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Vortex interaction between two tandem flexible propulsors with a paddling-based locomotion

  • Sung Goon Park (a1) and Hyung Jin Sung (a1)

Schooling behaviours among self-propelled animals can benefit propulsion. Inspired by the schooling behaviours of swimming jellyfish, flexible bodies that self-propel through a paddling-based motion were modelled in a tandem configuration. This present study explored the hydrodynamic patterns generated by the interactions between two flexible bodies and the surrounding fluid in the framework of the penalty immersed boundary method. The hydrodynamic patterns produced in the wake revealed flow-mediated interactions between two tandem propulsors, including vortex–vortex and vortex–body interactions. Two tandem flexible propulsors paddling with identical amplitude and frequency produced stable configurations as a result of the flow-mediated interactions. Both the upstream and downstream propulsors benefited from the tandem configuration in terms of the locomotion velocity and the cost, compared with an isolated propulsion system. The interactions were examined as a function of the initial gap distance and the phase difference in the paddling frequency. The equilibrium gap distance between two propulsors remained constant, regardless of the initial gap distance, although it did depend on the phase difference in the paddling frequency.

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S. Alben 2009 Wake-mediated synchronization and drafting in coupled flags. J. Fluid Mech. 641, 489496.

S. Alben  & M. Shelley 2005 Coherent locomotion as an attracting state for a free flapping body. Proc. Natl Acad. Sci. USA 102, 1116311166.

D. N. Beal , F. S. Hover , M. S. Triantafyllou , J. C. Liao  & G. V. Lauder 2006 Passive propulsion in vortex wakes. J. Fluid Mech. 549, 385402.

I. Borazjani 2015 Simulations of unsteady aquatic locomotion: from unsteadiness in straight-line swimming to fast-starts. Integr. Compar. Biol. 55, 740752.

J. O. Dabiri 2005 On the estimation of swimming and flying forces from wake measurements. J. Expl Biol. 208, 35193532.

J. O. Dabiri 2009 Optimal vortex formation as a unifying principle in biological propulsion. Annu. Rev. Fluid Mech. 41, 1733.

J. O. Dabiri , S. P. Colin , J. H. Costello  & M. Gharib 2005 Flow patterns generated by oblate medusa jellyfish: field measurements and laboratory analyses. J. Expl Biol. 208, 12571265.

M. Daghooghi  & I. Borazjani 2015 The hydrodynamic advantages of synchronized swimming in a rectangular pattern. Bioinspir. Biomim. 10, 056018.

F. E. Fish  & G. V. Lauder 2006 Passive and active flow control by swimming fishes and mammals. Annu. Rev. Fluid Mech. 38, 193224.

B. J. Gemmell , J. H. Costello , S. P. Colin , C. J. Stewart , J. O. Dabiri , D. Tafti  & S. Priya 2013 Passive energy recapture in jellyfish contributes to propulsive advantage over other metazoans. Proc. Natl Acad. Sci. USA 110, 1790417909.

W.-X. Huang  & H. J. Sung 2009 An immersed boundary method for fluid–flexible structure interaction. Comput. Meth. Appl. Mech. Engng 198, 26502661.

S. J. Jang , H. J. Sung  & P. Krogstad 2011 Effects of an axisymmetric contraction on a turbulent pipe flow. J. Fluid Mech. 687, 376403.

K. Kim , S. J. Baek  & H. J. Sung 2002 An implicit velocity decoupling procedure for incompressible Navier–Stokes equations. Intl J. Numer. Meth. Fluids 38, 125138.

S. Kim , W.-X. Huang  & H. J. Sung 2010 Constructive and destructive interaction modes between two tandem flexible flags in viscous flow. J. Fluid Mech. 661, 511521.

G. V. Lauder  & B. C. Jayne 1996 Pectoral fin locomotion in fishes: testing drag-based models using three-dimensional kinematics. Am. Zool. 36, 567581.

J. C. Liao , D. N. Beal , G. V. Lauder  & M. S. Triantafyllou 2003a Fish exploiting vortices decrease muscle activity. Science 302, 15661569.

J. C. Liao , D. N. Beal , G. V. Lauder  & M. S. Triantafyllou 2003b The Karman gait: novel body kinematics of rainbow trout swimming in a vortex street. J. Expl Biol. 206, 10591073.

P. F. Linden  & J. S. Turner 2004 ‘Optimal’ vortex rings and aquatic propulsion mechanisms. Proc. R. Soc. Lond. B 271, 647653.

M. J. Mchenry  & J. Jed 2003 The ontogenetic scaling of hydrodynamics and swimming performance in jellyfish (Aurelia aurita). J. Expl Biol. 206, 41254137.

S. G. Park , C. B. Chang , W. H. Huang  & H. J. Sung 2014 Simulation of swimming oblate jellyfish with a paddling-based locomotion. J. Fluid Mech. 748, 731755.

L. Ristroph  & J. Zhang 2008 Anomalous hydrodynamic drafting of interacting flapping flags. Phys. Rev. Lett. 101, 194502.

M. Sahin  & K. Mohseni 2009 An arbitrary Lagrangian–Eulerian formulation for the numerical simulation of flow patterns generated by the hydromedusa Aequorea victoria. J. Comput. Phys. 228, 45884605.

M. Sahin , K. Mohseni  & S. P. Colin 2009 The numerical comparison of flow patterns and propulsive performances for the hydromedusae Sarsia tubulosa and Aequorea victoria. J. Expl Biol. 212, 26562667.

S. J. Shin , W.-X. Huang  & H. J. Sung 2008 Assessment of regularized delta functions and feedback forcing schemes for an immersed boundary method. Intl J. Numer. Meth. Fluids 58, 263286.

E. D. Tytell  & G. V. Lauder 2004 The hydrodynamics of eel swimming. I. Wake structure. J. Expl Biol. 207, 18251841.

E. Uddin , W.-X. Huang  & H. J. Sung 2013 Interaction modes of multiple flexible flags in a uniform flow. J. Fluid Mech. 729, 563583.

D. Weihs 1973 Hydromechanics of fish schooling. Nature 241, 290291.

D. Zavodnik 1987 Spatial aggregations of the swarming jellyfish Pelagia noctiluca (Scyphozoa). Mar. Biol. 94, 265269.

J. Zhang , S. Childress , A. Libchaber  & M. Shelley 2000 Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature 408, 835839.

H. Zhao , J. B. Freund  & R. D. Moser 2008 A fixed-mesh method for incompressible fluid–structure systems with finite solid deformations. J. Comput. Phys. 227, 31143140.

X. Zhu , G. He  & X. Zhang 2014 Flow-mediated interactions between two self-propelled flapping filaments in tandem configuration. Phys. Rev. Lett. 113, 238105.

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Type Description Title
Locomotions of flexible propulsors as a function of the phase difference of the flapping frequency.

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