SECT. 2] 



SMALL-SCALE INTERACTIONS 



63 



water surface, mean-square slope and form drag by waves of different "wave 

 age", i.e. ratio of phase velocity, c, to wind velocity, u. This shows that mean- 

 square elevation, to which the low-frequency waves make by far the largest 

 contribution, is of very little significance in considering the aerodynamic 

 roughness of the sea surface. 



On Munk's theory the drag of the sea surface should not vary greatly with 

 fetch of the wind over the water, as the high-frequency wave motion reaches 

 the value for a fully developed sea much more rapidly than the low-frequency 

 components dominating the mean-square elevation. 



Cox and Munk (1954, 1954a) developed an interesting method for obtaining the 

 slope statistics of the sea surface from aerial photographs of the sun's glitter on 

 the water. Visual observation of the glitter had long been known as a way of 

 determining the maximum water slopes, but Cox and Munk, by means of 



0.05 



0.04 



Q- 0.03 - 



0.02 



0.01 



4 6 8 10 



Wind speed , m/sec 



Fig. 9. Mean-square slope of the sea surface related to the wind speed at 12 m height. 

 (After Cox and Munk, 1954a, Fig. 5.) 



O Natural sea surface 



Oil slick on sea 



densitometric measurements of suitable out-of-focus negatives, were able to 

 derive the frequency distribution of slope and the mean-square slope. The fre- 

 quency distribution they found to depart only slightly from the Gaussian form 

 and this indicates that a whole spectrum of wave motions is present. The 

 variation of mean-square water slope (up-and-down wind component) with 

 wind speed resulting from their trials near Hawaii is shown in Fig. 9. For the 

 cross-wind direction the mean -square slope exhibited a similar variation and 

 averaged about 70% of the up-and-down wind value. Conditions of slight to 

 moderate stability prevailed, the sea being from 0° to 2.5°C colder than the air 

 (mean 1.2°C). 



Munk (1955) incorporated the linear variation of mean-square slope with 

 wind speed shown in Fig. 9 in his form-drag analysis and found that this com- 

 ponent of the total drag of the sea surface should vary as u^. As the skin- 

 friction component should vary approximately as u'^, the final prediction is a 



