Mk 

 o 



1-M* 



k 



K - - £ — 

 o 1-M- 



then 



x = R cos®, (1 - M 2 ) 2 y - R sin© 

 "ko 



exp 



j-io R cos©- (0 2 - K 2 ) 2 R sin©|dO 



exp 



which is now capable of asymptotic estimation by the formula (8.29) for 

 static fluid. 



To make the algebra less complicated, suppose the Mach number M 

 is small so that M 2 can be neglected compared with unity. Then the field 

 associated with the second contribution in (9.21) turns out to be 



fc» 



iv (1 - Mq/k ) 



\ 1+M/ 



sine/2 exp {ik r - ik Mx - ^} (9.23) 



[q - k (cos9 - M)] 



there being no difference between r and k or between 6 and © if 

 M 2 « 1. The field (9.23) is a trivial modification of (8.30). 



The distant field associated with the first term in (9.21), with 

 the Kutta condition value (9.20) for A comes out as 



/ 1_ f iV o (I - ^' V _M 

 ~ \iTr/ 



( q "W 



— -, 8in6/ 2 exp{ik r - ik Hx - -f) 

 (1- M cos8) ° ° * 



69 



