component. Also of interest are the location of spectral peal<(s) or valley(s) at any 

 particular x-value and the value of x beyond which a specified spectral component 

 may be considered to be in equilibrium. In the first case 9 F/9 f = and the tangent 

 to a particular F-contour will be parallel to the f-axis. On the other hand, for an 

 equilibrium condition 9 F/9 x = and the contour tangent will be parallel to the 



x-oxis. 



7.0 RESULTS 



7.1 Qualitative Discussion of the f-x Diagrams 



It is apparent from Figures 12 and 13 that the type of spreading factor used to 

 solve {7a) and (8a) had little qualitative effect on the outcome of the results. This 

 is due to the fact that while each of the spreading functions used had a different 

 mathematical form and physical interpretation, they all confined the wave energy to 

 a fairly narrow, directional band about the wind direction. An isotropic spreading 

 factor, say, would have yielded quite different and quite unrealistic results. 



Another general comment that can be made is that the upwind diagrams appear 

 to have somewhat less energy content than the downwind diagrams. To some extent 

 this is true, but the effect is exaggerated by two facts. The area of greatest apparent 

 difference is generally in f-x regions where 9 F/9 x is relatively small. Hence, 

 small changes in F significantly affect the position of a contour line. This, coupled 

 with the contouring philosophy, partially accounts for the apparent result. However, 

 it is obvious that the f-x structure of the inner region is somewhat different between 

 the downwind and upwind runs. The discussion of this feature is deferred for the 

 moment . 



The essential features of the diagrams are: 



(i) The major spectral peak migrates toward lower frequencies with increasing 

 distance from shore. This feature, which was no surprise, is further illustrated by 

 showing the frequency of the major spectral peak, f^, versus x (Figure 14). The shape 

 of this curve is similar to that found by Hidy (1965) in wave channel experiments. The 

 form of the curve strongly hints at the importance of an instability-type of wave genera- 

 tion mechanism. 



(ii) There is a considerable amount of wave energy in the low frequency end 

 of the spectrum for even the small values of x. This indicates that energy was being 

 simultaneously added over the whole frequency range of the spectrum. This result is 

 in conflict with the concept that a given frequency component must be almost "fully 

 developed" before a lower frequency component can begin to grow, (e.g., Pierson, 

 et. al., 1955, Baer, 1962). 



35 



