62 



DEACON AND WEBB 



[chap. 3 



It is surprising at first sight that the very marked increase in height of the 

 waves with wind si)eed is not accompanied by a more marked rise of drag co- 

 efficient than shown by the observations. This is largely attributable to the fact 

 that the components of large amplitude, in a fully developed sea, travel down- 

 wind with a speed not much less than the wind speed. 



Francis (1951) has studied the drag coefficient of a water surface in wind- 

 tunnel experiments and found it to increase nearly linearly with wind speed. 

 When he extrapolated his air speeds at 10 cm height to the 10 m anemometer 

 height used for the sea, his drag coefficients were of very similar magnitude to 

 those shown in Fig. 6. Francis considered that this might well show that the 

 mechanism for drag is not controlled by the larger waves but largely by the tiny 

 wind ripples. 



The form drag of a spectrum of waves travelling on a water surface, each 

 component at its appropriate speed, has been treated theoretically by Munk 



0.5 - 



0.5 



1.0 

 c/u 



1.5 



2.0 



Fig. 8. Contributions to the mean-square elevation, mean-square slope and form drag by 

 waves of different wave age, c/m. 



c = phase velocity u = wind speed 



(1955). His analysis is based on a model first considered by H. Jeffreys in which 

 the air flow over a wave separates near the crest with the formation of a lee eddy. 

 As a result the main air current, instead of flowing steadily down into the troughs 

 and over the crests, merely slides over each crest and impinges on the next 

 wave at some point intermediate between the trough and the crest. By analogy 

 with the thrust of a current against a plane lamina inclined to the direction 

 of flow, the reaction^ is assumed to be related to wind speed and water slope by 



p = spu^ dhjdx, 



where s, the "sheltering coefficient" of Jeffreys, is of the order of 0.05 to judge 

 from wind-tunnel experiments on solid corrugated surfaces. Munk's analysis 

 brings out clearly the importance of the high frequency components of the wave 

 motion which contribute largely to the mean-square slope and even more largely 

 to the form drag. Fig. 8 gives the contributions to mean-square elevation of the 



