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Quantifying performance in the medusan mechanospace with an actively swimming three-dimensional jellyfish model

Published online by Cambridge University Press:  27 January 2017

Alexander P. Hoover*
Affiliation:
Department of Mathematics, Tulane University, New Orleans, LA 70118, USA
Boyce E. Griffith
Affiliation:
Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA Department of Biomedical Engineering, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA McAllister Heart Institute, University of North Carolina at Chapel Hill, School of Medicine, Chapel Hill, NC 27599, USA
Laura A. Miller
Affiliation:
Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA Department of Biology, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA
*
Email address for correspondence: ahoover2@tulane.edu

Abstract

In many swimming and flying animals, propulsion emerges from the interplay of active muscle contraction, passive body elasticity and fluid–body interaction. Changes in the active and passive body properties can influence performance and cost of transport across a broad range of scales; they specifically affect the vortex generation that is crucial for effective swimming at higher Reynolds numbers. Theoretical models that account for both active contraction and passive elasticity are needed to understand how animals tune both their active and passive properties to move efficiently through fluids. This is particularly significant when one considers the phylogenetic constraints on the jellyfish mechanospace, such as the presence of relatively weak muscles that are only one cell layer thick. In this work, we develop an actively deforming model of a jellyfish immersed in a viscous fluid and use numerical simulations to study the role of active muscle contraction, passive body elasticity and fluid forces in the medusan mechanospace. By varying the strength of contraction and the flexibility of the bell margin, we quantify how these active and passive properties affect swimming speed and cost of transport. We find that for fixed bell elasticity, swimming speed increases with the strength of contraction. For fixed force of contractility, swimming speed increases as margin elasticity decreases. Varying the strength of activation in proportion to the elasticity of the bell margin yields similar swimming speeds, with a cost of transport is substantially reduced for more flexible margins. A scaling study reveals that performance declines as the Reynolds number decreases. Circulation analysis of the starting and stopping vortex rings showed that their strengths were dependent on the relative strength of activation with respect to the bell margin flexibility. This work yields a computational framework for developing a quantitative understanding of the roles of active and passive body properties in swimming.

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Papers
Copyright
© 2017 Cambridge University Press 

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Hoover et al. supplementary movie

Swimming of the reference case jellyfish with nondimensional out-of-plane vorticity.

Download Hoover et al. supplementary movie(Video)
Video 9 MB

Hoover et al. supplementary movie

Swimming of the reference case jellyfish with nondimensional out-of-plane vorticity.

Download Hoover et al. supplementary movie(Video)
Video 5 MB

Hoover et al. supplementary movie

Swimming of the reference case jellyfish with isocontours of the nondimensional vorticity magnitude.

Download Hoover et al. supplementary movie(Video)
Video 9 MB

Hoover et al. supplementary movie

Swimming of the reference case jellyfish with isocontours of the nondimensional vorticity magnitude.

Download Hoover et al. supplementary movie(Video)
Video 5 MB

Hoover et al. supplementary movie

Swimming of the reference case jellyfish with isocontours of the nondimensional vertical velocity.

Download Hoover et al. supplementary movie(Video)
Video 28 MB

Hoover et al. supplementary movie

Swimming of the reference case jellyfish with isocontours of the nondimensional vertical velocity.

Download Hoover et al. supplementary movie(Video)
Video 14 MB

Hoover et al. supplementary movie

Swimming of the reference case jellyfish with isocontours of the nondimensional radial velocity.

Download Hoover et al. supplementary movie(Video)
Video 8 MB

Hoover et al. supplementary movie

Swimming of the reference case jellyfish with isocontours of the nondimensional radial velocity.

Download Hoover et al. supplementary movie(Video)
Video 4 MB

Hoover et al. supplementary movie

Swimming of the reference case jellyfish with nondimensional velocity vectors.

Download Hoover et al. supplementary movie(Video)
Video 9 MB

Hoover et al. supplementary movie

Swimming of the reference case jellyfish with nondimensional velocity vectors.

Download Hoover et al. supplementary movie(Video)
Video 4 MB

Hoover et al. supplementary movie

Swimming of the reference case jellyfish with the bell color indicating the instantaneous strength of contraction.

Download Hoover et al. supplementary movie(Video)
Video 5 MB

Hoover et al. supplementary movie

Swimming of the reference case jellyfish with the bell color indicating the instantaneous strength of contraction.

Download Hoover et al. supplementary movie(Video)
Video 3 MB

Hoover et al. supplementary movie

A comparison of the out-plane vorticity for Sect. 3.2.1, where the maximum applied tension is varied and the elastic profile of the bell is held fixed. The orange bell is the reference case, the red bell has a lower applied tension, and the yellow bell has a higher applied tension.

Download Hoover et al. supplementary movie(Video)
Video 4 MB

Hoover et al. supplementary movie

A comparison of the out-plane vorticity for Sect. 3.2.1, where the maximum applied tension is varied and the elastic profile of the bell is held fixed. The orange bell is the reference case, the red bell has a lower applied tension, and the yellow bell has a higher applied tension.

Download Hoover et al. supplementary movie(Video)
Video 2 MB

Hoover et al. supplementary movie

A comparison of the out-plane vorticity for Sect. 3.2.2, where the elastic modulus of the bell margin is varied and maximum applied tension is held fixed. The orange bell is the reference case, the red bell has a less stiff margin, and the yellow bell has a more stiff margin.

Download Hoover et al. supplementary movie(Video)
Video 4 MB

Hoover et al. supplementary movie

A comparison of the out-plane vorticity for Sect. 3.2.2, where the elastic modulus of the bell margin is varied and maximum applied tension is held fixed. The orange bell is the reference case, the red bell has a less stiff margin, and the yellow bell has a more stiff margin.

Download Hoover et al. supplementary movie(Video)
Video 2 MB

Hoover et al. supplementary movie

A comparison of the out-plane vorticity for Sect. 3.2.3, where the elastic modulus of the bell margin is varied and maximum applied tension is held in proportion. The orange bell is the reference case, the red bell has a less stiff margin, and the yellow bell has a more stiff margin.

Download Hoover et al. supplementary movie(Video)
Video 4 MB

Hoover et al. supplementary movie

A comparison of the out-plane vorticity for Sect. 3.2.3, where the elastic modulus of the bell margin is varied and maximum applied tension is held in proportion. The orange bell is the reference case, the red bell has a less stiff margin, and the yellow bell has a more stiff margin.

Download Hoover et al. supplementary movie(Video)
Video 2 MB

Hoover et al. supplementary movie

A comparison of the buckling of the margin for Sect. 3.2.3, where the elastic modulus of the bell margin is varied and maximum applied tension is held in proportion. The orange bell is the reference case, the red bell has a most stiff margin, and the yellow bell has the least stiff margin. Intermediate stiffnesses are included.

Download Hoover et al. supplementary movie(Video)
Video 19 MB

Hoover et al. supplementary movie

A comparison of the buckling of the margin for Sect. 3.2.3, where the elastic modulus of the bell margin is varied and maximum applied tension is held in proportion. The orange bell is the reference case, the red bell has a most stiff margin, and the yellow bell has the least stiff margin. Intermediate stiffnesses are included.

Download Hoover et al. supplementary movie(Video)
Video 9 MB
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