sinusoidal variation with one discrete spectral period. 
Finally, stated another way, most of the current theoretical 
work on wave theory would be correct if ocean waves were actually 
pure sine waves. Since ocean waves are not pure sine waves, the 
theory has been misapplied to situations it cannot possibly adequately 
describe. The derivations and considerations in this paper when they 
refer to Gaussian systems apply exactly to ocean waves as they act- 
ually are, except for non-linear effects. Ina later chapter a pres- 
sure record will be correctly analyzed, and the correct values of 
the surface wave record will be deduced from the analysis by the use 
of equation (12.43). 
To the reader, it may seem that the author is being unduly 
harsh with the authors of other works using the incorrect methods 
described above. The works of Wiener, Tukey, and Hamming did not 
appear until 1949, and the methods and techniques based on the sig- 
nificant height and period were undoubtedly the best that could be 
employed at the time. The literature on practical wave theory is 
full of such results, in particular, some of the results of Pierson 
[195la] which use the concept of significant height and period to 
obtain theoretical results are completely wrong and practically 
useless. 
The velocity field, kinetic energy, and energy flux in the 
transition zone 
From previous considerations, the u, v, and w velocities at the 
point of observation are given by equations (12.44), (12.45), and 
(12.46). The vertical velocity is zero at the bottom, and the functions 
automatically satisfy the equation of continuity and consequently 
60 
