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Transport of inertial particles by Lagrangian coherent structures: application to predator–prey interaction in jellyfish feeding

Published online by Cambridge University Press:  06 March 2009

J. PENG  and
J. O. DABIRI
J. PENG*
Affiliation:
Bioengineering, California Institute of Technology, Pasadena, CA 91125, USA
J. O. DABIRI
Affiliation:
Bioengineering, California Institute of Technology, Pasadena, CA 91125, USA Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: [email protected]
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Abstract

We use a dynamical systems approach to identify coherent structures from often chaotic motions of inertial particles in open flows. We show that particle Lagrangian coherent structures (pLCS) act as boundaries between regions in which particles have different kinematics. They provide direct geometric information about the motion of ensembles of inertial particles, which is helpful to understand their transport. As an application, we apply the methodology to a planktonic predator–prey system in which moon jellyfish Aurelia aurita uses its body motion to generate a flow that transports small plankton such as copepods to its vicinity for feeding. With the flow field generated by the jellyfish measured experimentally and the dynamics of plankton described by a modified Maxey–Riley equation, we use the pLCS to identify a capture region in which prey can be captured by the jellyfish. The properties of the pLCS and the capture region enable analysis of the effect of several physiological and mechanical parameters on the predator–prey interaction, such as prey size, escape force, predator perception, etc. The methods developed here are equally applicable to multiphase and granular flows, and can be generalized to any other particle equation of motion, e.g. equations governing the motion of reacting particles or charged particles.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 623 , 25 March 2009 , pp. 75 - 84
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Aref, H. 1984 Stirring by chaotic advection. J. Fluid Mech. 143, 1–21.CrossRefGoogle Scholar
Babiano, A., Cartwright, J. H. E., Piro, O. & Provenzale, A. 2000 Dynamics of a small neutrally buoyant sphere in a fluid and targeting in Hamiltonian systems. Phys. Rev. Lett. 84, 5764–5767.CrossRefGoogle Scholar
Benczik, I. J., Toroczkai, Z. & Tel, T. 2003 Advection of finite-size particles in open flows. Phys. Rev. E 67, 036303.Google ScholarPubMed
Costello, J. H. & Colin, S. P. 1994 Morphology, fluid motion and predation by the scyphomedusa Aurelia Aurita. Mar. Biol. 121, 327–334.CrossRefGoogle Scholar
Dabiri, J. O., Colin, S. P. & Costello, J. H. 2006 Fast-swimming hydromedusae exploit velar kinematics to form an optimal vortex wake. J. Exp Biol. 209, 2025–2033.CrossRefGoogle ScholarPubMed
Fields, D. M. & Yen, J. 1997 The escape behavior of marine copepods in response to a quantifiable fluid mechanical disturbance. J. Plankton Res. 19, 1289–1304.CrossRefGoogle Scholar
Franco, E., Pekarek, D. N., Peng, J. & Dabiri, J. O. 2007 Geometry of unsteady fluid transport during fluidstructure interactions. J. Fluid Mech. 589, 125–145.CrossRefGoogle Scholar
Haller, G. 2002 Lagrangian coherent structures from approximate velocity data. Phys. Fluids 14, 1851–1861.CrossRefGoogle Scholar
Haller, G. & Sapsis, T. 2008 Where do inertial particles go in fluid flows? Physica, D 237 573–583.Google Scholar
Koehl, M. A. R. & Reidenbach, M. A. 2007 Swimming by microscopic organisms in ambient water flow. Exps Fluids 43, 755–768.CrossRefGoogle Scholar
Maxey, M. R. & Riley, J. J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883–889.CrossRefGoogle Scholar
Michaelides, E. E. 1997 Review – The transient equation of motion for particles, bubbles, and droplets. J. Trans. ASME Fluids Engng 119, 233–247.CrossRefGoogle Scholar
Rom-Kedar, V., Leonard, A. & Wiggins, S. 1990 An analytical study of transport, mixing and chaos in an unsteady vortical flow. J. Fluid Mech. 214, 347–394.CrossRefGoogle Scholar
Shadden, S. C., Dabiri, J. O. & Marsden, J. E. 2006 Lagrangian analysis of fluid transport in empirical vortex ring flows. Phys. Fluids 18, 047105.CrossRefGoogle Scholar
Shadden, S. C., Lekien, F. & Marsden, J. E. 2005 Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D 212, 271–304.CrossRefGoogle Scholar
Strickler, J. R. 1975 Swimming of planktonic Cyclops species (Copepoda, Crustacea): Pattern, movements and their control. In Swimming and Flying in Nature (ed. Wu, T. Y. T., Brokaw, C. J. & Brennan, C.), pp. 599–613 Plenum.CrossRefGoogle Scholar
Sullivan, B. K., Garcia, J. R. & Klein-MacPhee, G. 1994 Prey selection by the scyphomedusan predator Aurelia Aurita. Mar. Biol. 121, 335–341.CrossRefGoogle Scholar
Wiggins, S. 1992 Chaotic transport in dynamical systems. Springer.CrossRefGoogle Scholar