563 



Sylt 730918 



to 



SCALE 



20" 



110° 



200 



k : 0.71 k 



k = 0.95kn 



k=1.19 k 



/..55 x10~^m"'' 



k : 1 .90 k, 



k=2.Ukm 



k3238kn 



k=2.62kn 



J_ 



k =2.86 km 



k = 3.10kn, 



FIGURE 13. Normalized directional 



-»- 

 distribution functions of the k- 



spectrum off Sylt, Sept. 18th, 



1973. Directions are relative to 



true North. 



The f-spectrum has been computed from the k- 

 spectrum according to the procedures described in 

 Section 3. The result for the spectrum off Sylt 

 is given in Figure 8 along with the corresponding 

 JONSWAP spectrum. The resolution is about 0.02 Hz 

 near the peakfrequency , which is 0.165 Hz, and 0.01 

 Hz at twice the peak frequency. The number of de- 

 grees of freedom for frequencies greater than 0.13 

 Hz is 250 or more. Considering the scatter in the 

 original data set of JONSWAP and taking into account 

 the resolution, it is concluded that the agreement 

 between the two spectra is fair. 



The frequency spectrum computed from the observed 

 k-spectrum of the second sortie is plotted in Fig- 

 ure 9 along with the frequency spectrum of the buoy. 

 The resolution of the spectrum based on the stereo 

 data is on the order of 0.02 Hz near the peak of 

 the swell and 0.015 Hz near the peak of the locally 

 generated wind sea. The number of degrees of free- 

 dom is 125 or more for frequencies greater than 

 0.10 Hz. For the spectrum of the buoy the resolu- 

 tion is about 0.02 Hz and the number of degrees of 

 freedom is about 48. 



The spectrum based on the stereo data seems to 

 be shifted in energy density. This may have been 

 caused by noise and to appreciate this influence 

 the it-spectrum was corrected. The noise was assumed 



to be uniformly distributed over the k-plane and the 

 variance was estimated at 0.002 m (based on the 

 anticipated measurement error of 0.03% of the alti- 

 tude of photography, see Section 2) . Accordingly 

 a uniform noise level of 0.018 m was subtracted 

 from the k-spectrum and the transformation was 

 carried out again. The differences were marginal 

 compared with the earlier results and the shift 

 cannot be explained with the anticipated noise uni- 

 formly distributed over the k-plane. Further in- 

 vestigation is needed to resolve the remaining 

 discrepancy. 



The frequency spectrum of the third sortie is 

 given in Figure 16 but no attempt has been made 

 to compare this spectrum with a "hindcasted" spec- 

 trum because the relatively simple relationships 

 for off-shore wind situations cannot be applied. 



6. DISCUSSION OF THE RESULTS 



In the area off Sylt, where the wind was almost 

 perfectly off-shore and fairly homogeneous and 

 stationary, one would expect to find a frequency 

 spectrum with a shape similar to the shape found 

 earlier in JONSWAP. Finding a JONSWAP-type spectrum 

 in the conditions off Noordwijk seems to be less 



