WIND CURRENTS AND WIND WAVES 145 



giving H = 0.44 PT, in good agreement with the results of Cornish as to 

 relation between wave height and wind. Kriimmel, on the other hand, 

 arrives at the conclusion that the maximum wave heights are greater 

 than those corresponding to a linear relationship, and Rossby has for 

 theoretical reasons suggested a formula of the type 



H = -W\ 

 9 



where G is a nondimensional constant. When G = 0.3, Rossby finds that 

 his formula fits the available data fairly well at high wind velocities, but 

 it may be stated nevertheless that the relation between wind velocity 

 and wave height is so complicated that no simple empirical formula has 

 so far been established. 



The same complication exists when the steepness of the waves is 

 expressed by means of the ratio between wave length and wave height, 

 L/H, which is inversely proportional to the steepness. Cornish's rela- 

 tions lead to the formula L/H = 0.85 PF, but this is evidently not valid 

 at wind velocities much below 10 m/sec, because the steepest possible 

 waves are characterized by a ratio L/H = 7. Zimmerman's values give 

 L/H = S.ITF^. These two results are in qualitative agreement, because 

 both indicate an increase of the ratio L/H with increasing wind velocity. 

 They are also in agreement with Jeffreys' explanation of the growth of 

 waves, according to which one must expect L/H to be greatest for the 

 longest waves. Schott, on the other hand, found that the ratio L/H 

 decreased with increasing wind velocity, and, in discussing a large number 

 of observations by Paris, he found the ratio to be constant. Observations 

 from lakes indicate that there the ratio varies between 10 and 12. 



A similar confusion exists regarding the relation between wave velocity 

 and wind velocity. Cornish found, as already stated, that c = O.SW, 

 but from Zimmerman's relation it follows that c = 2.36 TF^. According 

 to the latter equation the wave velocity is greater than that of the wind 

 up to a wind velocity of 13.2 m/sec, and smaller when the wind is above 

 that value, in disagreement with energy considerations, which lead to the 

 conclusion that the wave velocity must always be less than the wind 

 velocity. 



All these discrepancies indicate that wave height, wave profile, and 

 velocity of progress are not dependent upon the wind velocity at the time 

 of observation alone, but may also depend upon the length of time the 

 wind has blown, the state of the sea when the wind started blowing, and 

 the dimensions of the area over which the wind has blown. It can in 

 all events be stated that comprehensive observations are needed for 

 clearing up these questions. 



It was mentioned (p. 142) that the wave height depends upon the fetch 

 of the wind, and that for small bodies of water a simple empirical relation- 



