A storm of finite duration with a fetch of finite length 
The wave system given by F(t) as given by equation (7.40) 
as it operates upon equation (7.35) is unrealistic in one sense 
which can be eliminated without requiring that the system be of 
finite width and contain short crested waves. The storm which 
would conceivably produce the waves would have to extend along 
the entire y axis of a coordinate system located at the forward 
edge of the storm. In addition, the winds which would conceivably 
produce the waves could not exist for any values of negative x. 
That is, the waves could not exist for negative x and they would 
have to build up very rapidly to a full stationary state (within 
the storm) within a very narrow zone at x = 0. Under these con- 
ditions when the storm lasts for De (Duration of Storm) seconds 
and then ends suddenly, the duration of the waves is DL seconds, 
and dD = ie 
It is possible to formulate a somewhat more realistic case 
under the assumption that the same stationary conditions exist 
over a major portion of the fetch over which the waves passing 
x = O were generated that exist at x = 0 as the waves pass. 
This condition would occur in the fetch, or area of generation, 
if the wave spectrum had built up to the point where breaking at 
the erests due to non-linearity would dissipate the same amount 
of energy that is added to the wave system by the winds over the 
fetch. The exact mechanism is beyond the scope of this paper 
because of the non-linearity, but such a stationary state is with- 
in the realm of possibility. 
Sa 
