558 



FIGUPE 2. Sites of the field operations. The areas in 

 the boxes are shown enlarged in Figures 3 and 4. 



dulating function due to the fact that the estimated 

 value of E(k,e) is based on four values of E(k) which 

 are usually not equally weighted in the given in- 

 terpolation technique. They are equally weighted 

 only when a transformed gridpoint in the k,9-plane 

 coincides with the centre of a mesh in the k-plane. 

 In that case the number of degrees of freedom for 

 E(k,6) is four times the number of degrees of free- 

 dom for each individual estimate of E(k). This is 

 the upper extreme of the undulating function. The 

 lower extreme occurs when a transformed k,e grid- 

 point coincides with a gridpoint in the k-plane. 

 Then the number of degrees of freedom of the esti- 

 mate of E(k,9) is equal to the number of, degrees of 

 freedom of an individual estimate of E(k). The 

 values of the two extremes are 8n and 2n respectively. 



The f-Spectrum 



The f -spectrum is determined by integrating the f , 

 6 -spectrum over the range {0,ii) and multiplying the 

 result by two. The operation is given by Eq. 6. 



E(f) 



2 / E(f,e)de 

 



(6) 



The f ,e-spectruiti has been computed from the k- 

 spectrum. The relationship to transform from wave 

 number vector to frequency is based on the linear 

 dispersion relation for deep water corrected for 

 currents. This expression and the transformation 

 are given in Eqs . 7 , 8 , and 9 . 



(gk/2Tr) 



+ k.V 



(7) 



E{f,9) = E(k) IJ2I (8) 



J2 = Ih (g/2iT)'^"3/2 + yj^-l gog (Q _ e)]-l (9) 



V is the current vector and V and 6 are its magni- 

 tude and orientation. To determine the values of 

 E(k) the same procedure as described above was used. 

 The resulting spectrum is the frequency spectrum as 



observed in a point stationary with respect to the 

 sea bottom. This was done so as to be able to com- 

 pare the results with measurements carried out with 

 anchored buoys. Expressions for the approximate 

 resolution (Af) and number of degrees of freedom 

 (N) are given by Eqs. 10 and 11. 



Af 



II- Ak = ^ c Ak 

 3k 2ii g 



2^2 



8 n 



TT^f 



Ak 



(10) 

 (11) 



4. DESCRIPTION OF THE SITES AND THE WEATHER 

 CONDITIONS 



Maps of the areas off Sylt and off Noordwijk and 

 two bottom profiles are given in Figures 2 , 3 , 4 

 and 5. It may be noted that both areas are similar 

 in general appearance but an important difference 

 seems to be that the coast near Sylt recedes sharply 

 North and South of the island and is strongly asym- 

 metric with respect to the off-shore direction, 



-(- observolion tower 



FIGURE 3. The area of observation off Noordwijk. Lo- 

 cations of observations indicated by dots. 



