All of these normalizations are dependent on Equation (5). The validity of this 



on pi 

 relation has been examined from measured data. ' x It is interesting to observe 



that the variation of C /(C „ +C „ ) with ( 27rf ) is frequency and water 

 nn' n x n x ryry gk 



depth dependent. The deviations increase as the frequency increases. 



THE DIRECTIONAL SPREADING FUNCTION 

 Fourier Coefficient with Weight Parameter 



Wave directionalities are determined by the directional spreading functions. 

 A conventional spreading function is given by Longuet-Higgins et al. in Equation 

 (3) with W-, and W 2 equal to 2/3 and 1/6, respectively. For the discus buoy, the 

 spreading function with second order harmonics is given by 



H 1 (f , 9) = -[- + - (A 1 cose + B 1 sine) + i (A 2 cos26 + B 2 sin2e) ] (10 ) 



The results of angular spreading from Equation (10) indicate a wide spreading of 



22 

 energy and large angular resolution as shown by Kinsman. 



Values of the weight parameter, W i , have been proposed by other investiga- 



Mitsuyasu and his collee 



cloverleaf buoy data, proposed 



-i Q 



tors. Mitsuyasu and his colleagues , based on their field data obtained by a 



1+ 

 H 2 (f,e) =i[i + I W n (A n cos ne + B n sin ne) ] (ll) 



n=l 



if 2 



with W 1 = 8/9, W 2 = 28/1+5, W 3 = 56/165 and W^ = lH/99. Here, the cloverleaf buoy 

 not only measured surface slope but also surface curvature. The Fourier coef- 

 ficients can be evaluated up to the fourth order harmonics. However, when adapted 

 to second order Fourier expansions, only the first two weighting parameters can 

 be used. This will slightly alter the spreading. Recently, LeBlanc and 

 Middleton 2 ^ proposed a special weight function to improve the resolution, based on 

 some field measurements. They proposed W x = 0.?8l and W 2 = 0.31+8, with the angular 

 resolution of 110 degrees. They indicated these weight parameters can eliminate 

 some of the minor and negative lobes in the angular spreading. 



