the WIS Phase III sheltering angles. The total energy of the one-dimensional 

 and directional spectra must be equal. This requirement is expressed as 



f W f)df = f f E sea (f ' 9) d6 df (3) 



Q 1HH Sea 



where E (f,9) is the directional spectrum of the sea along the eastern 

 boundary of the ESCUBED grid. 



55. Assuming the relationship shown in Equation 4, Equation 5 can be 

 derived from Equation 3. The < in Equation 5 is a constant which is 

 determined by Equation 6. The limits of integration in Equation 6 match the 

 Phase II sheltering angles since the energy density outside these angles is 

 zero, as indicated below. 



E sea (f,9) = k cos 4 (9 - 9J E TMA (f) (4) 



J E TM (f) df = / K cos 4 (9 - 9 m ) d9 / E TMA (f) df (5) 



(5/.18)h u 

 J cos (9 - 9 ) d9 



(-1/6)ir m 



-1 



(6) 



The continuous spectrum, E (f,9) is discretized using a frequency incre- 

 ment Af = 0.01 Hz and a direction increment A9 = 20 deg . Let 



E (f.,9.) be this discrete spectrum, 

 sea i' i F 



56. The final step in determining a directional spectrum representing 



both sea and swell for the boundary condition at the eastern side of the grid 



is to add the swell to E sea ( f i> 9 i) • The swell can also be represented by a 



discrete spectrum, E (f.,9.) . If the energy of the swell is uniformly 



distributed over one frequency-direction band of the spectrum, then a discrete 



directional spectrum E ..(f.,9.) can be written as follows: 

 swell l l 



43 



