Plate 
Hl, JHE SIMILARITY SPE CrERUM 
The model of Phillips and Longuet-Higgins for the high fre- 
quency end of the spectrum appears to neatly solve the difficult pro- 
blem of describing the water surface spectrum by means of physical 
concepts, thus closing the gap between the purely mathematical des- 
cription of the surface and the physics of the generation process. Yet, 
there are a number of observed phenomena which do not fit into this 
model, There is, for example, practically no observed spectrum 
which does not possess "humps'"', or smalloscillations, of the high 
frequency end of the spectrum about the best fitting - 5 - power law. 
These humps appear regularly in the neighbourhood of higher harmo- 
nics of w, and are more pronounced in the laboratory data (for exam- 
ple, Hidy and Plate (1966)) than in field data (for example, Moskovitz 
et. al, (1962), or Liu,(197])). There is, also, no observational evi-= 
dence of a water surface on which waves of all wave lenghts or fre- 
quencies are breaking simultaneously. In fact, it appears unreasona- 
ble to expect that small waves and large waves should be affected by 
the wind in the same way, because larger waves are always exposed 
to the wind, while smaller waves either are exposed or sheltered, 
depending on where they are located with respect to the crests of the 
large waves. 
Add to this the strange phenomenon of the ''overshoot'', Both 
in the laboratory and in the field, if for identical wind conditions a 
plot is made of the spectral density at one particular frequency as a 
function of fetch it is observed that the spectral density first increa- 
ses very rapidly with fetch, then reaches a maximum (for that fetch 
at which the component coincided with the peak of the local spectrum), 
and with longer fetches decreased and developed into an oscillatory 
curve. An example of an overshoot plot is shown in figure 2 which is 
taken from a paper by Barnett and Sutherland (19). 
The experimental evidence and the theoretical models can 
be reconciled through the concept of the similarity spectrum, of 
which Phillips' law equation 1 is a special case. Similarity spectra 
are derived on the basis of the idea that by a proper non-dimensiona- 
lization of the frequency scale and the spectral density scale all ob- 
served spectra can be made to collapse upon a single curve. In the 
literature, one finds a number of different representations of a simi- 
larity spectrum which differ in the functional form of the spectral 
density distribution, as well as in the parameters by which the mea- 
sured quantities are non-dimensionalized. Well known is the simila- 
rity spectrum of Kitaigorodski (1962), but other forms are perhaps 
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