A Caltech Library Service

Hydromechanics of swimming propulsion. Part 3. Swimming and optimum movements of slender fish with side fins

Wu, T. Yao-Tsu (1971) Hydromechanics of swimming propulsion. Part 3. Swimming and optimum movements of slender fish with side fins. Journal of Fluid Mechanics, 46 (3). pp. 545-568. ISSN 0022-1120.

[img] PDF
See Usage Policy.


Use this Persistent URL to link to this item:


This paper seeks to evaluate the swimming flow around a typical slender fish whose transverse cross-section to the rear of its maximum span section is of a lenticular shape with pointed edges, such as those of spiny fins, so that these side edges are sharp trailing edges, from which an oscillating vortex sheet is shed to trail the body in swimming. The additional feature of shedding of vortex sheet makes this problem a moderate generalization of the paper on the swimming of slender fish treated by Lighthill (1960a). It is found here that the thrust depends not only on the virtual mass of the tail-end section, but also on an integral effect of variations of the virtual mass along the entire body segment containing the trailing side edges, and that this latter effect can greatly enhance the thrust-making. The optimum shape problem considered here is to determine the transverse oscillatory movements a slender fish can make which will produce a prescribed thrust, so as to overcome the frictional drag, at the expense of the minimum work done in maintaining the motion. The solution is for the fish to send a wave down its body at a phase velocity c somewhat greater than the desired swimming speed U, with an amplitude nearly uniform from the maximum span section to the tail. Both the ratio U/c and the optimum efficiency are found to depend upon two parameters: the reduced wave frequency and a 'proportional-loading parameter', the latter being proportional to the thrust coefficient and to the inverse square of the wave amplitude. The basic mechanism of swimming is examined in the light of the principle of action and reaction by studying the vortex wake generated by the optimum movement.

Item Type:Article
Additional Information:"Reprinted with the permission of Cambridge University Press." (Received 21 July 1970) I am very much indebted to Professor M. J. Lighthill for his interest in this and particularly for his kindness in giving me the privilege of knowing his great work (1970) prior to its publication. The enlightening discussions with him have enabled me to draw instructive comparisons between the conclusions reached in his work and in this part of my own. I am also grateful to Professor T. K. Caughey for some general discussions. This research was partially sponsored by the National Science Foundation, under Grant GK 10216, and by the Ofice of Naval Research, under Contract N00014-67-A0094-0012.
Issue or Number:3
Record Number:CaltechAUTHORS:WUTjfm71c
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:344
Deposited By: Theodore Yao-tsu Wu
Deposited On:05 Jun 2005
Last Modified:02 Oct 2019 22:32

Repository Staff Only: item control page