An Unsteady Cavity Flow 



and 



where 



A(T)e Ai[(iKGj) §] , 



A(T)e Al[(iK<o.) e 1] , 



A(T)e-'*^<'-'^^''Ai[(-lKco)'^^e] 

 -iw(t-KT^) 



A(T)e 



Ai[(-iKa)) e §] , 



A(T) = 



(e/x) 



1/4 



-7^:^77 _ i ' 



(93) 



(94) 



may be added to (87). 



We shall now study the behavior of' the solution (87) for 

 |t| > R, » 1, ^ Arg T < tt/Z, A circular arc of radius R| is 

 drawn in the (r-plane as indicated in Fig. 6. Also shown in that 

 figure is a hyperbola S representing the equation Re [ i((r - t')] =0. 



Fig. 6 Paths of integration for the solution given in 

 Eq. (87) when t is large 



207 



