Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-17T16:13:51.990Z Has data issue: false hasContentIssue false
  • English
  • Français

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 ,
Boyce E. Griffith  and
Laura A. Miller
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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Propulsion Biological Fluid Dynamics: Swimming/flying
Type
Papers
Information
Journal of Fluid Mechanics , Volume 813 , 25 February 2017 , pp. 1112 - 1155
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alben, S., Miller, L. A. & Peng, J. 2013 Efficient kinematics for jet-propelled swimming. J. Fluid Mech. 733, 100–133.Google Scholar
Balay, S., Abhyankar, S., Adams, M., Brown, J., Brune, P., Buschelman, K., Eijkhout, V., Gropp, W., Kaushik, D., Knepley, M. et al. 2009 PETSc http://www.mcs.anl.gov/petsc.Google Scholar
Balay, S., Gropp, W. D., McInnes, L. C. & Smith, B. F. 1997 Efficient management of parallelism in object-oriented numerical software libraries. In Modern Software Tools for Scientific Computing, pp. 163–202. Springer.Google Scholar
Bale, R., Hao, M., Bhalla, A. P. S. & Patankar, N. A. 2014 Energy efficiency and allometry of movement of swimming and flying animals. Proc. Natl Acad. Sci. USA 111 (21), 7517–7521.Google Scholar
Bhalla, A. P. S., Bale, R., Griffith, B. E. & Patankar, N. A. 2013 A unified mathematical framework and an adaptive numerical method for fluid–structure interaction with rigid, deforming, and elastic bodies. J. Comput. Phys. 250, 446–476.CrossRefGoogle Scholar
Cartwright, P., Halgedahl, S. L., Hendricks, J. R., Jarrard, R. D., Marques, A. C., Collins, A. G. & Lieberman, B. S. 2007 Exceptionally preserved jellyfishes from the middle cambrian. PLoS One 2 (10), e1121.Google Scholar
Colin, S. P. & Costello, J. H. 2002 Morphology, swimming performance and propulsive mode of six co-occurring hydromedusae. J. Expl Biol. 205 (3), 427–437.Google Scholar
Colin, S. P., Costello, J. H., Dabiri, J. O., Villanueva, A., Blottman, J. B., Gemmell, B. J. & Priya, S. 2012 Biomimetic and live medusae reveal the mechanistic advantages of a flexible bell margin. PloS One 7 (11), e48909.CrossRefGoogle ScholarPubMed
Costello, J. H., Colin, S. P. & Dabiri, J. O. 2008 Medusan morphospace: phylogenetic constraints, biomechanical solutions, and ecological consequences. Invertebrate Biol. 127 (3), 265–290.Google Scholar
Dabiri, J. O., Colin, S. P. & Costello, J. H. 2007 Morphological diversity of medusan lineages constrained by animal–fluid interactions. J. Expl Biol. 210 (11), 1868–1873.CrossRefGoogle ScholarPubMed
Dabiri, J. O., Colin, S. P., Costello, J. H. & Gharib, M. 2005 Flow patterns generated by oblate medusan jellyfish: field measurements and laboratory analyses. J. Expl Biol. 208 (7), 1257–1265.Google Scholar
Daniel, T. L. 1983 Mechanics and energetics of medusan jet propulsion. Canad. J. Zool. 61 (6), 1406–1420.Google Scholar
Daniel, T. L. 1985 Cost of locomotion: unsteady medusan swimming. J. Expl Biol. 119 (1), 149–164.Google Scholar
Demont, M. E. & Gosline, J. M. 1988a Mechanics of jet propulsion in the hydromedusan jellyfish, polyorchis pexicillatus: I. Mechanical properties of the locomotor structure. J. Expl Biol. 134 (1), 313–332.CrossRefGoogle Scholar
Demont, M. E. & Gosline, J. M. 1988b Mechanics of jet propulsion in the hydromedusan jellyfish, polyorchis pexicillatus: III. A natural resonating bell; the presence and importance of a resonant phenomenon in the locomotor structure. J. Expl Biol. 134 (1), 347–361.Google Scholar
Falgout, R. D. & Yang, U. M. 2002 Hypre: a library of high performance preconditioners. In Computational Science ICCS 2002, pp. 632–641. Springer.Google Scholar
Fauci, L. J. & Peskin, C. S. 1988 A computational model of aquatic animal locomotion. J. Comput. Phys. 77 (1), 85–108.CrossRefGoogle Scholar
Feitl, K. E., Millett, A. F., Colin, S. P., Dabiri, J. O. & Costello, J. H. 2009 Functional morphology and fluid interactions during early development of the scyphomedusa Aurelia aurita . The Biological Bulletin 217 (3), 283–291.CrossRefGoogle ScholarPubMed
Gambini, C., Abou, B., Ponton, A. & Cornelissen, A. J. M. 2012 Micro-and macrorheology of jellyfish extracellular matrix. Biophys. J. 102 (1), 1–9.Google Scholar
Gemmell, B. J., Colin, S. P., Costello, J. H. & Dabiri, J. O. 2015a Suction-based propulsion as a basis for efficient animal swimming. Nat. Commun. 6, 8790.CrossRefGoogle ScholarPubMed
Gemmell, B. J., Costello, J. H. & Colin, S. P. 2014 Exploring vortex enhancement and manipulation mechanisms in jellyfish that contributes to energetically efficient propulsion. Commun. Integrative Biol. 7 (4), e29014.Google Scholar
Gemmell, B. J., Costello, J. H., Colin, S. P., Stewart, C. J., Dabiri, J. O., Tafti, D. & Priya, S. 2013 Passive energy recapture in jellyfish contributes to propulsive advantage over other metazoans. Proc. Natl Acad. Sci. USA 110 (44), 17904–17909.Google Scholar
Gemmell, B. J., Troolin, D. R., Costello, J. H., Colin, S. P. & Satterlie, R. A 2015b Control of vortex rings for manoeuvrability. J. R. Soc. Interface 12 (108), 20150389.Google Scholar
Gladfelter, W. B. 1972 Structure and function of the locomotory system of the scyphomedusa cyanea capillata. Mar. Biol. 14 (2), 150–160.Google Scholar
Griffith, B. E. & Luo, X.2012 Hybrid finite difference/finite element version of the immersed boundary method, arXiv:1612.05916.Google Scholar
Hamlet, C., Santhanakrishnan, A. & Miller, L. A. 2011 A numerical study of the effects of bell pulsation dynamics and oral arms on the exchange currents generated by the upside-down jellyfish Cassiopea xamachana . J. Expl Biol. 214 (11), 1911–1921.CrossRefGoogle ScholarPubMed
Herschlag, G. & Miller, L. 2011 Reynolds number limits for jet propulsion: a numerical study of simplified jellyfish. J. Theor. Biol. 285 (1), 84–95.Google Scholar
Hoover, A. & Miller, L. 2015 A numerical study of the benefits of driving jellyfish bells at their natural frequency. J. Theor. Biol. 374, 13–25.Google Scholar
Hornung, R. D., Wissink, A. M. & Kohn, S. R. 2006 Managing complex data and geometry in parallel structured AMR applications. Engng Comput. 22 (3–4), 181–195.Google Scholar
Horridge, G. A. 1954 The nerves and muscles of medusae. I. Conduction in the nervous system of Aurelia aurita Lamarck. J. Expl Biol. 31 (4), 594–600.CrossRefGoogle Scholar
HYPRE2011 Hypre: high performance preconditioners. http://www.llnl.gov/CASC/hypre.Google Scholar
IBAMR2014 IBAMR: an adaptive and distributed-memory parallel implementation of the immersed boundary method. http://ibamr.googlecode.com/.Google Scholar
Jones, S. K., Laurenza, R., Hedrick, T. L., Griffith, B. E. & Miller, L. A. 2015 Lift versus drag based mechanisms for vertical force production in the smallest flying insects. J. Theor. Biol. 384, 105–120.Google Scholar
Joshi, K., Villanueva, A., Smith, C., Maurya, D., Blottman, J. & Priya, S. 2013 Aurelia aurita inspired artificial mesoglea. Integr. Ferroelectr. 148 (1), 53–66.CrossRefGoogle Scholar
Kirk, B. S., Peterson, J. W., Stogner, R. H. & Carey, G. F. 2006 libMesh: a C + + library for parallel adaptive mesh refinement/coarsening simulations. Engng Comput. 22 (3–4), 237–254.Google Scholar
Lucas, K. N., Johnson, N., Beaulieu, W. T., Cathcart, E., Tirrell, G., Colin, S. P., Gemmell, B. J., Dabiri, J. O. & Costello, J. H. 2014 Bending rules for animal propulsion. Nat. Commun. 5, 3293.Google Scholar
McHenry, M. J. 2007 Comparative biomechanics: the jellyfish paradox resolved. Curr. Biol. 17 (16), R632–R633.CrossRefGoogle ScholarPubMed
McHenry, M. J. & Jed, J. 2003 The ontogenetic scaling of hydrodynamics and swimming performance in jellyfish (Aurelia aurita). J. Expl Biol. 206 (22), 4125–4137.CrossRefGoogle ScholarPubMed
Megill, W. M.2002 The biomechanics of jellyfish swimming. PhD thesis, The University of British Columbia.Google Scholar
Megill, W. M., Gosline, J. M. & Blake, R. W. 2005 The modulus of elasticity of fibrillin-containing elastic fibres in the mesoglea of the hydromedusa polyorchis penicillatus. J. Expl Biol. 208 (20), 3819–3834.Google Scholar
Miller, L. A. & Peskin, C. S. 2004 When vortices stick: an aerodynamic transition in tiny insect flight. J. Expl Biol. 207 (17), 3073–3088.Google Scholar
Miller, L. A. & Peskin, C. S. 2005 A computational fluid dynamics of ‘clap and fling’ in the smallest insects. J. Expl Biol. 208 (2), 195–212.CrossRefGoogle ScholarPubMed
Miller, L. A. & Peskin, C. S. 2009 Flexible clap and fling in tiny insect flight. J. Expl Biol. 212 (19), 3076–3090.Google Scholar
Mittal, R. & Iaccarino, G. 2005 Immersed boundary methods. Annu. Rev. Fluid Mech. 37, 239–261.Google Scholar
Park, S. G., Chang, C. B., Huang, W.-X. & Sung, H. J. 2014 Simulation of swimming oblate jellyfish with a paddling-based locomotion. J. Fluid Mech. 748, 731–755.Google Scholar
Peskin, C. S. 1977 Numerical analysis of blood flow in the heart. J. Comput. Phys. 25 (3), 220–252.Google Scholar
Peskin, C. S. 2002 The immersed boundary method. Acta Numerica 11, 479–517.Google Scholar
Sahin, M., Mohseni, K. & Colin, S. P. 2009 The numerical comparison of flow patterns and propulsive performances for the hydromedusae Sarsia tubulosa and Aequorea victoria. J. Expl Biol. 212 (16), 2656–2667.Google Scholar
SAMRAI2007 SAMRAI: structured adaptive mesh refinement application infrastructure. http://www.llnl.gov/CASC/SAMRAI.Google Scholar
Schmidt-Nielsen, K. 1972 Locomotion: energy cost of swimming, flying, and running. Science 177 (4045), 222–228.Google Scholar
Taylor, G. K., Nudds, R. L. & Thomas, A. L. R. 2003 Flying and swimming animals cruise at a strouhal number tuned for high power efficiency. Nature 425 (6959), 707–711.Google Scholar
Tytell, E. D., Hsu, C.-Y., Williams, T. L., Cohen, A. H. & Fauci, L. J. 2010 Interactions between internal forces, body stiffness, and fluid environment in a neuromechanical model of lamprey swimming. Proc. Natl Acad. Sci. USA 107 (46), 19832–19837.Google Scholar
Videler, J. J. 1993 Fish Swimming, vol. 10. Springer Science & Business Media.Google Scholar
Wainwright, S. A. 1982 Mechanical Design in Organisms. Princeton University Press.CrossRefGoogle Scholar
Zhang, C., Guy, R. D., Mulloney, B., Zhang, Q. & Lewis, T. J. 2014 Neural mechanism of optimal limb coordination in crustacean swimming. Proc. Natl Acad. Sci. USA 111 (38), 13840–13845.CrossRefGoogle ScholarPubMed

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 4.9 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 9.1 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 4.7 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 27.6 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 13.7 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 7.8 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 4.1 MB

Hoover et al. supplementary movie

Swimming of the reference case jellyfish with nondimensional velocity vectors.

Download Hoover et al. supplementary movie(Video)
Video 8.6 MB

Hoover et al. supplementary movie

Swimming of the reference case jellyfish with nondimensional velocity vectors.

Download Hoover et al. supplementary movie(Video)
Video 4.5 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 5.1 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 2.7 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 4.2 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 2.1 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 4.3 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 2.1 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 4.3 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 2.1 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 18.9 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 9.4 MB