724 



[chap. 21 



increasing linearly with wind speed (when the water surface is clean) as shown 

 in Fig. 3. When the water surface is contaminated by a surface-active agent, 

 the mean square slope is not greatly affected at low wind speeds but increases 

 much less rapidly for high wind speeds. We shall see (page 725) that these 

 surface "slicks" remove ripples completely but scarcely affect any but very 

 short gravity waves. Therefore, the difference between mean square slope with 

 and without slick provides a measure of the contribution by ripples. 



The foregoing statements can be made plausible by comparison of the 

 calculated contribution by gravity waves to the mean square slope with 

 observations of the mean square slope when the water surface is covered with 

 oil slicks. We adopt the form (7) for the total slope spectrum in the equilibrium 

 region. In order to permit calculation of the integral 



Sx^ + s, 



y^ = ^{S. 



+ Sy)df, 



(8) 



0.04 



Fig. 3. Mean square slope (ordinate) as a function of wind speed (abscissa). Long dashes 

 show best-fitting straight Une to data of Cox and Munk (1954) for mean square total 

 slope, Sx^ + Sy^, when sea surface is clean and fetch is unlimited. Circles show measure- 

 ments of Sx^ + Sy^ from same source when surface is contaminated to form a slick. 

 Solid line shows contribution to Sx'^ + Sy^ by gravity waves only according to equation 

 (9). Short dashes show Sx^ as measured at a fetch of 2.1 m in the laboratory. The 

 wind speed has been adjusted to an anemometer height of 10 m. 



we must provide both a low- and a high-frequency cutoff. To find the contribu- 

 tion solely by gravity waves, one takes the upper limit as f^n, but the presence 

 of an oil slick seems to damp out short gravity waves as well. The low-frequency 

 cutoff is provided by the fact that long waves are not in the equilibrium part 

 of the spectrum and very little energy is supplied to waves which run faster 

 than the wind. A reasonable form for the cutoff has been provided by Neumann 

 (1953). Joining Philhps' saturated spectrum to Neumann's cutoff, yields, for 

 wind speed U measured at an anemometer height of roughly 10 m, 



Sx+Sy = ^/-iexp[-2j72/(47r2/2C72)]. 



