v e on an Infinite plate has been split off; that field is exponen- 

 tially large ay x ■*■ - 00 , and the <J> that remains is assumed to be just an 

 outward propagating wave. 



We now have the following problem for <J>: 



<-!*♦!.£>• 



(t?5)] 



$ » o 



|i. 



3y 



(y = 0, x < 0) 

 v D(-q) 



A exp(— ) + 1Ry 



exp(iqx) (y = 0, x > 0) 



(9.7) 



(9.8) 

 (9.9) 



and we have to examine conditions as x ■* ± °°. Write k = k + ik , 



o 1 2 



to/U = (k s + ik 2 )/M, q = qj + iq . As x + - », <J> must behave like an out- 

 going acoustic wave, whose decay will be like that of a plane wave 

 propagating against the flow, so that 



iaix 



- exp <-iut - 



c -U 



.exp 



mi 



(9.10) 



As x -*• +■ °°, <j> may behave either like an acoustic wave propagating with 

 the flow 



-. exp 



exp <- 



lwt + 



k.x 



lux 

 c + U 



1 + M 

 or may behave as it does in the wake, 



(9.11) 



64 



