Vortex Theory for Bodies Moving tn Water 
(She O, 4B) eyes 04), (3. 4) 
is kinematically equivalent to the body inside D, and generates 
inside Dj a fictitious ‘motion identical with the Guedes of the body. 
The relative velocity Ve = V-V' fulfils the condition 
V, =\0 jon pay (3.5) 
Therefore, the vortex sheet ones allows the fluid to be 
adherent to the solid wall pee of the body. ‘This gives the image of 
a very thin boundary layer which the real boundary layer would reduce 
to if the fluid viscosity m were going to zero. 
It is easily seen that curl V = 0 inside D, » so that 
WIEV . @) inside Dos 
@ being the unique solution of the Neumann problem with the boun- 
dary condition 
For the sake of brevity, let us put: 
Bee te T(M') se E 
foo =f ne MM' ddu(M'), i. ze [fF ~MM'~ =, 
(3. 6) 
The components of Jr are continuous and continuously dif- 
ferentiable inside 0 oe 1D (and harmonic within i) Those of J. 
and of curl J are benaien tad ai through Pe because 
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