96 



Generation, Growth and Propagation of Waves 



-^max*-' 



A = 



aU 

 D 



1 + 



(IV.41) 



a and fi are constants to be determined empirically. A max is the wave 

 amplitude of matured waves, that is after a great fetch and lengthy wind 

 action. Thorade reasons rightly that this equation in the form 



A -^ max C/(l-e-^)(l-^ m '«)) 



(IV.42) 



would be more justified. Boergen has tried to test his formula to observations 

 made by Paris; Krummel (1911, Vol. II, p. 66), however, is of the opinion 

 that the observations are not suited for this purpose. 



The relationship between wave height and wind velocity as given by 

 Sverdrup and Munk is H = (2n/g) U 2 dft 2 , i. e. it depends not only on the 

 wind velocity, but also on the fetch and the duration of the wind, since d 

 and ft are functions of these variables. The maximum wave height is found 

 by setting in this relation /3 = @ M , and for d = d m , and therefore depends 

 upon the wind velocity only. H m = (0-26/ g) U 2 , a relation which is in good 

 agreement with a formula suggested by Rossby and Montgomery (1935, 

 p. 1011) from quite different considerations. 



Linear relations between wind velocity and general wave height (not 

 maximal) have been derived and were already discussed previously. It was 

 pointed out that both the length of the fetch and the duration of the wind 

 action exert an influence on the wave height and that the simple linear 

 relations of Cornish and Zimmermann are only rough approximations of 

 the reality. 



Table 12. Average wave characteristics in tradewind regions 



Locality 



Observations U 



made by (cm/sec) 



c 

 (cm/sec) 



(clU) 



d 

 (HI A) 



The same applies for the relation of wave velocity and wind velocity. 

 Here also partly linear and partly more complicated formulae were selected. 

 According to Zimmermann, c = 2-35£/' 2/3 and hence c exceeds U for minor 

 velocities above 1331 cm/sec but, according to Cornish, c = 0SU, and ac- 



