Lee 





k:| 



where ^^=^0" J^s' 

 On the body: 



^i»(^n'yn)f'('^o) - ^iv = - ^O"! ^ ° ^ ^ = ^ ^^^^ 2, (A'-4) 



^ixK'yo)f'K) - ^iy = - V ^^(i-2)xy (^cYo^^'^^o) " •i^(i-2)yy) 



= nrijix^.y^) for 1 = 3 and 4, (A-5) 



and 



^Tx^'^o^^'K) - ^7y = - 7 ^"^jE^^lxy^^o'Vo) + "i^Zxy^^'^) " ^lyy ' ^2yy] 

 = m^(x^,y^). (A -6) 



In the far field 



<p. (x , - cx>) = for i = 1 , 2 , 3 , 4 , and 7 



and at |x| = oo the potentials «pj for i = 1, 2, 3, and 4 should 

 represent outgoing plane waves. For the steady potential <p- the 

 condition at f x | = co should be determined by the law of mass con- 

 servation (see Lee [ 1968]). 



Symmetric flow condition: 



^j(x,y) = ^j(-x,y) for i = 1, 2, 3, 4, and 7. 



In the limiting case of (t. = o-^ the forcing motion given by 

 Eq. (7) reduced to 



y(t) = 2ho sin cr| t 



and if we let e = 2hQ/b, the perturbation expansion given by Eq. (17) 

 reduces to 



-j<r|t -J2or,t 2 



$(x,y,t) = e^,(x,y)e +ev»(x,y)e + € <p^(x,y) 



942 



