567 



suitable for a comparison with data published by 

 Mitsuyasu et al. (1975). 



Mitsuyasu et al. (1975) presented results of a 

 number of measurements (five) which were carried 

 out with a cloverleaf buoy at several locations 

 around the Japanese islands. The observed wave 

 fields were generated by various types of wind 

 fields, including on-shore and off-shore winds. It 

 appears from the ratio of the wind speed to the phase 

 speed of the peak frequency of these observations, 

 that the state of development of the wave fields was 

 rather advanced (the ratios ranging from 0.75 to 

 1.25). Based on the observed values of s, relation- 

 ships in the frequency domain were suggested. The 

 relevant expressions have been transformed here to 

 the wave number domain to produce Eqs . 15 and 15. 



s = k' 



■1 .25 



_ v2-5 



for k. 



for k < 1 



11.5 (U/c 



-2.5 



(15) 



(16) 



where s = s/Sj,, and k = k/kjj,, 

 of s, kj[ 



speed of the peak wave number, and U is the wind 

 speed. The data of Mitsuyasu et al . (1975) are 

 probably obtained in situations where tidal currents 

 were negligible and in the above transformation the 

 deep water linear relationship between frequency and 

 wave number was used. 



Equations 15 and 16 are also plotted in Figure 18 

 and the agreement is fair, the scatter being on the 

 same order of magnitude as the scatter in the data 

 of Mitsuyasu et al . (1975). The values of Sn, com- 

 puted from the stereo data are 6.0 for the spectrum 

 off Sylt, 5.0 for the first spectrum off Noordwijk. 

 These are also in fair agreement with the values 

 suggested by Mitsuyasu et al . (1975) which are 4.5 

 and 6.1 respectively. However, for the second spec- 

 trum off Noordwijk the observed value of s is 27.4 

 whereas the value following from expression 15 is 

 5.9. This is a very large discrepancy which is 

 possibly due to the rather extreme asymmetry of the 

 coastline around the wind direction where the sug- 



o Sylt 730919 



A NDOrdwijk 76Q323 

 + Noordwijk 761112 



04 06 00 10 



20 30 iO 60 80 100 k 



FIGURE 18. The normalized spreading parameter as a 

 function of the normalized wave number. 



gestions of Mitsuyasu et al (1975) may not be ap- 

 plicable. 



The above discussion concerned rather overall- 

 characteristics of the directional distributions. 

 It is planned to investigate these functions more 

 in detail. For instance, in the Ic-spectrum off 

 Sylt one aspect which will require closer study is 

 the shape of the directional distribution near the 

 peak of the spectrum in a sector around the wind 

 direction. Two peaks at + and - 15° relative to 

 the wind direction can be identified and this phe- 

 nomenon seems to be "real" in the sense that the 

 directional resolution seems sufficiently high (20°) 

 to resolve these peaks in terms of statistical sig- 

 nificance. The resonance theory of Phillips (1957) 

 predicts a bimodal distribution for frequencies in 

 the initial stage of development, but the components 

 around the peak have passed that stage and there is 

 no relation with this theory. More relevant seem 

 to be the theory and calculations of Hasselmann 

 (1963) , Longuet-Higgins (1976) , and Fox (1975) which 

 produce a non-linear energy transfer in wave number 

 space with two lobes towards the lower wave nimibers 

 and two lobes towards the higher wave numbers . Fox 

 (1975) noted that this function resembles a "butter- 

 fly." Also the results of Tyler et al . (1975), who 

 observed directional distributions of wind generated 

 waves with high-frequency radio-wave backscatter, 

 may be of interest since some of the distributions 

 have a bimodal character around the mean direction. 



7 . CONCLUSIONS 



Three, two-dimensional, wave nim±>er spectra have 

 been computed from stereophotographic data obtained 

 in off-shore wind conditions. The agreement with 

 ground-true information is reasonable but some dis- 

 crepancy needs to be resolved. 



The directional distribution of the wave energy 

 near the peak of the first spectrum is strongly 

 asymmetric . In the third spectrirai the main direc- 

 tion of the waves differs appreciably from the wind 

 direction. It is speculated that these phenomena 

 are due to asymmetry in the up-wind coastline. The 

 directional distribution functions of the second 

 spectrum are more symmetric and unimodal, at least 

 in an overall sense. 



A bimodality in a sector around the wind direction 

 is observed near the peak of the first spectrum. 

 This bimodality may be related to a multi-modal non- 

 linear interaction in the spectrum. 



The observed normalized directional spreading 

 parameter as function of a normalized wave number 

 is in fair agreement with published data. The ab- 

 solute values are about 30% larger for the first 

 spectrum and about 20% lower for the second spectrum. 

 The values for the third spectrum are almost five 

 times too large. This may be due to the rather 

 extreme asymmetry of the coastline where a compari- 

 son with the published data may not be proper. 



The results reported herein are preliminary. 

 Additional analysis of available data is being 

 carried out. 



ACKNOWLEDGMENTS 



The helicopters were provided by the Royal Nether- 

 lands Air Force and they were flown by the Search 

 and Rescue team of Soesterberg airbase (the Nether- 



