Computation of Shallow Water Ship Mottons 
3 fe zh Hi aor 4. al 
where H is the section at station x , and n is outward from the 
hull (into the fluid). Now the contour integral can be evaluated entire- 
ly in the near field region as follows. 
ooo 
\e 
BIs< 
Aa 
N 
Q 
~ 
I 
a 
| ea ileal 
Qy gy 
B|< 
As 
Nh 
! 
< 
Q 
|S 
SS) 
Q 
rao) 
+ 
ee 
ale 
A=- 
Q 
a) 
| 
ea 
aa 
Bix 
oe 
ang 
Pile 
N 
==, 
oF 
os) 
1 
Tae | 
QQ 
x 
6 
\¥ 
ees 
SS 
where F denotes the free surface, B the bottom, Ry and Le 
vertical lines at y = +~ and y = -o respectively in the inner (y, z) 
plane, as shown in Figure 5.1. 
The first integral above vanishes by Green's theorem and 
there is no contribution from F or B in the second integral since 
both ait and — oy vanish on F and B. On Ly, ato = do j 
whereas on R., 3b == deo . Hence (using also ii 1. 9) } 
0 ok ie 
oy 4 dg i 
(i oa = is | dz |e, -y sez | to, Su Xi )ise (5. 4) 
ist ai vier oe 
But the boundary condition for the inner potential $, is (Tuck 1970) 
¢, — yV + 1/2Ag, age y— > +a (5.5) 
= 
Hence 
1561 
