(ii) One can also account for the result by allowing the wind near the 

 coast to either drop on the upwind run or be higher for the downwind run. Such 

 wind changes would induce either more or less (even negative) curvature, respectively, 

 to the growth curves. Since (B is essentially a measure of this curvature, the result 

 could be as shown on Figure 16. Please note that such wind changes will be most 

 dramatically visible in estimates of /3 but significantly less apparent in estimates of 

 OC and in the qualitative description of the general spectral field. 



The aforegoing discussion serves to re-emphasize the fact that the numerical 

 estimates of /3 , and to a lesser extent OC , should be considered as order of magni- 

 tude values. 



Taking into consideration the previous remarks, it is of interest to compare 

 theory and observation. The predictions of the theory of Miles are shown in Figure 

 16 by the curve designated M . It is clear that this predicted curve is in agreement 

 with none of the data. A similar conclusion about Miles' theory was reached by 

 Snyder and Cox (1966), The other curve shown on Figure 16 (labeled SC) Is an empiri- 

 cal relation for /S suggested by those authors on the basis of this data and is defined 

 for the case of waves travelling downwind by 



^ = 2Tr sf (W/c - 1) (15) 



where s is the ratio of the densities of air and sea water and W is the wind at a 

 critical wave length above the mean sea surface . Neglecting the upwind run, it 

 must be admitted that the agreement between measurement and the predictions of (15) 

 is quite remarkable. This cannot be construed as a verification, but it does strongly 

 suggest that there may be a good deal of physical truth in the apparently simple relation 



One of the features of Figure 16 which seems particularly significant is the 

 fact that/S is positive for waves travelling at phase speeds equal to or greater than the 

 wind speed. Such a result seems contrary to the predictions of most instability theories. 

 One possible explanation of this result has been given by O. M. Phillips (personal 

 communication and in press).* Briefly, he proposes that ^ is the sum of two different 

 physical processes which are acting on the wave regime. The firstis identical with 

 that proposed by Miles (1957). The second, however, is an induced effect arising 

 from the undulatory turbulent flow over the waves. For waves travelling at or faster 

 than the wind speed, the Miles "critical layer", or "matched layer" as Phillips calls 

 it, contributes little or no momentum to the waves. The contribution from the undula- 

 tory turbulent flow, however. Is not insignificant and, hence, now dictates the sign 

 and magnitude of /S . For a more detailed discussion of the entire concept the reader 

 is referred to Phillips'forthcoming work. 



*We are very much indebted to Professor Phillips for making preliminary details 

 of his new theory available to us. 



44 



