h7 



between the different authors and methods . The strong increase of the 

 friction coefficient with decreasing wind speed, which characterizes 

 Neumann's result, is now generally assumed to be biased by data of insuf- 

 ficent accuracy, however. Then the problem remains whether increase with 

 growing speed or constancy is correct. During the last years, a certain 

 tendency could be observed to diminish the slope and so to approach the 

 contsmcy proposed by Brocks . 



These values refer (or should refer) to adiabatic conditions. The 

 question arises whether there is an influence of thermal stratification 

 on the wind stress . Visual observations are in favor of such an effect. 

 The ocean waves appear to be higher and steeper, the production of foam 

 and spray is more intense with cold air over warm water than vice versa. ;x-~_X, 

 Some relevant evidence was reported by Darbyshire (1955) who obtained ______ — 



stress coefficients that, for a given wind speed, were twice as "^^eat in T)avl 

 unstable cases than in stable ones . More convincing measurements were 

 reported by Garstang (1965). This stability effect can also be calculated 

 with the help of the theories of Monin and Obukhov and of Ellison. We 

 then may express the drag coefficient Cg^ at the level z = a by the relation 



k2 



^a = -l-r^ (3) 



{in-^ + a Ri}2 



o 



where k is von Karman constant, a = constant ( = 3.7), Ri = Richardson num- 

 ber. 

 This relationship remains to be checked by suitable measurements . 



Regarding th§ possible influence of the fetch on the wind stress, 

 there is no uniform result up to now. A few scientists found favorable 

 evidence, whereas the majority could not verify such an effect. There is 

 some reason to believe that the wind set-up measurements which indicated 

 such an influence of fetch were biased by coastal wave effects. _- , 



The results reported so far on the variation of the drag coefficient 

 with wind speed are empirical. There is only one theoretical approach, 

 namely Munk's (1955) interpretation of Van Dom's (1953) wind set-up data 

 which is based on Jeffreys' "sheltering hypothesis." Herewith the existence 

 of sheltered regions with eddies to the leeward of the wave crests is as- 

 sumed, which implies a phase lag between the wave profile and the pressure 

 distribution. Under the assumption that the Neumann spectrum is valid for 

 the wave energy density Munk (1955) computed the form drag caused by a 

 fully developed sea and found that the young high-frequency waves contribute 

 much more to wave sloi)e and form drag than the low-frequency waves do, which 

 mainly determine the elevation statistics. Consequently, these low- frequency 

 waves seem to be of little significance for the aerodynamics of the sea 

 surface, a conclusion which confirms the findings of other scientists who 

 were led to believe that the form drag is principally caused by the small, 

 slowly moving ripples and wavelets. This would also explain that the drag 

 is much less affected by limitations in fetch and duration than the wave 



