Advertisement

The Fluid Dynamics of Feeding In the Upside-Down Jellyfish

  • Christina Hamlet
  • Laura A. Miller
  • Terry Rodriguez
  • Arvind Santhanakrishnan
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 155)

Abstract

The jellyfish has been the subject of numerous mathematical and physical studies ranging from the discovery of reentry phenomenon in electrophysiology to the development of axisymmetric methods for solving fluid-structure interaction problems. In the area of biologically inspired design, the jellyfish serves as a simple case study for understanding the fluid dynamics of unsteady propulsion with the goal of improving the design of underwater vehicles. In addition to locomotion, the study of jellyfish fluid dynamics could also lead to innovations in the design of filtration and sensing systems since an additional purpose of bell pulsations is to bring fluid to the organism for the purposes of feeding and nutrient exchange. The upside-down jellyfish, Cassiopea spp., is particularly well suited for feeding studies since it spends most of its time resting on the seafloor with its oral arms extended upward, pulsing to generate currents used for feeding and waste removal. In this paper, experimental measurements of the bulk flow fields generated by these organisms as well as the results from supporting numerical simulations are reviewed. Contraction, expansion, and pause times over the course of many contraction cycles are reported, and the effects of these parameters on the resulting fluid dynamics are explored. Of particular interest is the length of the rest period between the completion of bell expansion and the contraction of the next cycle. This component of the pulse cycle can be modeled as a Markov process. The discrete time Markov chain model can then be used to simulate cycle times using the distributions found empirically. Numerical simulations are used to explore the effects of the pulse characteristics on the fluid flow generated by the jellyfish. Preliminary results suggest that pause times have significant implications for the efficiency of particle capture and exchange.

Key words

Animal locomotion fluid dynamics of feeding jellyfish fluid-structure interaction immersed boundary methods 

References

  1. [1].
    Arai MN (1997) A functional biology of scyphozoa. Chapman and Hall, LondonGoogle Scholar
  2. [2].
    Arai MN (2001) Pelagic coelenterates and eutrophication: a review. Hydrobiologia 451:69–87MathSciNetCrossRefGoogle Scholar
  3. [3].
    Bigelow RP (1900) The anatomy and development of Cassiopeia xamachana. Boston Soc Nat Hist Mem 5:191–236Google Scholar
  4. [4].
    Brown GO (2002) Henry Darcy and the making of a law. Water Resour Res Volume 38, Issue 7, pp. 11–1.CrossRefGoogle Scholar
  5. [5].
    Colin SP, Costello JH (2002) Morphology, swimming performance, and propulsive mode of six co-occurring hydromedusae. J Exp Biol 205:427–437Google Scholar
  6. [6].
    Costello JH, Colin SP (1994) Morphology, fluid motion and predation by the scyphomedusa Aurelia aurita. Mar Biol 121:327–334CrossRefGoogle Scholar
  7. [7].
    Costello JH, Colin SP, Dabiri JO (2008) Medusan morphospace: phylogenetic constraints, biomechanical solutions, and ecological consequences. Invertebr Biol 127:265–290CrossRefGoogle Scholar
  8. [8].
    Daniel TL (1983) Mechanics and energetics of medusan jet propulsion. Can J Zool 61:1406–1420CrossRefGoogle Scholar
  9. [9].
    Daniel TL (1984) Unsteady aspects of aquatic locomotion. Am Zool 24:121–134Google Scholar
  10. [10].
    Dabiri JO, Colin SP, Costello JH, Gharib M (2005) Flow patterns generated by oblate medusan jellyfish: field measurements and laboratory analyses. J Exp Biol 208:1257–1265CrossRefGoogle Scholar
  11. [11].
    Dabiri JO, Colin SP, Costello JH (2006) Fast-swimming jellyfish exploit velar kinematics to form an optimal vortex wake. J Exp Biol 209:2025–2033CrossRefGoogle Scholar
  12. [12].
    Dabiri JO, Colin SP, Costello JH (2007) Morphological diversity of medusan lineages is constrained by animal-fluid interactions. J Exp Biol 210:1868–1873CrossRefGoogle Scholar
  13. [13].
    Fauci JJ, Peskin CS (1988) A computational model of aquatic animal locomotion. J Comput Phys 77:85–108MathSciNetzbMATHCrossRefGoogle Scholar
  14. [14].
    Fogelson AL (1984) A mathematical model and numerical method for studying platelet adhesion and aggregation during blood clotting. J Comput Phys 56:111–134MathSciNetzbMATHCrossRefGoogle Scholar
  15. [15].
    Hamlet C, Santhanakrishnan A, Miller LA (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 spp. J Exp Biol 214:1911–1921CrossRefGoogle Scholar
  16. [16].
    Hayward RT (2007) Modeling experiments on pacemaker interactions in scyphomedusae. Master’s thesis, University of North Carolina at Wilmington, Department of Biology and Marine BiologyGoogle Scholar
  17. [17].
    Heller HC, Sadava DE, Orians GH (2006) Life, the science of biology. W.H. Freeman, New YorkGoogle Scholar
  18. [18].
    Herschlag G, Miller LA (2011) Reynolds number limits for jet propulsion: a numerical study of simplified jellyfish. J Theor Biol 285:84–95CrossRefGoogle Scholar
  19. [19].
    Jung E, Peskin CS (2001) Two-dimensional simulations of valveless pumping using the immersed boundary method. SIAM J Sci Comput 23:19–45MathSciNetzbMATHCrossRefGoogle Scholar
  20. [20].
    Kim Y, Peskin CS (2006) 2-D Parachute simulation by the immersed boundary method. SIAM J Sci Comput 28:2294–2312MathSciNetzbMATHCrossRefGoogle Scholar
  21. [21].
    Larson RJ (1991) Diet, prey selection and daily ration of Stomolophus meleagris, a filter- feeding scyphomedusa from the NE Gulf of Mexico. Estuar Coast Shelf Sci 32:511–525MathSciNetCrossRefGoogle Scholar
  22. [22].
    Lim S, Peskin CS (2004) Simulations of the whirling instability by the immersed boundary method. SIAM J Sci Comput 25:2066–2083MathSciNetzbMATHCrossRefGoogle Scholar
  23. [23].
    Lipinski D, Mohseni K (2009) Flow structures and fluid transport for the hydromedusae Sarsia tubulosa and Aequorea victoria. J Exp Biol 212:2436–2447CrossRefGoogle Scholar
  24. [24].
    McHenry MJ, Jed J (2003) The ontogenetic scaling of hydrodynamics and swimming performance in jellyfish Aurelia aurita. J Exp Biol 206:4125–4137CrossRefGoogle Scholar
  25. [25].
    Miller LA, Peskin CS (2004) When vortices stick: an aerodynamic transition in tiny insect flight. J Exp Biol 207:3073–3088CrossRefGoogle Scholar
  26. [26].
    Miller LA, Peskin CS (2009) Flexible clap and fling in tiny insect flight. J Exp Biol 212:3076-3090CrossRefGoogle Scholar
  27. [27].
    Omoto C, Dillon RH, Fauci LJ, Yang X (2007) Fluid dynamic models of flagellar and ciliary beating. Ann N Y Acad Sci 1101:494–505CrossRefGoogle Scholar
  28. [28].
    Peskin CS (2002) The immersed boundary method. Acta Numer 11:479–517MathSciNetzbMATHCrossRefGoogle Scholar
  29. [29].
    Peskin CS, McQueen DM (1996) Fluid dynamics of the heart and its valves. In: Othmer HG, Adler FR, Lewis MA, Dallon JC (eds) Case studies in mathematical modeling: ecology, physiology, and cell biology, 2nd edn. Prentice-Hall, New JerseyGoogle Scholar
  30. [30].
    Peskin CS, Kramer PR, Atzberger PJ (2008) On the foundations of the stochastic immersed boundary method. Comput Method Appl Mech Eng 197:2232–2249MathSciNetzbMATHCrossRefGoogle Scholar
  31. [31].
    Sahin M, Mohseni K, Colin SP (2009) The numerical comparison of flow patterns and propulsive performances for the hydromedusae Sarsia tubulosa and Aequorea victoria. J Exp Biol 212:2656-2667CrossRefGoogle Scholar
  32. [32].
    Santhanakrishnan A, Hamlet C, Dollinger M, Colin S, Miller LA Flow structure and transport characteristics of feeding and exchange currents generated by upside-down Cassiopea jellyfish. J Exp Biol. 215: 2369–2381Google Scholar
  33. [33].
    Satterlie RA (2002) Neuronal control of swimming in jellyfish: a comparative story. Canad J Zool 80:1654–1669CrossRefGoogle Scholar
  34. [34].
    Stockie JM (2009) Modelling and simulation of porous immersed boundaries. Comput Struct 87:701–709CrossRefGoogle Scholar
  35. [35].
    Templeman MA, Kingsford MJ (2010) Trace element accumulation in Cassiopea sp. (Scyphozoa) from urban marine environments in Australia. Mar Environ Res 69:63–72CrossRefGoogle Scholar
  36. [36].
    Todd BD, Thornhill DJ, Fitt WK (2006) Patterns of inorganic phosphate uptake in Cassiopea xamachana: a bioindicator species. Mar Poll Bull. 52:515–521CrossRefGoogle Scholar
  37. [37].
    Verde EA, McCloskey LR (1998) Production, respiration, and photophysiology of the mangrove jellyfish Cassiopea xamachana symbiotic with zooxanthellae: effect of jellyfish size and season. Mar Ecol Prog Ser 168:147–162CrossRefGoogle Scholar
  38. [38].
    Welsh DT, Dunn RJK, Meziane T (2009) Oxygen and nutrient dynamics of the upside down jellyfish (Cassiopea sp.) and its influence on benthic nutrient exchanges and primary production. Hydrobiologia 635:351–362CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Christina Hamlet
    • 1
  • Laura A. Miller
    • 2
  • Terry Rodriguez
    • 2
  • Arvind Santhanakrishnan
    • 3
  1. 1.Department of MathematicsNorth Carolina State UniversityRaleighUSA
  2. 2.Department of MathematicsUniversity of North CarolinaChapel HillUSA
  3. 3.Department of Biomedical EngineeringGeorgia Institute of TechnologyAtlantaUSA

Personalised recommendations