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Self-similar kinematics among efficient slender swimmers

Published online by Cambridge University Press:  07 February 2018

A. J. Wiens Open the ORCID record for A. J. Wiens [Opens in a new window]  and
A. E. Hosoi
A. J. Wiens*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02143, USA
A. E. Hosoi
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02143, USA
*
†Email address for correspondence: wiens@mit.edu
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Abstract

We present an analysis of efficient undulatory propulsion for slender animals swimming at high Reynolds number. Using Lighthill’s large-amplitude elongated-body theory, we show that optimally efficient swimming kinematics can be characterized through a single dimensionless variable $\unicode[STIX]{x1D713}$. This variable, $\unicode[STIX]{x1D713}$, is defined by a simple function of a swimming animal’s body wave properties. Physically, $\unicode[STIX]{x1D713}$ characterizes how the velocity of an animal’s tail varies throughout its swimming stroke. Lighthill’s model predicts that swimming efficiency is near optimal in the range $0.3<\unicode[STIX]{x1D713}<1.0$ and peaks at $\unicode[STIX]{x1D713}=0.87$. At this point, the average magnitude of the tail velocity is minimized and swimming kinematics are tuned such that the thrust coefficient is as close to constant as possible throughout the swimming stroke. We use a compiled dataset of over 250 unique measurements to show that species across a wide range of size and shape fall within the optimal region.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Propulsion Biological Fluid Dynamics: Swimming/flying
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 840 , 10 April 2018 , pp. 106 - 130
Copyright
© 2018 Cambridge University Press 

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