NON-LINEAR SHIP WAVE THEORY 
Gedeon Dagan 
Teehnton Hatfa, and Hydronauties Ltd 
Rechovoth, Israel 
ABSTRACT 
Systematic attempts to extend ship wave theory into 
the non-linear range are described. The basic deri- 
vations are carried out for two-dimensional flows 
and the bearing of the results on corresponding ship 
wavemaking problems is discussed, The maintopics 
are: (i) the derivation of the second order wave re- 
sistance for a body generated byan arbitrary distri- 
bution of sources, (ii) the wave resistance at low 
Froude numbers. A uniform solution, valid at low 
speeds, is forthe first time presented and (iii) a few 
preliminary experimental results on the bow break- 
ing wave. 
I - INTRODUCTION 
The linearization of the problem of free surface gravity flow 
past a ship body has (unlike the equivalent 2aerodynamical problem) 
a two-fold effect : not only the body boundary condition is simpli- 
fied, but also the free surface boundary condition is linearized. 
Although these two simplifications are associated with the same first 
order term ina perturbation expansion in which the uniform flow is 
the zero order leading term, the mathematical difficulties associated 
with the nonlinearity of each one are quite different. It is relatively 
easy with the present large computers to derive a solution which sa- 
tisfies the boundary condition of zero normal velocity on the hull 
body. It is extremely difficult, if not impossible, to satisfy the non- 
linear free surface condition, even by numerical approaches. Itis 
no wonder, therefore, that effort has been spent in the last years for 
solving the flow past ship like bodies, while keeping the free surface 
condition in its linearized version (the so called Neumann - Kelvin 
problem). The aim of such studies was to determine the range of 
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