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Effects of body elasticity on stability of underwater locomotion

Published online by Cambridge University Press:  28 November 2011

F. Jing
Affiliation:
Aerospace & Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
E. Kanso*
Affiliation:
Aerospace & Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
*
Email address for correspondence: kanso@usc.edu

Abstract

We examine the stability of the ‘coast’ motion of fish, that is to say, the motion of a neutrally buoyant fish at constant speed in a straight line. The forces and moments acting on the fish body are thus perfectly balanced. The fish motion is said to be unstable if a perturbation in the conditions surrounding the fish results in forces and moments that tend to increase the perturbation, and it is stable if these emerging forces tend to reduce the perturbation and return the fish to its original state. Stability may be achieved actively or passively. Active stabilization requires neurological control that activates musculo-skeletal components to compensate for the external perturbations acting against stability. Passive stabilization on the other hand requires no energy input by the fish and is dependent upon the fish morphology, i.e. geometry and elastic properties. In this paper, we use a deformable body consisting of an articulated body equipped with torsional springs at its hinge joints and submerged in an unbounded perfect fluid as a simple model to study passive stability as a function of the body geometry and spring stiffness. We show that for given body dimensions, the spring elasticity, when properly chosen, leads to passive stabilization of the (otherwise unstable) coast motion.

Type
Papers
Copyright
Copyright © Cambridge University Press 2011

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References

1. Alben, S. 2008 The flapping-flag instability as a nonlinear eigenvalue problem. Phys. Fluids 20, 104106.CrossRefGoogle Scholar
2. Argentina, M. & Mahadevan, L. 2005 Fluid-flow-induced flutter of a flag. Proc. Natl Acad. Sci. 102, 18291834.CrossRefGoogle ScholarPubMed
3. 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, 385402.CrossRefGoogle Scholar
4. Borazjani, I. & Sotiropoulos, F. 2008 Numerical investigation of the hydrodynamics of carangiform swimming in the transitional and inertial flow regimes. J. Expl Biol. 211, 15411558.CrossRefGoogle ScholarPubMed
5. Borazjani, I. & Sotiropoulos, F. 2009a Numerical investigation of the hydrodynamics of anguilliform swimming in the transitional and inertial flow regimes. J. Expl Biol. 212, 576592.CrossRefGoogle ScholarPubMed
6. Borazjani, I. & Sotiropoulos, F. 2009b Vortex induced vibrations of two cylinders in tandem in the proximity wake interference region. J. Fluid Mech. 621, 321364.CrossRefGoogle ScholarPubMed
7. Brennen, C. E. 1982 A review of added mass and fluid inertial forces. Report CR 82.010, Naval Civil Engineering Laboratory, contract N62583-81-MR-554.Google Scholar
8. Fish, F. 2002 Balancing requirements for stability and maneuverability in cetaceans. Integr. Compar. Biol. 42, 8593.CrossRefGoogle ScholarPubMed
9. Griffin, O. M. 1984 Vibrations and flow induced forces caused by vortex shedding. In Symposium on Flow-Induced Vibrations (ed. Paidousois, M. P., Griffin, O. M. & Servik, M. ). AMSE , vol. 1. pp. 113.Google Scholar
10. Jing, F. 2011 Part I: Viscous evolution of point vortex equilibria. Part II: Effects of body elasticity on stability of fish motion. PhD dissertation, USC.CrossRefGoogle Scholar
11. Kanso, E. 2009 Swimming due to transverse shape deformations. J. Fluid Mech. 631, 127148.CrossRefGoogle Scholar
12. Kanso, E., Marsden, J. E., Rowley, C. W. & Melli-Huber, J. 2005 Locomotion of articulated bodies in a perfect fluid. J. Nonlinear Sci. 15, 255289.CrossRefGoogle Scholar
13. Kanso, E. & Oskouei, B. 2008 Stability of a coupled body–vortex system. J. Fluid Mech. 800, 7794.CrossRefGoogle Scholar
14. Lamb, S. H. 1932 Hydrodynamics. Cambridge University Press.Google Scholar
15. Leonard, N. E. 1997 Stability of a bottom-heavy underwater vehicle. Automatica 33 (3), 331346.CrossRefGoogle Scholar
16. Mandre, S. & Mahadevan, L. 2010 A generalized theory of viscous and inviscid flutter. Proc. R. Soc. A 466 (2113), 141156.CrossRefGoogle Scholar
17. Marsden, J. E. 1992 Lectures on Mechanics, London Mathematical Society Lecture Note Series , vol. 174. Cambridge University Press.CrossRefGoogle Scholar
18. Michelin, S., Llewellyn-Smith, S. G. & Glover, B. J. 2008 Vortex shedding model of a flapping flag. J. Fluid Mech. 617, 110.CrossRefGoogle Scholar
19. Nair, S. & Kanso, E. 2007 Hydrodynamically coupled rigid bodies. J. Fluid Mech. 592, 393411.CrossRefGoogle Scholar
20. Oskouei, B. & Kanso, E. 2011 Stability of passive locomotion in periodically-generated wakes. IMA Volume on Natural Locomotion in Fluids and on Surfaces: Swimming, Flying, and Sliding (in press).CrossRefGoogle Scholar
21. Shashikanth, B. N., Marsden, J. E., Burdick, J. W. & Kelly, S. D. 2002 The Hamiltonian structure of a 2-D rigid circular cylinder interacting dynamically with point vortices. Phys. Fluids 14, 12141227.CrossRefGoogle Scholar
22. Shelley, M., Vandenberghe, N. & Zhang, J. 2005 Heavy flags undergo spontaneous oscillations in flowing water. Phys. Rev. Lett. 94, 094302.CrossRefGoogle ScholarPubMed
23. Shen, L. & Zhang, X. et al. 2003 Turbulent flow over a flexible wall undergoing a streamwise travelling wave motion. J. Fluid Mech. 484, 197221.CrossRefGoogle Scholar
24. Taneda, S. & Tomonari, Y. 1974 An experiment on the flow around a waving plate. J. Phys. Soc. Japan 36 (6), 16831689.CrossRefGoogle Scholar
25. Tchieu, A. A., Crowdy, D. & Leonard, A. 2010 Fluid–structure interaction of two bodies in an inviscid fluid. Phys. Fluids 22 (10), 107101.CrossRefGoogle Scholar
26. Videler, J. J. & Weihs, D. 1982 Energetic advantages of burst-and-coast swimming of fish at high speeds. J. Expl. Biol. 97, 169178.CrossRefGoogle ScholarPubMed
27. Weihs, D. 2002 Stability versus maneuverability in aquatic locomotion. Integr. Compar. Biol. 42, 127134.CrossRefGoogle ScholarPubMed
28. Williamson, C. H. K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36, 413.CrossRefGoogle Scholar