Equation (11„42) can also be written as equation (llo44). 



,2 



(11.44) [A{H.,e)]'^ = 



Z _ ^elf^gA-) ^^^^^^^ _ ,-(,v/g)4/2j ^ (, 30 _ 0.46 e-('^-/g)^/2) • 



6 

 M- 4. 



(cos 9)^ + (1.28e-<l^^/g) /^)(cos 9)^] 



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



2 4 



If [JL is smallj the angular term in (11.44) becomes 0.04(cos9) +1.28(cos9) 



which shows that the spectrum is more peaked at low frequencies than had been J 



assumed in (llo43)o Conversely if |ji is larger, the angular term in (11.44) be- 



comes 0.25 + 0,50(cos9) which shows that the spectrum is more evenly spread 



out at high frequencies than had been assumed previously. 



The angular spreading factor used in Pierson, Neumann and James [1955] 



can be derived from equation (11,43) and it is given by equation (11.45). 



(11.45) 



The angular spreading factor from equation (11.42) can be written as equation (11.46). 



.1,0, (0.50 + 0.82 e'^^^^^g^^^^sin 29 , 0.32 e'^^^^^^^^^ 

 ' 2 IT 2ir 4^ 



F(9) =^+| + -^i|^ for -it/2< 9<Tr/2. 



(11.46) F(Hi,i 



for -it/2 < 0< it/2. 



The curves for f(9) as given by (11.45) and for F(fi, 9) with jjl = and 

 |JL = 03 as given by (11.46) are given in figure 11.32. Equation (11.43) is seen 

 to be a compromise between the two extremes indicated by equation (11.42). 



The new results, if correct, indicate that long period swell will be higher 

 on a line through the center of the generating area parallel to the wind direction 

 than it would be using the methods of Pierson, Neumann and James [1955] and 

 that the short period waves which follow later would be lower. Stated another 



way, the long period components of the spectrum are more concentrated in 



240 



