Generation, Growth and Propagation of Waves 87 



to the initial generation of waves and obtained for the minimum velocity 

 a value of about 70 cm/sec. A similar result was arrived at by Neumann 

 (1949). At first he tried to get a quantitative value of the frictional coefficients 

 c d for actual waves. By means of corresponding comparison values he de- 

 termined these coefficients as a function of wind speed and found a simple 

 proportionality between c d and d (the siope of the wave), contrary to Jeffreys 

 and Motzfeld (see p. 84). The balance equation, which states that the energy 

 supplied by the wind must at least be equal to the energy dissipated by 

 friction if the wave is to be generated or maintained, leads in the case of 

 deep water to a lower limit of wind speed for the generation of initial waves 



t/ m in = 69-6 cm/sec. (IV. 33) 



This value agrees very well with the value given by Wiist. Neumann finds 

 for the length of the initial waves 



/ 



n 

 9g 



9g J g . 



(IV. 34) 



The root becomes zero for U m = 69-5 cm/sec and T = 73 cm 3 /sec~", that 

 is, the first wave has a length of 1 -72 cm and a minimum velocity of 

 c miQ = 23 T 5 cm/sec. However, these are the values for the smallest capillary 

 waves. This result is due to the fact that the energy transmitted to the waves 

 by the wind attains a maximum when U is three times the wave velocity. 

 For the generation of the slowest waves with c min = 23 T 5 cm/sec the in- 

 fluence of a wind U min = 3c min = 69-5 cm/sec is most favourable. New de- 

 terminations of the minimum wind speed and of the length of the initial 

 waves in wind-wave channel experiments gave mostly U min = 200-300 cm/sec 

 (Weinblum, 1938; W. Wust, 1939; Schooley, 1955), that means much too 

 high values. Observations and measurements by Roll (1951) at undisturbed 

 water surfaces show that in closed water basins the first distinctly noticeable 

 waves will not appear in the immediate vicinity of the windward edge but 

 only at a certain leeward distance from it. This distance increases rapidly 

 with decreasing wind speed, and for U = 100 cm/sec it amounts to about 

 40 m. Thus, there are considerable differences between the wave generation 

 in nature and in experiments. It is quite obvious that in the relatively short- 

 wave channels, as used in laboratories, much higher wind speeds are required 

 than in nature to generate the first waves. 



4. Theory of the Growing of Significant Waves by Wind 



The former theories of wave generation supposed that initially there must 

 be small disturbances on the sea surface which may then grow by the wind. 

 Eckart (1953) has studied the cause of such primary disturbances. First, 

 he considered the effect of a single gust on the water surface. The disturbed 



