singular Perturbation Problems in Ship Hydrodynamics 



t, (x,y}c) terms in a far-field expansion of t,(x,y;e) (cf, 

 Zn(x,y;€) ) 



t,(z) function mapping the complex variable z onto an 



auxilliary (t,) plane (in Section 5) 



Ti(x,y) steady part of free-surface deflection in ship-motion 



problem 



'n(x) free- surface deflection in problems in two dimensions 



T)q(x) part of free- surface deflection in low-speed problem in 



two dimensions (see (5-7) ) 



angle variable in cylindrical coordinate system 



0(x,y,t) time -dependent part of free-surface deflection in ship- 



motion problem 



K g/U , a wave number in steady-motion problems 



\^(z) density of dipoles on a line (see (2-40) ) 



|JLp(z) density of dipoles on a line (see (2-40) ) 



\s^{x,z;€) density of dipoles on a surface 



V « /g, a wave number in oscillation problems 



^j(t) displacement in the j-th mode of motion (see Section 



2.32) 



p water density 



a^(x;€) density of sources on a line 



(rf,(x,z;c) density of sources on a surface 



^x,y,z,t) velocity potential (the arguments may vary, but <^ 



generally denotes the complete potential function in a 

 problem) 



^^Xfj) in Section 5.4, potential for the problem in which the 



free surface is replaced by a rigid wall 



(^j^(x,y ,zj€) terms in a far-field expansion of ^(x,y,z;€) 



^j(x,y,z) normalized potential functions (see (2-73), (3-28) ) 



4'f,(x,y ,z;€) terms in a near-field expansion of 4)(x,y,z;€) 



$j(x,y,z) normalized potential functions (see (3-44) ) 



X(x,y,z) velocity potential for the perturbation of a unit-strength 

 incident stream by a slender ship 



4'i(x,y,z) normalized potential functions (see (2-76) ) 



i}j(x,y,z,t) time-dependent part of velocity potential in ship-motion 

 problem (with forward speed) 



^j(x,y,z) normalized potential functions (see (3-45) ) 



CO radian frequency of sinusoidal oscillations 



J2.(x,y,z) normalized potential functions (see (3-46)) 



665 



