85 

 than and less than the mean direction (see Fig. 5.2): 



01 = angle TT J^ ^m where: 9 < angle(^„) < 6 + tt 



/ 1 ^^' \ 



62 = angle I — 2^ Dm 1 where: 6 — tt < angle(^m) < 6 



(5.14) 



Frequency Once the dominant directions have been identified, the approximate 

 frequency must be determined. This is accomplished by examining the water surface 

 at the center of the array, as interpolated by the finite difference approximation 

 described above (Eq. 5.11). The method used is identical to that used in the two 

 dimensional method, (Ch. 3): 



' ^'^^- (5.15) 



Vc,m dt^ 



where —9^ is computed from the smoothed spline used for to compute -^p for the 

 direction estimate. If the wave field is unimodal it is expected that there will be a 

 single dominant local frequency. The calculated frequencies at each time step will be 

 similar in magnitude, and the mean over the record is used as the first estimate of the 

 frequency for the single wave. In the two wave method, it is assumed that the bimodal 

 sea is the result of reflection, so that the frequency of the incident and reflected modes 

 should be the same, and the mean frequency is used as the first estimate for both 

 waves. 



Wave Numbers Once the frequency is known, the wave numbers are estimated 

 from the linear dispersion relation. 



{u - KnUnf = gKn tauh /\„/i, k:c,n = A'n COS 6^ ky^ri = A'„ sin 6'„ (5.16) 



where Un is the component of the Eulerian current in the direction of the nth wave. 



U^ = ^Vl + VI cos (^tan-^ (^ - Q^ (5.17) 



