Chapter 3. TYPES OF PERIODIC FUNCTIONS AND NON-PERIODIC 
FUNCTIONS AND THEIR REPRESENTATION BY DISCRETE 
AND CONTINUOUS SPECTRA 
Introduction 
The surface of the oceans, if represented accurately every- 
where, would have to be given by a function of latitude, longi- 
tude, and time. The function would include the effects of tides, 
piled up water due to wind stress, other things, capillary waves, 
and gravity waves. This representation for the sea surface 
would be an extremely complicated function. In fact, it is so 
complex that it is necessary to restrict the scope of the prob- 
lem and to study the various effects separately. 
This study will be restricted to the mathematical analysis 
of ocean gravity waves with periods ranging from one or two 
minutes through one half seconds. Even this restriction is not 
enough. It is also necessary to restrict attention to homogene- 
ous areas of the ocean over which conditions can be expected 
to be relatively the same and to line segments on which the 
waves as they pass are the same in essential character for a 
relatively long time. A generating area or fetch such as the 
ones treated in the Sverdrup-Munk Theory [1944a, 1947] might 
be such an area of study if the waves have reached a steady 
state condition. It will be shown that the usual measurements 
of significant height and period are not sufficient to character- 
ize such a steady state condition. 
Frequently the character of recorded wave data changes 
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