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Pump or coast: the role of resonance and passive energy recapture in medusan swimming performance

Published online by Cambridge University Press:  29 January 2019

Alexander P. Hoover Open the ORCID record for Alexander P. Hoover [Opens in a new window] ,
Antonio J. Porras  and
Laura A. Miller
Alexander P. Hoover*
Affiliation:
Department of Mathematics, Tulane University, New Orleans, LA 70118, USA
Antonio J. Porras
Affiliation:
Department of Life and Physical Sciences, Fisk University, TN 37208, 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
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Abstract

Diverse organisms that swim and fly in the inertial regime use the flapping or pumping of flexible appendages and cavities to propel themselves through a fluid. It has long been postulated that the speed and efficiency of locomotion are optimized by oscillating these appendages at their frequency of free vibration. In jellyfish swimming, a significant contribution to locomotory efficiency has been attributed to the effects passive energy recapture, whereby the bell is passively propelled through the fluid through its interaction with stopping vortex rings formed during each expansion of the bell. In this paper, we investigate the interplay between resonance and passive energy recapture using a three-dimensional implementation of the immersed boundary method to solve the fluid–structure interaction of an elastic oblate jellyfish bell propelling itself through a viscous fluid. The motion is generated through a fixed duration application of active tension to the bell margin, which mimics the action of the coronal swimming muscles. The pulsing frequency is then varied by altering the length of time between the application of applied tension. We find that the swimming speed is maximized when the bell is driven at its resonant frequency. However, the cost of transport is maximized by driving the bell at lower frequencies whereby the jellyfish passively coasts between active contractions through its interaction with the stopping vortex ring. Furthermore, the thrust generated by passive energy recapture was found to be dependent on the elastic properties of the jellyfish bell.

JFM classification

Biological Fluid Dynamics: Propulsion Biological Fluid Dynamics: Swimming/flying
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 863 , 25 March 2019 , pp. 1031 - 1061
Copyright
© 2019 Cambridge University Press 

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Hoover et al. supplementary movie 1

Free vibration simulation for $\bar{\eta}_{mathrm{ref}}$. Tension is applied and sustained on the bell and then release. The bell then passively elastic material properties drive the expansion of the bell. The frequency of free vibration is then recorded from the oscillations of the bell radius during the expansion of the bell. Note that the initial contraction causes the bell to propel forward.

Download Hoover et al. supplementary movie 1(Video)
Video 11.8 MB

Hoover et al. supplementary movie 2

Video of $\bar{\omega}_{\mathrm{y}}$ for bells with $\bar{tau}=0.5$ over the propulsive cycle, $\bar{t}^{\mathrm{c}}$, for $\bar{\eta}$ equal to (left)$\frac{1}{3}\bar{\eta}_{\mathrm{ref}}$, (middle)$\frac{2}{3}\bar{\eta}_{\mathrm{ref}}$, and (right) $\bar{\eta}_{\mathrm{ref}}$. Note that the most flexible bell does not fully expand.

Download Hoover et al. supplementary movie 2(Video)
Video 20.9 MB

Hoover et al. supplementary movie 3

Video of $\bar{\omega}_{\mathrm{y}}$ over the same point of phase of the propulsive cycle, $\bar{t}^{\mathrm{c}}, for bells with $\bar{tau}^{*}=2.5$ for $\bar{\eta}$ equal to (left)$\frac{1}{3}\bar{\eta}_{\mathrm{ref}}$, (second from left)$\frac{2}{3}\bar{\eta}_{\mathrm{ref}}$, and (center) $\bar{\eta}_{\mathrm{ref}}$ $\bar{\eta}_{\mathrm{ref}}$, (second from right) $\frac{4}{3}\bar{\eta}_{\mathrm{ref}}$, and (right) $\frac{5}{3}\bar{\eta}_{\mathrm{ref}}$. Note that the driving period, $\bar{t}$, varies for all of the bells, but the resulting swimming speed is similar for bells with $\bar{\eta}\geq\frac{2}{3}\bar{\eta}$.

Download Hoover et al. supplementary movie 3(Video)
Video 19.9 MB