value for the power present. For Tx equal to 10 seconds, the power 
6 em (equivalent to a purely 
could be of the order of 3.28 10 
sinusoidal wave approximately eighteen meters high) between 277/10 
and infinity. For Tx equal to 1 second, the power between 27 and 
infinity could be of the order of 328 em (equivalent to a purely 
sinusoidal wave 18 cm high). 
Of course, for much smaller values of T,, these formulas begin 
to lose significance because the elemental waves are no longer 
gravity waves but capillary waves. The modification of these equa- 
tions by the appropriate forms for capillary waves might yield ad- 
ditional theoretical information about the high end of the spectrum. 
The bound given on [Ace 1c by these considerations is most 
likely an overestimate as to when the linear theory fails. That 
is, if the inequality is not satisfied, then the linear theory 
certainly fails, but if the inequality is satisfied, then the linear 
theory may still fail in one or more theoretical aspects. In 
addition, it would be fairly safe to predict that functional forms 
for [aC uw 1° will never be found in nature which fail to satisfy 
the requirements given in equation (11.24) because were the winds 
to attempt to build such a wave system, the system would be destroyed 
as fast as it is formed by breaking and turbulence at the crests. 
The "outsize" waves predicted by The Gaussian distribution would 
presumably be very unstable. 
The shape and properties of the possible power spectra 
Equations (11.16), (11.19), (11.21) and (11.24) taken together 
yield a considerable amount of information on what power spectra 
are possible, on the shape of the power spectra, and on the appear- 
15 
