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Summary 
The three models based on the Lagrangian equations proposed 
in this paper show some features of waves that are observed to occur and 
that do not appear to be present in models based on the Eulerian equations. 
The probability structures of the various resulting free surfaces are not 
understood. However, in the simplest model, free surfaces can be con- 
structed that show very interesting properties. There is some hope that 
the effects of breaking waves can be studied by means of these models. 
It is also evident that the measurement of random seas needs to be con- 
siderably refined so as to detect the higher order effects possible in 
these various different models. 
Acknowledgments 
The material presented in this technical report was stimulated 
by a conversation with Dr. Leo J. Tick in which he asked whether or not 
random wave theory could be approached from any other point of view 
than that presently in use. If breaking waves are ever to be studied at 
all, the perturbation procedure in the Eulerian system of equations 
does not seem to come close enough soon enough. These results are 
a start toward trying to understand waves from another point of view. 
The help of Dr. Tick in the formulation of the theoretical developments 
is also appreciated. 
Stimulating conversations with Dr. G. Neumann with reference to 
eddy viscosity effects and visual nonlinear effects of breakers were most 
helpful. 
