Chapter 8. SHORT CRESTED WAVE SYSTEMS 
Introduction 
The possibilities of models with infinitely long crests 
have been analyzed in the past chapters of this paper. Unfortu- 
nately for theoretical purposes, storms are finite in width and 
waves at the edge of a storm at sea are short crested. These 
two facts have not been adequately treated in past forecasting 
theories and it is necessary to treat them adequately now. Waves 
are observed at angles up to forty-five degrees to the direction 
of the wind in a fetch of finite width. The waves therefore 
spread out over areas considerably wider than the width of the 
Storm. The potential energy per unit area of the waves in the 
decay area must therefore be lower, and the waves must therefore 
be lower due to this effect. 
In this chapter, then, the basic material for the analysis 
of short crested waves will be derived. In Chapter 9, the Lebesgue 
Power Integral for a short crested sea surface will be derived, 
and the behavior of the waves outside of a storm of finite width 
will be studied. In Chapter 9, the results will be so general 
that they will form an adequate theoretical base for a wave fore- 
casting system. 
Elementary short crested wave systems 
Short crested waves are discussed somewhat briefly in Lamb 
[1932] and in most other references on wave theory. The usual 
analysis is of such an elementary nature that it is necessary 
to start from these elementary concepts and show how they can 
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