Untformly Valtd Soluttons of Laplace Equatton 
streamline (I') goes to ( L,) and makes the vortex growing. 
Ill. THE SINGULAR BEHAVIOUR OF THE OUTER SOLUTION ON 
THE PLANFORM EDGE ( ) ) 
In this section, we look for the behaviour of the outer solu- 
tions ol) and »'? , in the vicinity of a round leading edge, ora sharp 
trailing edge. To this end, a carefull description of the body geome- 
try is required, 
III. I The body geometry 
Let us denote by »(s ), the outward normal to ( } ) in the 
plane z = o, 
Figure 3 The leading Figure 4 The local 
edge geometry (upper curvilinear coordi- 
surface), nates, 
We define a reference frame aXYZ, with aZ parallel to the z-axis, 
and the unit vector » inthe Y-direction. Figure 4 shows the local 
curvilinear coordinates (s, Y,Z): 
OM = Oa(s)+Yv(s)+ZK 
DM =h,rds + vdY +kdZ (6) 
hy, Sy ear C ( Ss ) 
C (s) stands for the curvature of the planform edge ( ) ). 
If this quantity does not vanish for any value of s , the mapping 
(x,y,z )++(s, Y,Z ) is a one to one transformation in a region of 
thickness less than s™lco(s)|, surrounding the curve ( ) ).In this 
region, the body equation may be written under the form : 
1745 
