Hostname: page-component-76d6cb85b7-xh428 Total loading time: 0 Render date: 2026-07-20T17:39:28.067Z Has data issue: false hasContentIssue false
  • English
  • Français

Swimming of a waving plate

Published online by Cambridge University Press:  28 March 2006

T. Yao-Tsu Wu
T. Yao-Tsu Wu
Affiliation:
California Institute of Technology, Pasadena, California
Get access Rights & Permissions [Opens in a new window]

Abstract

The purpose of this paper is to study the basic principle of fish propulsion. As a simplified model, the two-dimensional potential flow over a waving plate of finite chord is treated. The solid plate, assumed to be flexible and thin, is capable of performing the motion which consists of a progressing wave of given wavelength and phase velocity along the chord, the envelope of the wave train being an arbitrary function of the distance from the leading edge. The problem is solved by applying the general theory for oscillating deformable airfoils. The thrust, power required, and the energy imparted to the wake are calculated, and the propulsive efficiency is also evaluated. As a numerical example, the waving motion with linearly varying amplitude is carried out in detail. Finally, the basic mechanism of swimming is elucidated by applying the principle of action and reaction.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 10 , Issue 3 , May 1961 , pp. 321 - 344
Copyright
© 1961 Cambridge University Press

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.)

Article purchase

Temporarily unavailable

References

Erdelyi, A. 1953 (Ed.) Higher Transcendental Functions (Bateman Manuscript Project). New York: McGraw-Hill.
Erdélyi, A. & Kermack, W. O. 1945 Note on the equation f(z)K'n(z) − g(z)Kn(z) = 0. Proc. Camb. Phil. Soc. 41, 74–5.Google Scholar
Kármán, Th. van & Burgers, J. M. 1943 General aerodynamic theory—perfect fluids. DivisionE II, Aerodynamic Theory (Ed. W. F. Durand).Google Scholar
Küssner, H. G. & Schwarz, L. 1940 The oscillating wing with aerodynamically balanced elevator. Luftfahrt-Forsch. 17, 337–54. (English translation: 1941, NACA TM 991.)Google Scholar
Lighthill, M. J. 1960a Mathematics and aeronautics. J. Roy. Aero. Soc. 64, 373–94.Google Scholar
Lighthill, M. J. 1960b Note on the swimming of slender fish. J. Fluid Mech. 9, 305–17.Google Scholar
Luke, Y. & Dengler, M. A. 1951 Tables of the Theordorsen circulation function for generalized motion. J. Aero. Sci. 18, 478–83.Google Scholar
Nekrasov, A. I. 1948 Wing theory for unsteady flow. Aero. Res. Coun. no. 11792.
Robinson, A. & Laurmann, J. A. 1956 Wing Theory. Cambridge University Press.
Taylor, G. I. 1951 Analysis of the swimming of microscopic organisms. Proc. Roy. Soc. A, 209, 447–61.Google Scholar
Taylor, G. I. 1952a The action of waving cylindrical tails in propelling miscroscopic organisms. Proc. Roy. Soc. A 211, 225–39.Google Scholar
Taylor, G. I. 1952b Analysis of the swimming of long and narrow animals. Proc. Roy. Soc. A, 214, 158–83.Google Scholar
Watson, G. N. 1944 A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge University Press.