Wu 



involves the difficult problem of vinsteady boundary -layer and hydrodynamic 

 stability theory. This general subject remains as an important and crucial 

 problem. The mechanism of swimming motion has been elucidated based on 

 the potential flow theory by von Karman and Burgers (1943) for the simple case 

 of a rigid plate in transverse oscillation and rotation. Swimming of slender 

 fish has been treated by Lighthill (1960); and the swimming of a two-dimensional 

 waving plate has been calculated by Wu (1961). 



In the other extreme, movements of microscopic bodies always correspond 

 to small Reynolds numbers. The propulsion in this range depends almost en- 

 tirely on the viscous stresses, since the inertial forces are then extremely 

 small, except possibly for motions at very high frequencies. Oscillatory mo- 

 tion in a viscous fluid was discussed as early as 1851 by Stokes. Various stud- 

 ies of the swimming of microscopic organisms have been led by Taylor (1951, 

 1952a,b), who discussed the propulsion of a propagating, monochromatic, trans- 

 verse wave along a sheet immersed in a very viscous fluid, and later evaluated 

 the action of waving cylindrical tails of microscopic organisms. Further stud- 

 ies in this field have been contributed by Hancock (1954), Gray and Hancock 

 (1955), Reynolds (1965), and by Tuck (1968). 



Apart from the mode of propagating transverse waves, which a great ma- 

 jority of swimming creatures adopt as the principal means of propulsion, there 

 are still other kinds of body motions, such as (a) actually ejecting a liquid, as 

 employed by squids, shrimps, and lobsters, (b) propagating waves along fringe 

 belts as used by some flat fishes, and waving motion produced by bending a 

 large number of dense tassels underneath a starfish, and (c) squirming motion 

 by changing the body shape of a tailless object in slow motion through a viscous 

 fluid. Problem (a) has been discussed by Siekmann (1963), and (c) has been 

 analyzed by Lighthill (1952). The problem of self -propulsion of a deformable 

 body in a perfect fluid has been treated by Saffman (1967). 



Hydrodynamics of swimming is only a part of the whole problem. From 

 the viewpoint of bioengineering, the entire process begins with the biochemical 

 energy stored in the swimming being, which can be converted, with efficiency 

 Vi, into mechanical energy for maintaining the body motion, the latter is in 

 turn transformed, with efficiency v^^ into hydrodynamic energy for swimming. 

 A part (fraction 173, say) of the hydrodynamic energy is spent as the useful 

 work done by the thrust, which balances the work done by frictional drag, and 

 the remaining part becomes the energy lost, or dissipated, in the flow wake. 



It is in the effort of making a self-contained balance of energy that some ap- 

 parently astonishing observations have been reported. For example, Johan- 

 nessen and Harder (1960) reported several impressively high speeds (about 20 

 to 22 knots) attained by porpoises, killer whales, and black whales. The 



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