SECT. 5] Rrrn.ES 721 



Ripples are of importance because they form the fine-scale roughness of the 

 sea surface. Sea surface roughness controls the friction of wind over water 

 (Munk, 1955) as well as the reflection, refraction and scattering of sound and 

 light (Katzin, 1957; Cox and Munk, 1954). 



1. Spectrum and Mean Square Slope 



Owing to the difficulty of observing minute ripples in the presence of large 

 gravity waves, there have been no successful measurements of the spectrum 

 of ripples in the sea. In these circumstances, we must rely on measurements of 

 ripples observed in laboratory wind and water channels and try to deduce the 

 conditions at sea from indirect measurements. 



Spectra of slopes of waves in a laboratory channel are reported by Cox (1958). 

 The channel, 6.1 m long and 26 cm broad, was filled to a depth of 14 cm with 

 water. Air was pulled through a passage of height 26 cm over the water. The 

 component of water-surface slope in the direction of the wind was measured 

 by an optical method which required no physical contact with the water. The 

 wind fetch to the position of measurement was 2.14 m. The spectral intensity, 

 Sx, is the contribution to the mean square of the slope by waves in a unit 

 frequency band. Thus 



= jy.{f)df, 



(3) 



where Sx is the slope component in the direction of the wind and/ is frequency. 

 Measured values of frequency times Sx{f) are shown in Fig. 2. 



At low wind speeds there are two peaks in the curves. The low frequency 

 peak represents gravity waves ; the sharp cutoff for lower frequencies pre- 

 sumably results from the very short fetch in the wind channel. The high 

 frequency peak represents ripples. The cutoff at still higher frequencies results 

 from the inability of the wind to supply energy to shorter waves at a sufficiently 

 rapid rate to overcome viscosity. The position of the trough between the gravity 

 wave and rijjple peak is close to the frequency of minimum phase velocity, 

 /r„=13 c/s. 



As the wind speed increases, the gravity peak moves to lower frequencies 

 while the ripple peak moves to higher frequencies and broadens. The changes 

 are such as to keep the waves of both types moving at a speed proportional to 

 the wind. At very high wind speeds the trough between the spectral peaks 

 disappears. 



The wind speeds measured in the laboratory are average values for the 

 entire air channel. They are not directly comparable with those measured at 

 sea because of the presence of boundary layers around the walls and roof of 

 the laboratory channel and because wind speeds at sea are usually reported for 

 an "anemometer level" of 10 m or so above the sea. One may estimate that the 

 wind speed measured in the laboratory channel is equivalent to the wind speed 

 at 4 to 8 cm above the sea ; this is the effective anemometer height for the 

 laboratory measurements. In order to compare with oceanic measurements, it 



24— s. 1 



