Wang 



; = le 



•2i^ 



F = IFe 



•i/9 



(56) 



which transforms (54) into 





+ (1 - SjKco cos 2P)F = - 4iGe 



31)8 



(57) 



This is Mathieu's differential equation. The flow region now occupies 

 in the P-plane a semi-infinite strip shown in Fig. 4. In principle, 

 a general solution of (57), or (54), can be obtained. If we denote the 

 solutions of the homogeneous equation of (54) by F|(^) and 'S'^i.'Qt 

 then a general solution of (54) is 



Y{t,) =^^^j^r-^{F^{t,)^ T^{\)G{\) d\ - T^{t,) ^ F,(MG(Md\|, 



where 



(58) 



W(F,,F3)=^F, -^F, 



(59) 



which is a constant. 



^-plane 



(rr/4.0) (3n-/4.0) 



Fig. 4 A conformal mapping plane of the basic flow 



200 



