outflow of wave energy from the storm area. From arguments similar 
to those which have been used above, the wave power will not be 
bounded unless equation (11.21) holds. 
Equation (11.20) has a particularly important application in 
wave forecasting theory. At the forward edge of a storm at Sea, 
it measures the energy which is being transmitted into the area of 
calm by the waves as they leave the edge of the storm area. The 
storm winds in the atmosphere by some mechanism transfer energy to 
the waves in the generating area. The energy in the wave motion 
in the generating area flows out of the generating area at a rate 
given by equation (11.20) (plus a component in the y direction). 
The important point is that in order to maintain the same amplitude 
of the power spectrum near » equal to 27/10 that is maintained 
near # equal to 27/5, the atmosphere must transmit twice as much 
energy per unit time to the generating area near frequencies given 
by p | to 27/10 than is required near # equal to 27/5. 
Consider, for example, two power spectra. One is given by 
[a,(# 40) ]° equals a constant over the area bounded by # equal to 
2m/1l and 27/9 and by © equal to + 7/36. The other is given by 
[anu 58)1* equals the same constant over the area bounded by “ 
equal to 27/5.24 and 27/4.74, and by © equal to + 1/36. The two 
power spectra have the same band width and the same value of Emax? 
but were such power spectra actually to exist over a generating 
area, twice as much energy would have to be transmitted to the 
sea surface by the atmosphere in order to maintain the waves for 
the first power spectrum than would have to be transmitted to the 
surface in order to maintain the second power spectrun. Energy 
val 
