Plate 
tory and theoretical studies by the latter. In this paper, it will be 
shown that the two concepts are not mutually exclusive but complement 
each other. It will be shown that the dominant wave concept may have 
some important advantages foranunderstanding of the physical proces- 
ses involved in the energy transfer from the wind to the water surface. 
In particular, it will be shown that the equilibrium spectrum constant 
8 of Phillips can be associated with the slope of the dominant wave. 
Consequences of this relationship between the dominant wave and the 
spectrum will be pointed out. 
Y. THE EQUILIBRIUM SPECTRUM 
In calculations of forces exerted by wind-generated waves on 
off-shore structures two different views of the wave field have been 
held. The engineer of older days has used what is called the ''design 
wave'' for his structures : starting from the observation that for a long 
duration wind there arises a wave field in which similar waves of ap- 
proximately equal lengths and frequency but of variable height domina- 
te the motion of the water surface, he defined an average wave from 
the largest third or so of the observed waves and used the correspon- 
ding height or length for his design. Such concepts lead to the repre- 
sentation of the design waves in the form of a fetch graph (see Wiegel 
(1970) for the latest version of this graph). We shall call henceforth 
this wave the ''dominant wave". 
This essentially physical view of the ocean surface is con- 
trasted by the more recent, essentially mathematical representation 
of the water surface at a point as a random time series as used by 
many modern writers. This time function has some interesting prop- 
erties which were determined experimentally. It was found, for exam- 
ple, that the elevations of the surface at a point constitute, aftera 
long duration wind, a stationary sample of a Gaussian distributed en- 
semble (Longuet-Higgins (1953), Hess et.al. (1969)) with Rayleigh 
distributed extrema, with a variance that can be decomposed into a 
variance spectrum. Physics enters into this latter concept through 
the spectrum. As sinusoidal waves satisfy the linear equations gover- 
ning surface waves, the spectrum was thought to represent a super- 
position of very many ''component waves", thatis, linear waves of ve- 
ry small amplitude who by superposition form the large waves. Empi- 
rically, it was found soon enough that the spectra of the water surface 
at many different points in many different regions of the oceans had 
a somewhat similar shape, and attemps were made - which are by 
now classical - to empirically associate a functional form with the 
spectrum, whose parameters were empirically correlated with local 
independent parameters, such as wind speed and fetch. 
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