OgiZvie 



fO(.lf<L CCM'ONENT ^ 



RADIAL CO^ONENT 



FLUID VELXITY 



>- X 



Fig. (2-2). Fluid Velocity Near a Slender Body- 

 in Steady Motion 



The physical ideas behind slender-body theory were developed 

 fifty years ago, and the original way of looking at this problem is 

 perhaps still the best way. Take a reference frame which is fixed 

 with respect to the fluid at infinity. As a slender body moves past, 

 one may imagine that its greatest effect on the fluid is to push it 

 aside; the body also imparts to the fluid a velocity component in the 

 axial direction, but this component should be quite small compared 

 with the transverse component. Both components should be small 

 compared with the forward speed of the body. 



In modern slender-body theory, we attempt to formalize this 

 estimate of the relative velocity- component magnitudes. We devise 

 a procedure that automatically arranges velocities in the anticipated 

 order: 



1) Forward speed 



2) Transverse perturbation 



3) Longitudinal perturbation 



When this pattern comes out of the boundary- value problenm, we 

 then investigate further to see what other patterns follow from the 

 same assumptions. The whole body of assumptions, results, and 

 intermediate mathematics constitute what we call "slender-body 

 theory. " 



In aerodynamics , the original intuitive approach of Munk was 

 not completely displaced until the late 1940 's. The newer, more 

 systematic approach which developed then is described well by Ward 



710 



