replacing the hydrodynamic resistance tensor. Analytical insight into the swimming of a deformable body is obtained through an expansion of the nonlinear spatial dependence of the hydrodynamic interactions and connections between previous studies of swimming in Stokes flow to those in potential flow are made.

JFM classification

Biological Fluid Dynamics: Propulsion Complex Fluids: Active matter
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 952 , 10 December 2022 , R5
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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