722 



[chap. 21 



is necessary to allow for the ratio of wind speeds measured at 4 to 8 cm above 

 water to wind speed measured at, say, 10 m. This ratio can be estimated on the 

 basis of an assumed logarithmic velocity profile with "roughness length" 

 estimated at 0.1 cm. This yields a ratio of 0.45 with a large uncertainty. 



We shall now attempt to relate the laboratory measurements of ripple 

 spectra with measurements at sea. There are two avenues of approach. The 



f (c/s) 



Fig. 2. Ordinate : Spectra of the component of slope in the direction of the wind, Sx, times 

 frequency, /. Abscissa : frequency. The four curves represent data from a wind-water 

 channel with wind speeds U as noted. The equivalent anemometer height was 4 to 

 8 cm above water level. The dashed line to the left of each curve represents the 

 calculated value /(iS'a;+(S'2/) = 1.5 x 10~2 for a long fetch according to equation (7). 



first is to make a direct comparison of wave spectra in the ocean and in the 

 laboratory channel in the frequency region where the two overlap. The second 

 is by intercomparison of the integral of the slope spectrum, i.e. the mean square 

 slope measured at sea and in the laboratory. 



The high frequency portion of the spectrum of gravity waves at sea has been 

 discussed by Phillips (1958). After generation over a sufficiently long fetch 

 (much greater than Cox's laboratory channel) and duration, high frequency 

 gravity waves reach an equilibrium of "saturated" values limited by non- 

 linear processes related to white capping. The spectrum of wave amplitudes in 

 the equilibrium range is shown to have the form 



A = (277)-4^sr2/-5. (4) 



