illustrated in the inset of Figure 18 where a schematic spatial history of a spectral 

 component is presented in non-dimensional form. The abscissa is distance down- 

 wind in wave lengths and the ordinate is the value of the component, F, at a given 

 X divided by the maximum value, Fp^, that the component achieves throughout its 

 spatial history. 



The major portion of Figure 18 shows the number of wave lengths (x/ L) from the 

 leeward fetch edge at which F^ occurs for the various frequencies. The data shown 

 for the downwind run have neglected the near zone peak area previously mentioned. 

 Data for only the K3 directional assumption are presented but either of the other two 

 spreading factors would have served as well. While there is some scatter in the data, 

 it appears that high frequency components will reach their maximum value in fewer 

 wave lengths than the longer, lower frequency waves. 



It is informative to investigate the correspondence of the observations with 

 proposed frequency power law formulations of the equilibrium range. Figure 19 is 

 a log-log plot of wave frequency f versus F^, the maximum spectral value. Only 

 upwind values of F^ have been used. Also included in the figures are estimates, 

 obtained through averaging, of the eventual equilibrium value Fg for both runs.* 

 While neither of the exponents of the estimated best fit lines can be considered as 

 precise, the relative difference between the two lines is significant. A difference 

 of this magnitude occurs for all directional assumptions. 



Whatever the ultimate cause of the "overshoot" effect, it does seem to present 

 a possible explanation to the controversy over the form of the representation used to 

 describe the equilibrium range of the wave spectrum. Depending on the experimental 

 design, the amount of data taken and the frequency range considered, it would be 

 possible to bias the results inadvertently toward either higher or lower estimates of a 

 pure power law exponent. It is reasonable to suggest that an explanation such as 

 given in 7.1, and a representation of the form (14) are required to more fully des- 

 cribe the establishment and maintenance of spectral equilibrium. 



8.0 CONCLUSIONS 



By using a modified airborne radar altimeter and subsequently solving a Fredholm 

 integral equation of the first kind, it has been possible to obtain sequential estimates 

 of fetch limited wave spectra. Since these spectra were representative of fetch 

 distances from 3 to 190 nautical miles, it was possible to simultaneously 

 follow the development of a number of spectral components from their very 

 beginnings to their final, fully developed state. Although this data was taken under 

 but one typical wind condition, it still provides unique insights into the processes of 

 wave generation and dissipation. The more important results of this paper are 

 summarized below: 



(i) The peak of the spectrum moves toward lower frequencies with distance from 



*lt turns out that Fe/Fm for both runs is between .35 to ,75 with the data 

 being badly scattered. 



48 



