Darrozes 
re atl) ~(2) 
b= x te (x, y) + aS E +oaz £! 1F (5) 
1~ 0) 380), 9 BB0 ey Se et 
a + he Sea a + ty Of) ae 
2~ 
0° 4 oA @’ =- 0 
Oz? xy 
rs + 36 a Sie ~ = 
OP DS ake ae Sey, f! Od on z= f (x, y) 
OZ E Ox yy. ay 
+ Matching conditions at infinity. 
The expansion ( 5 ) is shown to be the exact inner solution. Therefore, 
the inner region exhibits nothing more than the behaviour of the outer 
solution, This means that the outer expansion is regular at any point 
(x,y )€S, and the inner region is not required. 
Figure 2 Sketch of the flow when € goes to zero. 
The streamling I generates the streamlines I’ 
from the leading edge. The streamlines II’gives 
only the streamline II. 
Figure 2 shows the flow in the xoy-plane, when € vanishes, There 
exist physical reasons to explain the singular behaviour of the outer 
solution on the lines ( A ) and ( L,). Ona round leading edge, the slo- 
pe is infinite and the normal velocity w = SeAz is o(1) instead of 
o(e ), At any point of the angular trailing edge, the Kutta- Joukowski 
condition requires a velocity tangent to the curve ( \ ), which contre- 
dicts the fact that there is a uniform flow in the first approximation, 
On the line ( L;) , the streamlines I' closed to the streamline II rolls 
up, and generates the apex vortex. At infinity downstream, any 
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