Non-Linear Shtp Wave Theory 
obtain a uniform solution, the basic nonuniform flow (on which the 
variable coefficients of the free-surface condition are based) has to 
include the rigid wall, as well as the next term, of a naive small 
Froude solution of flow past the actual body. The singularity distribu- 
tion on the body surface may be taken from the rigid wall solution 
solely. This results suggests that solving for the actual body shape, 
but with a linearized free-surface condition with constant coefficients 
(the Neumann-Kelvin problem) does not yield a uniformly valid solu- 
tion at small Froude numbers. 
The above conclusions are based on the assumption that the 
results obtained in the two dimensional case may be extrapolated to 
the ship wave resistance problem, at least in principle. Only solving 
for actual three-dimensional flows will make the conclusions valid 
in both qualitative and quantitative terms. Such three-dimensional 
solutions pose, however, difficult mathematical problems which 
have not yet been touched. 
The picture of the nonlinear ship wave resistance theory is 
not complete unless we refer to two components which are somehow 
related to viscous effects : the bow breaking wave and the wake. 
Only the first component has been considered in our studies. 
ACKNOWLEDGMENT. 
The present work has been supported by ONR under con- 
tract No. N00014-71-C-0080 BR 062-266 with hydronautics Inc. 
Most of the material is based on Hydronautics Rep. 7203-2 and 
7203-3 (Dagan 1972a and 1972b in References). I wish to express 
my gratitude to M. P. Tulin for the stimulating discussions we had 
on the subject and for his collaboration in the different stages of the 
work. 
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