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Hydrodynamically coupled oscillators

Published online by Cambridge University Press:  19 April 2011

R. TIRON,
E. KANSO and
P. K. NEWTON
R. TIRON
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
E. KANSO*
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
P. K. NEWTON
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USADepartment of Mathematics, University of Southern California, Los Angeles, CA 90089, USA
*
†Email address for correspondence: kanso@usc.edu
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Abstract

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A submerged spring–mass ring is analysed as a simple model for the way in which an underwater swimmer couples its body deformations to the surrounding fluid in order to accomplish locomotion. We adopt an inviscid, incompressible, irrotational assumption for the surrounding fluid and analyse the coupling response to various modes of excitation of the ring configuration. Due to the added mass effect, the surrounding fluid provides an environment which effectively couples the ‘normal modes’ of oscillation of the ring, leading to nonlinear trajectories if the ring is free to accelerate based on the effective forces the oscillations induce. Through a series of examples, we demonstrate various features that the model supports, including the locomotion on curved paths as a result of energy and angular momentum exchange with the surrounding fluid.

JFM classification

Nonlinear Dynamical Systems: Nonlinear Dynamical SystemsBiological Fluid Dynamics: Swimming/flying

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 677 , 25 June 2011, pp. 589 - 606
Copyright
Copyright © Cambridge University Press 2011

References

REFERENCES

Beal, D. N., Hover, F. S., Triantafyllou, M. S., Liao, J. C. & Lauder, G. V. 2006 Passive propulsion in vortex wakes. J. Fluid Mech. 549, 385–402.CrossRefGoogle Scholar
Brennen, C. E. 1982 A review of added mass and fluid inertial forces, Tech. Rep. CR 82.010. Naval Civil Engineering Laboratory, N62583-81-MR-554.Google Scholar
Burton, D. A., Gratus, J. & Tucker, R. W. 2004 Hydrodynamic forces on two moving disks. Theor. Appl. Mech. 31, 153–188.Google Scholar
Crowdy, D. G., Surana, A. & Yick, K.-Y. 2007 The irrotational flow generated by two planar stirrers in inviscid fluid. Phys. Fluids 19, 018103.CrossRefGoogle Scholar
GrottaRagazzo, C. Ragazzo, C. 2002 Dynamics of many bodies in a liquid: added-mass tensor of compounded bodies and systems with a fast oscillating body. Phys. Fluids 14 (5), 1590–1601.Google Scholar
GrottaRagazzo, C. Ragazzo, C. 2003 On the motion of solids through an ideal liquid: approximated equations for many body systems. SIAM J. Appl. Math. 63 (6), 1972–1997.Google Scholar
Kanso, E., Marsden, J. E., Rowley, C. W. & Melli-Huber, J. 2005 Locomotion of articulated bodies in a perfect fluid. J. Nonlinear Sci. 15, 255–289.Google Scholar
Kanso, E. & Newton, P. K. 2009 Passive locomotion via normal-mode coupling in a submerged spring–mass system. J. Fluid Mech. 641, 205–215.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Dover.Google Scholar
Long, H. J. & Nipper, K. S. 1996 The importance of body stiffness in undulatory propulsion. Am. Zool. 36, 678–694.Google Scholar
Long, J., Hale, M., Mchenry, M. & Westneat, M. 1996 Functions of fish skin: flexural stiffness and steady swimming of longnose gar, Lepisosteus osseus. J. Exp. Biol. 199, 2139–2051.Google Scholar
Nair, S. & Kanso, E. 2007 Hydrodynamically-coupled rigid bodies. J. Fluid Mech. 592, 393–411.Google Scholar
Videler, J. J. 1993 Fish Swimming. Springer.Google Scholar
Videler, J. J. & Weihs, D. 1982 Energetic advantages of burst-and-coast swimming of fish at high speeds. J. Exp. Biol. 97, 169–178.CrossRefGoogle ScholarPubMed
Wang, Q. X. 2004 Interaction of two circular cylinders in inviscid fluid. Phys. Fluids 16, 4412–4425.Google Scholar