Landwebev 



Put h|(Q',p,0) = H| , hglc^, (3,0) = H^; let K^ , K^ be the curvatures 

 in the plane tangent to S of the arcs a = const, and P = const,; let 

 K , K be the principal curvatures of the surface S corresponding 

 to the directions of increasing a and (3, Then we have [ 26] 



h, =H,(1 +K^Y), h2=H2(i+K^Y) (16) 



whence 



J_ U^ K^ _L 92l2 - K4 



h, av 1 + K3Y * h^ dy 1 + K^v 



and, also from [ 26] 



hjhg Ba 1 +K^Y * hjhg 8p l+Kj-Y 

 Hence the expressions for i,f],^ become 



(17) 



9ho Ki 1 8h| _ Kp /4o\ 



(19) 

 (20) 



r - _L IX 1 9u , K|V Kpu ,_,. 



^ " h. 8c^ " h, ap 1 + K V ■ 1 + K_v • ^ ' 



At the wall, the nonslip condition gives 



— — 8v , — 8u /,-,v 



" = - ^1 a^ "^ ^2 8^? • ^2^^ 



Since the shear-stress vector at the wall is 



we see that 



7 = |j.w Xe^. (24) 



This indicates that the vorticity lines and the skin-friction lines on 

 S formi an orthogonal net, as is well known. 



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