Dagan 
0 0 
2 2 Zz 4F@ 0 
1 ja) +22) a ral ue + 2r* u ve ae y= 0 
(y = 0) (73) 
on the unperturbed free-surface, similar to (64). w? =v -iv® is 
the rigid wall solution for flow past the actual body and w! is the 
next term of the naive small Froude number solution. 
(73) has a simple physical interpretation : it represents the 
equation satisfied by waves generated on a stream of variable speed 
w2 +F? w!, beneath y=0. Ogilvie (1968) has retained only the 
first term in (73), i.e. has replaced (73) by 
Im fire rh = -w] = 0 (y = 0) (74) 
He has based the derivation of (74) on the intuitive reasoning that at 
small F the wave length of the free waves becomes small compared 
to the body length scale (which governs the rigid wall solution) and, 
therefore, the waves are travelling on a basic stream of varying 
velocity. Although the argument valid in principle, (74) is nota 
uniform asymptotic ap prosime non: as shown in the preceding sec- 
tion. To determine W~ , satisfying (73), is a difficult task which is 
not pursued here. 
(iii) ¢=0(1), F*. =0(1),... €/F* =0(1) (thin body, small 
length Froude number, finite thickness Froude number), W =eWy + 3, 
By analogy with (70) we (z) satisfies the boundary condition 
aw? 
Im [iF* (1+2ew)) —+ - wi |= 0 Goh eee 
1 dz 1 
the radiation condition 
0 
Ww, — 0 (x + ©) (76) 
and the body condition 
0 0 
Wie aed (dx)< lg-y.=--h)... (il 
along the skeleton of the body. wp the linearized rigid wall solu- 
tion has the expression 
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