Non-Linear Shtp Wave Theory 
speed, rather than a uniform flow, as an "unpurturbed" state. This 
new approximation is the natural extension of the thin body theory 
into the range of small Froude numbers. 
The basic equations of flow past a body of finite thickness 
moving at low Froude number have been also derived. Again, to ob- 
tain a uniform solution one has to satisfy simultaneously the bounda- 
ry condition on the full body and a free-surface condition in which a 
flow of varying velocity is taken as the basic state. This basic flow 
is derived by solving for the two terms of the naive small Froude 
number expansion (rigid wall and first order Neumann type problem). 
To solve for flow past the actual body, while keeping the 
free-surface condition in its usual linearized form, may lead to 
erroneous results in the range of small Froude numbers. 
V - PRELIMINARY EXPERIMENTS ON THE TWO DIMENSIONAL 
BREAKING WAVE. 
An important free-surface nonlinear effect, present in the 
case of blunt bow ships, is related to the breaking wave. At the 8th 
Naval Hydrodynamics Symposium we have presented (Dagan & Tulin 
1972) theoretical models of the breaking wave inception and of the 
bow jet. Recently, experiments have been conducted at Hydronautics 
Inc. under the supervision of Mr. M. Altman in order to visualise 
the two-dimensional breaking wave. The detailed results of these 
experiments will be reported elsewhere. Herewith a few prelimina- 
ry observations. 
A rectangular body has been towed at constant speed in the 
small Hydronautics towing tank. The water depth was 38 cm and the 
model has been submerged at (i) 2.5 cm and (ii) 1.25 cm beneath the 
unperturbed level, such that the effect of the bottom was negligible. 
The model has been towed at six different speeds in the range 0. 61l- 
1.46 m/sec. The model motion has been recorded through the chan- 
nel glass wall on a 16 mm color film at 64 frames per second. Tak- 
ing the pictures has started after 3.5 m of run (the tank total length 
is 24 m). In fig. 9 we have reproduced two pictures for the 2.5 cm 
model : at 0.61 m/sec and at 1.46 m/sec, the corresponding draft 
Froude numbers being 1.22 and 2. 93, respectively. 
The free-surface in front of the body had vertical pulsations 
which became more violent as the speed increased. This made quite 
difficult the definition of the average free-surface profile. It seems 
that the oscillations are related to gravity effects since the periods 
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