

p 



! 



SygfHt RMOW.i^uu 



be finite at the edge (note that the velocities in the part of 1 . 

 split off in (9. A) are finite, but non-zero, near the edge) by choosing 

 a wake strength 



v D(-q) 



A « - 



l(-£)m-<> 



(9.20) 



It is easy to see that the Q part of (9.18) contains terms like (s + q) -1 , 



(s + k /M)*" 1 which (as in $8) make no contrioution to <f> for x < 0, 

 o 



y ■ 0+ and that with th« choice (9.20) the first term in the expansion 



5 



of ♦ (s,0+) as s ■+ °° in R is 0(s ). This corresponds to 



<fr - 0(x 2 ) 

 near the edge, though the pressure 



The expression for the potential in y > is found to be 



is 0(x 2 ) because p - -Pl-jp + U "jr - ) <t>. 



H 



F(s) exp(-isx - C y) ds 



with 



F(s) 



£ (e) 



iA 



(=4) 



k iv D(-q) 



c (- -£> + 



M 



S + (-q) (S + q) 



In the exponential factor we write 



-isx - [s 2 - (k + Ms) 2 ] 2 y 



» - isx 

 so that if we define 



a ■-■««>*, {(s-^) : 



a^F) 2 



(9.21) 



68 



