Abstract
It is shown that an approximation to the initial stages of overturning in an irrotational gravity wave is given by the potential function
X
= 2/3i
g
½
z
3/2
+ 2
Az
½
, where
g
denotes acceleration due to gravity,
z
is a complex coordinate in the plane of motion, and
A
is a linear function of the time
t
. By adding to the above expression a third term, linear in
z
, an expression is obtained which can describe the development of sharp corners or cusps in the free surface.
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