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Passive and active bodies in vortex-street wakes

Published online by Cambridge University Press:  02 December 2009

SILAS ALBEN
SILAS ALBEN*
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA
*
†Email address for correspondence: [email protected]
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Abstract

We model the swimming of a finite body in a vortex street using vortex sheets distributed along the body and in a wake emanating from its trailing edge. We determine the magnitudes and distributions of vorticity and pressure loading on the body as functions of the strengths and spacings of the vortices. We then consider the motion of a flexible body clamped at its leading edge in the vortex street as a model for a flag in a vortex street and find alternating bands of thrust and drag for varying wavenumber. We consider a flexible body driven at its leading edge as a model for tail-fin swimming and determine optimal motions with respect to the phase between the body's trailing edge and the vortex street. For short bodies maximizing thrust or efficiency, we find maximum deflections shifted in phase by 90° from oncoming vortices. For long bodies, leading-edge driving should reach maximum amplitude when the vortices are phase-shifted from the trailing edge by 45° (to maximize thrust) and by 135° (to maximize efficiency). Optimal phases for intermediate lengths show smooth transitions between these values. The optimal motion of a body driven along its entire length is similar to that of the model tail fin driven only at its leading edge, but with an additional outward curvature near the leading edge. The similarity between optimal motions forced at the leading edge and all along the body supports the high performance attributed to fin-based motions.

JFM classification

Biological Fluid Dynamics: Propulsion Biological Fluid Dynamics: Swimming/flying Wakes/Jets: Vortex streets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 642 , 10 January 2010 , pp. 95 - 125
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Abrahams, M. V. & Colgan, P. W. 1987 Fish schools and their hydrodynamic function: a reanalysis. Environ. Biol. Fishes 20 (1), 79–80.CrossRefGoogle Scholar
Alben, S. 2008 a Optimal flexibility of a flapping appendage at high Reynolds number. J. Fluid Mech. 614, 355–380.CrossRefGoogle Scholar
Alben, S. 2008 b The flapping-flag instability as a nonlinear eigenvalue problem. Phys. Fluids 20, 104–106.CrossRefGoogle Scholar
Alben, S. 2009 On the swimming of a flexible body in a vortex street. J. Fluid Mech. 635, 27–45.CrossRefGoogle Scholar
Alben, S., Madden, P. G. & Lauder, G. V. 2007 The mechanics of active fin-shape control in ray-finned fishes. J. R. Soc. Interface 4 (13), 243–256.CrossRefGoogle ScholarPubMed
Alben, S., Shelley, M. & Zhang, J. 2004 How flexibility induces streamlining in a two-dimensional flow. Phys. Fluids 16, 1694.CrossRefGoogle Scholar
Ambrose, D. M. & Wilkening, J. 2008 Global paths of time-periodic solutions of the Benjamin–Ono equation connecting arbitrary travelling waves. Preprint. ArXiv:0811.4205.Google Scholar
Bainbridge, R. 1963 Caudal fin and body movement in the propulsion of some fish. J. Exp. Biol. 40 (1), 23–56.CrossRefGoogle Scholar
Barrett, D. S., Triantafyllou, M. S., Yue, D. K. P., Grosenbaugh, M. A. & Wolfgang, M. J. 1999 Drag reduction in fish-like locomotion. J. Fluid Mech. 392, 183–212.CrossRefGoogle Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Bisplinghoff, R. L. & Ashley, H. 2002 Principles of Aeroelasticity. Dover.Google Scholar
Cheng, J.-Y., Pedley, T. J. & Altringham, J. D. 1998 A continuous dynamic beam model for swimming fish. Phil. Trans. R. Soc. Lond B 353, 981–997.CrossRefGoogle Scholar
Drucker, E. G. & Lauder, G. V. 2001 Locomotor function of the dorsal fin in teleost fishes: experimental analysis of wake forces in sunfish. J. Exp. Biol. 204 (17), 2943–2958.CrossRefGoogle ScholarPubMed
Drucker, E. G. & Lauder, G. V. 2005 Locomotor function of the dorsal fin in rainbow trout: kinematic patterns and hydrodynamic forces. J. Exp. Biol. 208 (23), 4479–4494.CrossRefGoogle ScholarPubMed
Eloy, C., Lagrange, R., Souilliez, C. & Schouveiler, L. 2008 Aeroelastic instability of cantilevered flexible plates in uniform flow. J. Fluid Mech. 611, 97–106.CrossRefGoogle Scholar
Hou, T. Y., Lowengrub, J. S. & Shelley, M. J. 2001 Boundary integrals methods for multicomponent fluids and multiphase materials. J. Comput. Phys. 169, 302–362.CrossRefGoogle Scholar
Jones, M. 2003 The separated flow of an inviscid fluid around a moving flat plate. J. Fluid Mech. 496, 405–441.CrossRefGoogle Scholar
Krasny, R. 1991 Vortex sheet computations: roll-up, wakes, separation. Lect. Appl. Math. 28, 385–402.Google Scholar
Liao, J. C., Beal, D. N., Lauder, G. V. & Triantafyllou, M. S. 2003 Fish exploiting vortices decrease muscle activity. Science 302 (5650), 1566–1569.CrossRefGoogle ScholarPubMed
Lighthill, J. M. 1969 Hydromechanics of aquatic animal propulsion. Annu. Rev. Fluid Mech. 1, 413–446.CrossRefGoogle Scholar
Lissaman, PBS & Shollenberger, C. A. 1970 Formation flight of birds. Science 168 (3934), 1003–1005.CrossRefGoogle ScholarPubMed
Ristroph, L. & Zhang, J. 2008 Anomalous hydrodynamic drafting of interacting flapping flags. Phys. Rev. Lett. 101 (19), 194502.CrossRefGoogle ScholarPubMed
Saffman, P. 1992 Vortex Dynamics. Cambridge University Press.Google Scholar
Shelley, M., Vandenberghe, N. & Zhang, J. 2005 Heavy flags undergo spontaneous oscillations in flowing water. Phys. Rev. Lett 94, 094302.CrossRefGoogle ScholarPubMed
Sparenberg, J. A. 1995 Hydrodynamic Propulsion and Its Optimization: Analytic Theory. Springer.CrossRefGoogle Scholar
Streitlien, K., Triantafyllou, G. S. & Triantafyllou, M. S. 1996 Efficient foil propulsion through vortex control. AIAA J. 34 (11), 2315–2319.CrossRefGoogle Scholar
Thwaites, B. 1987 Incompressible Aerodynamics: An Account of the Theory and Observation of the Steady Flow of Incompressible Fluid Past Aerofoils, Wings and Other Bodies. Dover.Google Scholar
Weihs, D. 1973 Hydromechanics of fish schooling. Nature 241 (5387), 290–291.CrossRefGoogle Scholar
Weimerskirch, H., Martin, J., Clerquin, Y., Alexandre, P. & Jiraskova, S. 2001 Energy saving in flight formation. Nature 413 (6857), 697–698.CrossRefGoogle ScholarPubMed
Wu, T. Y. 1971 Hydromechanics of swimming propulsion. Part 1. Swimming of a two-dimensional flexible plate at variable forward speeds in an inviscid fluid. J. Fluid Mech. 46 (2), 337–355.CrossRefGoogle Scholar
Wu, T. Y. & Chwang, A. T. 1975 Extraction of flow energy by fish and birds in a wavy stream. In Swimming and Flying in Nature (ed. Wu, T. Y.-T., Brokaw, C. J. & Brennen, C.), vol. 2, pp. 687–702. Plenum.CrossRefGoogle Scholar