Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-21T17:19:57.719Z Has data issue: false hasContentIssue false
  • English
  • Français

Hydrodynamically coupled rigid bodies

Published online by Cambridge University Press:  14 November 2007

SUJIT NAIR  and
EVA KANSO
SUJIT NAIR
Affiliation:
University of Southern California, Los Angeles, CA 90089, USA
EVA KANSO
Affiliation:
University of Southern California, Los Angeles, CA 90089, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers a finite number of rigid bodies moving in potential flow. The dynamics of the solid--fluid system is described in terms of the solid variables only using Kirchhoff potentials. The equations of motion are first derived for the problem of two submerged bodies where one is forced into periodic oscillations. The hydrodynamic coupling causes the free body to drift away from or towards the oscillating body. The method of multiple scales is used to separate the slow drift from the fast response. Interestingly, the free body, when attracted towards the forced one, starts to drift away after it reaches certain separation distance. This suggests that the hydrodynamic coupling helps in preventing collisions. The fluid's role in collision avoidance and motion coordination is examined further through examples. In particular, we show that a free body can coordinate its motion with that of its neighbours, which may be relevant to understanding the coordinated motion in fish schooling.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 592 , 10 December 2007 , pp. 393 - 411
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Burton, D. A., Gratus, J. & Tucker, R. W. 2004 Hydrodynamic forces on two moving discs. Theor. Appl. Mech. 31, 153–188.CrossRefGoogle Scholar
Childress, S. 1981 Mechanics of Swimming and Flying. Cambridge University Press.CrossRefGoogle Scholar
Crowdy, D., Surana, A. & Yick, K.-Y. 2007 The irrotational flow generated by two planar stirrers in inviscid fluid. Phys. Fluids 19, 018103.CrossRefGoogle Scholar
Hess, J. L. & Smith, A. M. O. 1966 Calculation of potential flow about arbitrary bodies. Prog. Aeronaut. Sci. 8, 1–139.CrossRefGoogle Scholar
Hoare, D., Ward, A. J., Couzin, I. D., Croft, D. & Krause, J. 2001 A grid-net technique for the analysis of fish positions in free-ranging fish schools. J. Fish Biol. 59, 1667–1672.Google Scholar
Kanso, E. & Marsden, J. E. 2005 Optimal motion of an articulated body in a perfect fluid. 44th IEEE Conference on Decision and Control, vol. 44, pp. 2511–2516.CrossRefGoogle 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.CrossRefGoogle Scholar
Kelly, S. D. 1998 The mechanics and control of robotic locomotion with applications to aquatic vehicles. PhD thesis, California Institute of Technology.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th Edn. newblock Dover.Google Scholar
Liao, J. C., Beal, D. N., Lauder, G. V. & Triantafyllou, M. S. 2003 Fish exploiting vortices decrease muscle activity. Science 302, 1566–1569.CrossRefGoogle ScholarPubMed
Lighthill, M. J. 1975 Mathematical Biofluiddynamics. Society for Industrial and Applied Mathematics, PA.CrossRefGoogle Scholar
Moran, J. 1984 An Introduction to Theoretical and Computational Aerodynamics. newblock John Wiley & Sons.Google Scholar
Müller, U. K. 2003 Fish'n Flag. Science 302, 1511–1512.CrossRefGoogle ScholarPubMed
Nayfeh, A. H. 1973 Perturbation Methods. Wiley-Interscience.Google Scholar
Radford, J. 2003 Symmetry, reduction and swimming in a perfect fluid. PhD thesis, California Institute of Technology.Google Scholar
Shaw, E. 1975 Fish in schools. Natural History 84 (8), 40–46.Google Scholar
Shaw, E. 1970 Schooling in fishes: critique and review. In Development and Evolution of Behavior, pp. 452–480. W. H. Freeman and Company, San Francisco.Google Scholar
Taylor, G. I. 1952 Analysis of the swimming of long and narrow animals. Proc. R. Soc. Lond. A 214, 158–183.Google Scholar
Wang, Q. X. 2004 Interaction of two circular cylinders in inviscid fluid. Phys. Fluids 16, 4412–4425.CrossRefGoogle Scholar
Webb, P. W. 1991 Composition and mechanics of routine swimming of rainbow trout Oncorhynchus mykiss. Can. J. Fish. Aquat. Sci. 48, 583–590.CrossRefGoogle Scholar
Wu, T. Y. 1971 Hydrodynamics of swimming fish and cetaceans. Adv. Appl. Maths 11, 1–63.Google Scholar