The Wave Generated by a Ftne Shtp Bow 
matically, in the sense of the method of matched asymptotic expan- 
sions, We can say that the new analysis actually encompasses the 
usual slender-ship theory, in that the formulas and equations of the 
new analysis include all of the terms in the corresponding expres- 
sions, plus some extra terms that would be considered as of higher 
order, in the usual theory. 
It is quite striking how the solution of the bow-near-field 
problem goes over into the solution for the usual slender-body near 
field : In a region extremely close to the bow, the flow has the cha- 
racter expected of a high-Froude-number flow, i.e., the fluid velocity 
is mostly perpendicular to the plane of the undisturbed free surface. 
However, as x/e Y2= X00 , the fluid velocity at the plane of the un- 
disturbed free surface becomes approximately parallel to that plane. 
The wave elevation alongside the body changes order of magnitude in 
this transition : Wave elevation is O(e 3/2 ) in the bow near field, but 
it is O(e?) in the usual slender-ship near field ; the present analysis 
shows how this change takes place. 
Finally, it should be mentioned that this analysis probably 
contains no information that is not inherent in a thin-ship analysis. 
However, the information which is available from the present analysis 
is quite easily obtainable, in contrast to the usual situation with thin- 
ship calculations. For example, the calculation of wave profile along 
the side of the ship was carried out in a few hours with a desk cal- 
culator ! Also, there are other possible applications of the ideas 
contained herein, applications which would probably not be feasible 
with thin-ship theory as a starting point. For example, Hirata [4] 
has treated the case of a cambered thin ship (actually with zero thick- 
ness) and Baba [5] has analyzed a flat ship by this basic method. 
The latter problem was partly anticipated by Maruo [6] 
Il. THE BOW-FLOW PROBLEM 
Let the ship be travelling in the negative x direction, the 
origin of coordinates being fixed to the bow. The z axis points up- 
wards, The ship geometry is defined by the formula 
y lo=n0 lsh bhexzi ; 
where the non-negative function b(x,z) is the hull offset correspond- 
ing to the point (x,0,z) on the ship centerplane. The free surface 
shape is given by the formula 
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