Hsu and Yu 



and its roughness can be described by the ripple standard deviation 

 (J- of the water surface elevation about the mean-wave profile. It 

 was observed that (t increased ^ith wind speed at the same fetch. 

 In general, cr increased as y^u /v increased. The values of cr 

 are listed in Table 1 and vary from about 0.001 to 0.039 ft. 



From a least- square fit of the velocity profile Eq, (5) to the 

 measured data, values of U| and y^ can be obtained and hence the 

 values of y,., ky^, and p (see Sec. 2). The values of yg are com- 

 piled in Table 2 and vary from 0.004 to 0.011 ft. The values in 

 Table 1 and Table 2 show that the ripple standard deviation is larger 

 then the critical layer thickness in all cases. It seems that the 

 surface roughness or ripples should destroy the organized actions 

 of vorticity which Lighthill [ 1962] presented as the physical expla- 

 nation of Miles' instability nnechanism. Thus, Miles' interpretation 

 of the energy transfer mechanism (adopted from Lin [ 1955] ) as the 

 perturbation Reynolds stress working against the mean velocity pro- 

 file at the critical layer is severely strained by the existence of a 

 ripple layer large enough to obliterate the critical layer. 



The potential energies of wind*-generated ripples with and 

 without mechanically generated waves are presented in Table 3. 

 The presence of the generated waves decreases ripple energy sig- 

 nificantly. Although there are many irregularities, ripple energy 

 generally decreases as wave frequency increases. Exceptions occur 

 at 300 rpm and 60 ft fetch where the 1.2 and 1.4 cps waves are 

 breaking and ripple energy is sharply decreased. Sample power 

 spectra of the ripples superposed on a 1.1 cps wave were obtained 

 by subtracting the mean 1. 1 cps wave profile from the originail water 

 surface elevation time series. The remaining time series, which 

 contains only ripple variation, was then spectral analyzed. The 

 resulting power spectra of wind- generated ripple with and without 

 mechanically generated waves is exhibited in Fig. 1. Spectral 

 peaks for the two cases appear at about the same frequency, but 

 spectral density is drastically reduced when waves are present. 



The two possible reasons for ripple attenuation in the 

 presence of waves are 



a. sheltering effects retard ripple generation by the wind, 



b, non-linear wave-wave interactions cause ripple energy 

 to be dissipated and to be transferred to the waves as 

 suggested by Longuet-Higgins [ 1969] (see later discussion 

 on wave energy). 



4. 2. Mean Wave Profiles 



Mean wave profiles were determined by phase -averaging 

 over records of 35 waves. A sample of corresponding pairs of 

 mean wave profiles and their corresponding original recordings for 



18 



