transmission for low values of # is much greater than for high 
values of » and it is therefore more difficult for the storm winds 
to maintain that part of a power spectrum which applies to low 
values ofp. 
a 
considerations 
It is dangerous to attempt to apply non-linear criteria to 
linearized systems. The linearized theory presented so far has 
gone a long way toward explaining the properties of actual storm 
generated ocean waves, and it appears to give consistent results. 
A linearized theory usually has one fault in that the theory in 
itself seldom yields information on when it will fail. 
For example, the requirement that ee ay be bounded was imposed 
in Chapter 7 for the first time and equations such as equation 
(11.15), (11.16), (11.19), and (11.21) have been deduced from this 
property and other considerations. However [a,(u ,0)1° is still 
undetermined to within a constant factor. That is, if a given 
functional form for [a,(u ,6)]° satisfies all of the requirements 
which have been deduced, it is still undetermined to within a con- 
stant factor because it can be multiplied by a factor of 10 or 100 
or 1000 and it would still satisfy all of these requirements. 
This is, of course, against good sense and against the initial 
assumption that the disturbance was small. There is no way to tell 
when the theory will get seriously out of hand for large magnitudes 
for the function from any of the previously given formulas. 
It is possible to make an educated guess about when the theory 
will certainly fail, and sometimes an educated guess is a very good 
12 
