singular Perturbation Problems in Ship Hydrodynamics 



TABLE 2-1 

 SYMMETRICAL THIN BODY 



Near- Field (Inner) Expansion y = 0(e) 



<t>(x,y,z;c)~ Ux + or, (x,z;e) + Q'2(x,z;€) + -i- a, (x,z;e) |y | 



0( ) 0(e) O(e^) 



J ■(2 



+ Q'3(x,z;e) + y o-2(x,z;e) |y| - -| |y| (a,^^ + or,^^} 



^ 



0(€2) 



+ O(e^) 



Far-Field (Outer) Expansion y = 0(1) 



^(x.y.z;e)~Ux-f y rr 'f'''l'^^^^\,, 



^^ „^ J ^H [(x-e)' +y' + (z-U']"^' 



0(1) 0(e") 



From Matching 



o-,(x,z;c) = 2Uhj^(x,z;c) ; 



(r2(x,z;€) = 2[(a,^h)^ + (Q^i^h)J ; 

 etc, ; 



^ -^"^H [(x-e) +(z-ur 



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