It is interesting to note that there is some tendency for o secondary 

 spectral peak to appear near the approximate wind frequency fw(fw = g/2 ir W~ 

 0.10 cps). This is the frequency at which the Phillips' mechanism would be expected 

 to be most effective in generating waves. However, this apparent feature of the f-x 

 diagrams is only mentioned in passing and cannot be taken seriously on the basis of 

 the present data. All that can be said is that there was a significant amount of 

 energy spread over the entire low frequency range and that all frequencies appear to 

 be growing simultaneously. 



(iii) Consider a cut along the x-axis for fixed frequency f somewhat greater 

 than fw. The magnitude of the f component will increase with x until at some 

 distance x = x^, f will be the location of the spectral peak and F (f, x^) - ^m- '* 

 would traditionally be expected that for all x >Xm/ Fa; Fm- The f-x diagrams indicate 

 that this is not the case. Instead, for x > Xm, it will be observed that F is always less 

 than Fm and by a statistically significant amount. In physical terms this means that as 

 a spectral component grows, it apparently "overshoots" its eventual equilibrium value. 

 Thereafter, the component gives up energy and soon settles down to the final equili- 

 brium value. For the highest frequencies shown on the diagrams this effect is obscured 

 by the fact that the area in which the overshoot occurs was not sampled. A more quan- 

 titative discussion of the entire phenomena is given in Section 7.3. 



To attempt to explain completely the "overshoot" behavior of the individual 

 spectral components is beyond the scope of this paper. One might speculate, however, 

 that the phenomena is the result of some wave breaking, wave-wave interaction type 

 of effect. Alternatively, one might imagine as did Neumann and Pierson (1963) that 

 the occurrence of breaking seas of approximate frequency f tends to cause partial 

 annihilation of wave energy associated with frequencies f > f. Waves with frequencies 

 less than f would feel little or no effect of this breaking since their wave isngths are 

 greater than the scale of wave induced turbulence. All of this suggests that the actual 

 representation for the one dimensional equilibrium spectrum (Equation 13) might be 

 closer to that considered briefly by Phillips (1963), 



2 -5 

 H (f)ccg f . R(f /f) (14) 



o 



where R is a dimensionless function of f and the frequency of the local spectral peak 

 is fo. The true frequency has been used in place of circular frequency in order to 

 maintain consistency in the discussion. The form of Equation (14) raises some rather 

 fundamental questions concerning the causes of the equilibrium range. Implicit in 

 Phillips' (1958B) formulation of the equilibrium theory was the assumption that wave 

 breaking was local "at a point". However, localness in x-space does not necessarily 

 imply localness in f-space and, therefore, a simple form such as Equation (13) need 

 not adequately describe the equilibrium range. In fact. Equation (13) was only meant 



37 



