Pierson, Tick, and Baer 



long enough time, and if swell does not enter the area from some other region, 

 the spectrum in the area will settle down eventually to the fully developed spec- 

 trum represented by 



S(c.,^,v)=^e"^^'^°''^^' [F(-,^*.v)] . (1) 



where a = 8.1 x 10 ■ 3, /3 = 0.74, and Wq = g/vjg j and where 



F(c^,e*,v) = ^ 



1. (o.50+0.82e-^"^»'-^'^^'/')cos2^%0.32e-^'^^»^-5/^)'''' cos 46* 



(2) 



for -7T/2 < 0* < rr/2 and is zero otherwise {0* being measured with reference to 

 the direction of the wind). 



The fully developed sea develops as the waves originally present propagate 

 out of the area, which may take a long time, and as the effect of fetch and dura- 

 tion become established. 



This fully developed sea, designated by s^ (f . , eij ) is approximated over a 

 band of frequencies and directions f . , i = 1, 2, . . . , 15, and , j = 0, 1, . . . , 23, 



by 



f J + A f J 9 .+Ae . 

 Sco(fi-^j)-J j' ' S(27Tf, 0, Vi9 5) de 277df , (3) 



f J - A f J e .- ^e . 



where Eqs. (1) and (2) define S(27rf, 0, Vjg j), the (9. are 0, 15°, 30°, etc., and 

 all A^'s are 7.5°. 



In general, the spectrum at a particular grid point differs from the 360 

 numbers defined by Eq. (3) (half of them are zero from Eq. (2)) because the sea 

 is not necessarily a fully developed sea, because components outside the range 

 of ±90° to the wind may be present, and because higher components from other 

 winds can remain. The spectrum actually present is also described by 360 

 numbers according to the formula 



f . + A f • 6 .+A9 . 

 S(f.,0j)= \ S(27Tf, ^)de 277df . (4) 



After the procedure has gone through a number of time steps, there will in 

 general be 360 values of s (f . , ^. ) at a particular grid point. For the particular 

 time step a wind speed v and a wind direction 0^ will be given for that grid 

 point. 



For appropriately defined angles certain 0- will be within ±90° to the wind 

 direction: 



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