Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-28T18:31:39.943Z Has data issue: false hasContentIssue false
  • English
  • Français

Simulation of swimming oblate jellyfish with a paddling-based locomotion

Published online by Cambridge University Press:  08 May 2014

Sung Goon Park ,
Cheong Bong Chang ,
Wei-Xi Huang  and
Hyung Jin Sung
Sung Goon Park
Affiliation:
Department of Mechanical Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Republic of Korea
Cheong Bong Chang
Affiliation:
Department of Mechanical Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Republic of Korea
Wei-Xi Huang
Affiliation:
Department of Engineering Mechanics, Tsinghua University, 100084 Beijing, China
Hyung Jin Sung*
Affiliation:
Department of Mechanical Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Republic of Korea
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The hydrodynamics of a swimming jellyfish depends on the morphology of the species. For example, oblate jellyfish appear to generate wide vortex structures near the bell margin. The vortex structures affect both the propulsion system and the feeding structure because the swimming and prey capturing activities are interrelated processes in these taxa. A three-dimensional computational model was established for an oblate jellyfish to analyse how the vortex structures present in the wake affect the swimming mechanism and the propulsion efficiency, which is defined as the ratio of power output (thrust multiplied by centre velocity) to power input (energy rate required for bell contraction). An improved penalty immersed boundary method was adopted to consider the interactions between the swimming jellyfish and the ambient fluid. The vortex structures in the wake of the swimming jellyfish were investigated in detail. The vortices generated by the contraction and expansion of the jellyfish bell interact with the vortex structures generated by the forward-moving behaviour of the jellyfish. The resulting vortex structures not only transfer momentum to the swimming jellyfish via the fluid, thereby providing the main source of thrust, but also have an implication for feeding. The effects of the elastic properties of the jellyfish on the propulsion were examined. The propulsion efficiency reaches its optimum value at particular elastic properties. We also investigated the effect of the swimming pattern of jellyfish on the propulsion efficiency. The efficiency increases with the flapping frequency and force duration.

JFM classification

Biological Fluid Dynamics: Propulsion Biological Fluid Dynamics: Swimming/flying Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 748 , 10 June 2014 , pp. 731 - 755
Copyright
© 2014 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.CrossRefGoogle Scholar
Barthes-Biesel, D., Diaz, A. & Dhenin, E. 2002 Effect of constitutive laws for two-dimensional membranes on flow-induced capsule deformation. J. Fluid Mech. 460, 211–222.Google Scholar
Cirak, F., Ortiz, M. & Schroder, P. 2000 Subdivision surfaces: a new paradigm for thin-shell finite-element analysis. Intl J. Numer. Meth. Engng 47, 2039–2072.3.0.CO;2-1>CrossRefGoogle Scholar
Colin, S. P. & Costello, J. H. 2002 Morphology, swimming performance and propulsive mode of six co-occurring hydromedusae. J. Expl Biol. 205, 427–437.CrossRefGoogle ScholarPubMed
Colin, S. P., Costello, J. H. & Klos, E. 2003 In situ swimming and feeding behavior of eight co-occurring hydromedusae. Mar. Ecol. Prog. Ser. 253, 305–309.Google Scholar
Costello, J. H. 1992 Foraging energetics in hydromedusae. Sci. Mar. 56, 185–191.Google Scholar
Costello, J. H. & Colin, S. P. 1994 Morphology, fluid motion and predation by the scyphomedusa Aurelia aurita . Mar. Biol. 121, 327–334.Google Scholar
Costello, J. H. & Colin, S. P. 1995 Flow and feeding by swimming scyphomedusae. Mar. Biol. 124, 399–406.Google Scholar
Costello, J. H., Colin, S. P. & Dabiri, J. O. 2008 Medusan morphospace: phylogenetic contrants, biomechanical solutions, and ecological consequences. Invertebr. Biol. 127, 265–290.Google Scholar
Dabiri, J. O. 2005 On the estimation of swimming and flying forces from wake measurements. J. Expl Biol. 208, 3519–3532.Google Scholar
Dabiri, J. O., Colin, S. P., Costello, J. H. & Gharib, M. 2005 Flow patterns generated by oblate medusa jellyfish: field measurements and laboratory analyses. J. Expl Biol. 208, 1257–1265.CrossRefGoogle ScholarPubMed
Dabiri, J. O., Colin, S. P., Katijia, K. & Costello, J. H. 2009 A wake-based correlate of swimming performance and foraging behavior in seven co-occurring jellyfish species. J. Expl Biol. 213, 1217–1225.Google Scholar
Dabiri, J. O. & Gharib, M. 2003 Sensitivity analysis of kinematic approximations in dynamic medusa swimming models. J. Expl Biol. 206, 3675–3680.CrossRefGoogle Scholar
Daniel, T. 1983 Mechanics and energetics of medusan jet propulsion. Can. J. Zool. 61, 1406–1420.CrossRefGoogle Scholar
Daniel, T. 1985 Cost of locomotion: unsteady medusan swimming. J. Expl Biol. 119, 149–164.CrossRefGoogle Scholar
Demont, M. E. & Gosline, J. M. 1988a Mechanics of jet propulsion in the hydromedusan jellyfish, Polyorchis penicillatus: I, mechanical properties of the locomotor structure. J. Expl Biol. 134, 313–332.Google Scholar
Demont, M. E. & Gosline, J. M. 1988b Mechanics of jet propulsion in the hydromedusan jellyfish, Polyorchis penicillatus: II, energetics of the jet cycle. J. Expl Biol. 134, 333–345.CrossRefGoogle Scholar
Demont, M. E. & Gosline, J. M. 1988c Mechanics of jet propulsion in the hydromedusan jellyfish, Polyorchis penicillatus: III, a natural resonating bell; the presence and importance of a resonant phenomenon in the locomotor structure. J. Expl Biol. 134, 347–361.Google Scholar
Dular, M., Bajcar, T. & Sirok, B. 2009 Numerical investigation of flow in the vicinity of a swimming jellyfish. Engng Appl. Comput. Fluid Mech. 3, 258–270.Google Scholar
Ford, M. D. & Costello, J. H. 2000 Kinematic comparison of bell contraction by four species of hydromedusae. Sci. Mar. 64, 47–53.Google Scholar
Ford, M. D., Costello, J. H., Heidelberg, K. B. & Purcell, J. E. 1997 Swimming and feeding by the scyphomedusa Chrysaora quinquecirrha . Mar. Biol. 129, 355–362.Google Scholar
Fung, Y. C. & Tong, P. 2001 Classical and Computational Solid Mechanics. World Scientific.CrossRefGoogle Scholar
Herschlag, G. & Miller, L. 2011 Reynolds number limits for jet propulsion: a numerical study of simplified jellyfish. J. Theor. Biol. 285, 84–95.Google Scholar
Huang, W.-X., Chang, C. B. & Sung, H. J. 2011 An improved penalty immersed boundary method for fluid-flexible body interaction. J. Comput. Phys. 230, 5061–5079.Google Scholar
Huang, W.-X., Chang, C. B. & Sung, H. J. 2012 Three-dimensional simulation of elastic capsules in shear flow by the penalty immersed boundary method. J. Comput. Phys. 231, 3340–3364.CrossRefGoogle Scholar
Huang, W.-X. & Sung, H. J. 2009 An immersed boundary method for fluid-flexible structure interaction. Comput. Meth. Appl. Mech. Engng 198, 2650–2661.Google Scholar
Johnson, T. A. & Patel, V. C. 1998 Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378, 19–70.Google Scholar
Kim, K., Baek, S. J. & Sung, H. J. 2002 An implicit velocity decoupling procedure for incompressible Navier–Stokes equations. Intl J. Numer. Meth. Fluids 38, 125–138.Google Scholar
Lai, M.-C. & Peskin, C. S. 2000 An immersed boundary method with formal second-order accuracy and reduced numerical viscosity. J. Comput. Phys. 160, 705–719.CrossRefGoogle Scholar
Liao, J. C., Beal, D. N., Lauder, G. V. & Triantafyllou, M. S. 2003 Fish exploiting vortices decrease muscle activity. Science 302, 1566–1569.CrossRefGoogle ScholarPubMed
Lima, S. L. 1985 Maximizing feeding efficiency and minimizing time exposed to predators: a trade-off in the black-capped chickadee. Oecologia 66, 60–67.Google Scholar
Linden, P. F. & Turner, J. S. 2004 ‘Optimal’ vortex rings and aquatic propulsion mechanisms. Proc. R. Soc. Lond. B 271, 647–653.CrossRefGoogle ScholarPubMed
Liu, H., Wassersug, R. J. & Kawachi, K. 1996 A computational fluid dynamics study of tadpole swimming. J. Expl Biol. 199, 1245–1260.Google Scholar
Mchenry, M. J. & Jed, J. 2003 The ontogenetic scaling of hydrodynamics and swimming performance in jellyfish (Aurelia aurita). J. Expl Biol. 206, 4125–4137.Google Scholar
Mchenry, M. J., Pell, A. C. & Long, J. H. 1995 Mechanical control of swimming speed: stiffness and axial wave form in undulating fish models. J. Expl Biol. 198, 2293–2305.Google Scholar
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 hydormedusa Polyorchis penicillatus . J. Expl Biol. 208, 3819–3834.Google Scholar
Mills, C. E. 1981 Diversity of swimming behaviors in hydromedusae as related to feeding and utilization of space. Mar. Biol. 64, 185–189.Google Scholar
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. McGraw-Hill.Google Scholar
Rudolf, D. & Mould, D. 2010 An interactive fluid model of jellyfish for animation. Commun. Comput. Inform. Sci. 68, 59–72.Google Scholar
Sahin, M. & Mohseni, K. 2009 An arbitrary Lagrangian–Eulerian formulation for the numerical simulation of flow patterns generated by the hydromedusa Aequorea victoria . J. Comput. Phys. 228, 4588–4605.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, 2656–2667.CrossRefGoogle ScholarPubMed
Santhanakrishnan, A., Dollinger, M., Hamlet, C. L., Colin, S. P. & Miller, L. A. 2012 Flow structure and transport characteristics of feeding and exchange currents generated by upside-down Cassiopea jellyfish. J. Expl Biol. 215, 2369–2381.Google Scholar
Summers, A. P., Darouian, K. F., Richmond, A. M. & Brainerd, E. L. 1998 Kinematics of aquatic and terrestrial prey capture in Terrapene carolina, with implications for the evolution of feeding in Cryptodire turtles. J. Expl Zool. 281, 280–287.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. Lett. Nature 425, 707–711.Google Scholar
Ulrike, K. M. 2003 Fish ’n flag. Science 302, 1511–1512.Google Scholar
Zhao, H., Freund, J. B. & Moser, R. D. 2008 A fixed-mesh method for incompressible fluid–structure systems with finite solid deformations. J. Comput. Phys. 227, 3114–3140.Google Scholar

Park et al. supplementary movie

Comparison of the vortex structures generated in the wake between the intermittent swimming (τ = 0.4, T = 1.1) and the continuous swimming (τ = 0.4, T = 0.4).

Download Park et al. supplementary movie(Video)
Video 3.7 MB

Park et al. supplementary movie

Comparison of the vortex structures generated in the wake for the intermittent swimming cases with shorter (τ = 0.4, T = 1.1) and longer (τ = 0.8, T = 0.4) force durations.

Download Park et al. supplementary movie(Video)
Video 3.5 MB