theory. Before proceeding it was necessary to retrieve spectral growth data from the 

 f-x diagrams. This was simply done by taking cuts along the x-axis for various fre- 

 quencies. A selected amount of this growth data is shown in Appendix A. Also shown 

 are the best fit growth curves obtained in this section. 



Since the theory of Section 2.0 concerns itself with only the linear phases of 

 wave growth, it was necessary to use only data for which nonlinear effects were smalL 

 A good rule of thumb is that nonlinearities are negligible as long as the magnitude of 

 a particular spectral component is less than 30% of its maximum value (Snyder and Cox, 

 1966). Further limitations are imposed by the fact that no data were obtained for the 

 area between 15-25 nautical miles from the coast and also that data from the downwind 

 near zone "peak area" was useless. With these restrictions only a small amount of the 

 growth data was available for analysis. Once this data had been isolated, OC and ^ 

 were evaluated by the method of least squares so that the quantity 



^rF(x.)-S(x., 0C,^)j 



was a minimum. F (xj) is the observed value of a spectral component at the position 

 X = xi, S is the estimated value of F at xi, and wj are weighting factors. The w; are 

 chosen so as to be inversely proportional to the square of F (xj) unless F (x;) is less than 

 Im'^ - sec in which case w; = l/F (xi). Such a system tends to give equal weight to 

 each data point but discriminates against values below Im'^ - sec where noise is more 

 important. A comparable weighting scheme was employed by Snyder & Cos. The 

 resulting best estimates of CC and )S are shown versus wave frequency for the various 

 spreading factors in Figures 15 and 16, respectively. Also shown on these figures are 

 the theoretically predicted CC and /9 as discussed in the following sections. No effort 

 will presently be made to estimate the directional aspects of OCand/3 . 



7.2.2 Linear Wave Growth 



The results of the previous section indicate that the linear grov^h factor, 

 (£, is important in the initial generation of wind waves and in providing a substantial 

 amount of the energy near the eventual spectral peak. However, the magnitude of 

 OC is sufficiently small so that it cannot account for a majority of the observed wave 

 energy at the more advanced stages of spectral development. Also, apparent from 

 Figure 15 is that the choice of directional assumption had little significant influence 

 on the estimates of QC for an individual run. To be sure, there was almost a factor of 

 two difference in the corresponding magnitudes of the estimates, but in view of what 

 is to immediately follow, this is of small concern. The important thing is that the 

 dependence of OC on frequency is clearly the same for all three K's. 



The relative magnitude and distribution of OC with frequency appear 

 somewhat different between the two runs. The maximum value of OC for the 



39 



