This idealized directional spectrum still comes fairly close to agreeing 

 with the curves in 11.22. After proper angular rotation, the (cos 6) term 

 will give good agreement with the curves for low frequencies. Agreement 

 with the higher frequencies is also good. The secondary peak and the skew- 

 ness at intermediate frequencies is missed. 



Caution is recommended in the use of equation (11.42). Within the limita- 

 tions mentioned above it comes close to describing the sea observed for a wind 

 near 18.7 knots. For higher or lower values of the wind speed, however, it 

 may not work although as a working hypothesis it may lead to useful results. 

 Since only one spectrum was observed the variation in v of f(|j., 9) as fitted 

 cannot be tested. One could on the basis of the available data put v = 18.7 

 knots inside the square brackets of equation (11.42) and say that variation in 

 [A(p., 9)] as a function of v is caused solely by the occurrence of v in the 

 first term. 



However, there are two additional points that can be made in favor of 

 equation (11.42) as written. They are that it would appear to give more real- 

 istic swell forecasts than previously used formulas, and that the mean 

 square slope of the sea surface still varies linearly with wind speed as 

 observed by Cox and Munk [1954], 



A previously given equation for the directional spectrum of a wind 

 generated sea [Pierson, 1955] is shown in equation (11.43). 



T -2(g/|JLv) 7 



(11.43) [A(|i. 9)]"^ = ^ g (cos er 



for -it/2 < 9< Tr/2 , and zero otherwise. 



239 



