Chapter 6. SOME MODEL WAVE SYSTEMS IN WHICH THE 
CRESTS ARE INFINITELY LONG 
Introduction 
The usual wave record today in deep water is observed as a 
function of time at a fixed point. A question arises as to whether 
this one record is enough to characterize the sea surface and as to 
whether it can be used as a forecasting tool. The actual short 
erested appearance of the sea surface and the finite width of the 
storm cannot be determined from this one observation. Some elementary 
results (without the use of time series theory) can be obtained 
which demonstrate some of the effects of dispersion, but they will 
be shown to be inadequate even for the case of infinitely long 
crests. 
Equations (6.1) through (6.6) describe free surfaces as a function 
of time which might be observed at the edge of a storm at sea at 
the point x = 0 and y = 0. They increase in complexity, and they 
are described less and less precisely as functions. In equation 
(6.6), for example, a,(m) and b,(y) are unikmown functions which 
would have to be described before anything could be said about the 
behavior of the sea surface either at the origin as a function of 
time or at other points. 
Figure 10 shows portions of the graphs of 7 Ty (02t), 
1 rq76020,t), and 7 ty(0,0,t). The first graph is regular and 
repeats itself exactly. The second graph was constructed by pick- 
ing different values of An» on? and en at random for a few values 
and graphing the resulting function. 
= lige 
