Fluid Mechanics of Swimming Propulsion 

 0.14 



O.I2r- 



0.10 



COSf- 



0.06 »- 



Fig. 2 - Thrust coefficient C^ versus re^ 

 duced frequency a for k = 1/2 kC = n 



Another approach towards analyzing the mechanism of swimming is based 

 on the principle of action and reaction. Considering the inertial forces alone in 

 this inviscid approximation (i.e., leaving out the viscous effects of the boundary 

 layer and the viscous wake for a separate account), we find that the flow mo- 

 mentum at large distances is concentrated in the vortex wake, as should be ex- 

 pected in view of the trailing vortex sheet shed to the rear being thin, resulting 

 in a jet of fluid which is expelled from the plate. This mechanism can be seen 

 as follows. In the motion prescribed by (44), the tail (at x = 1) reaches the 

 uppermost position at t = k/co + 2mT (n = 0, 1, . . .), and the lowest position at 

 t = k/co + (2n + 1)77. After some calculation, it can be found from (42) that if 

 c > u (or a > k), vorticity shed from the plate is negative (or in counterclock- 

 wise sense) when the tail is at the highest position, and increases monotonically. 



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