Kim and Mercier 



and the time factor e~ is omitted in this and subsequent sections. 



This wave encounters the fixed arbitrarily shaped bodies and is dif- 

 fracted. 



The velocity potential corresponding to the incident wave is 



(o+e) = _iga_ e *z e i*y (16) 



I CO 



which can be expressed as odd and even function of y , 



(17) 



The odd function <p. corresponds to the part of the flow which is 

 asymmetric about the z-axis , while the even function ^ e ' corres- 

 ponds to the symmetric flow. 



The flows represented by the potentials <£. and <fl^ e ' are 

 disturbed in encountering the bodies. The disturbed flows correspond- 

 ing to (f}°' and <Pf e > are described by diffraction potentials, denot- 

 ed <Pd and Vrj , respectively. These potentials are represent- 

 ed in the same form as the radiation potentials [Eq.(13)] , but with 

 different source intensities, Q . 



The unknown source densities are determined by satisfying the 

 boundary conditions 



h~ (y a' Z a } = "— an~ (y a' Z a ) 



(y u ,zj = - — J (y^.zj (18) 



dn b J b cm b J b 



where = o or e , on the straight-line segments representing the 

 contours C & and C^ . Thus there are two separate boundary con- 

 ditions for the asymmetric and symmetric flows. 



810 



