88 Generation, Growth and Propagation of Waves 



pressure system (low pressure in front and high pressure in back) moves 

 over the water surface with the mean wind speed, the wind pressure being 

 perpendicular to the disturbed surface. He was able to show that such 

 a pressure disturbance generates a V-shaped "wake" similar to that generated 

 by ships. After the gust has passed, the waves progress as a group of free 

 gravity waves. The question as to the occurrence of the observed wave heights 

 remained unsolved, as the pressure differences associated with the passage 

 of the gust are not sufficient to form so high waves. 



The first theory of wave growth by wind was given by Motzfeld 

 (1937), based on his model experiments in wind channels. The main relation 

 starts out from the principle that, according to the conservation of energy, 

 the time variation of the total wave energy (equation IV. 20) must be equal 

 to the difference between the energy supplied and the energy dissipated by 

 internal friction (equation IV. 19). For the energy supply Motzfeld takes 

 only the work of normal pressure according to equation (IV. 25), where he 

 substitutes A 2 k 2 by A n k" according to his experiments (see p. 82). The influence 

 of the wind stress on the sea surface is ignored. It is found that to each 

 wind speed and to each amplitude there belongs a corresponding stationary 

 wave length, and to each wind speed a maximum wave length, which occurs 

 with a wind speed of U = 3c. In this theory it is not possible to make the 

 computed wave values agree with the observed values, even if the surface 

 tension is considered in addition. 



A more comprehensive theory of the growing of waves was developed 

 by Sverdrup and Munk (1946, 1951). It is based on the formerly shown 

 complexity of the actual wind sea and on the dependence of the wind sea 

 upon the effective fetch on the one hand, and upon the wind duration on the 

 other. If the wind duration were unlimited, the wind sea would depend solely 

 upon the wind speed and the effective fetch. With a sufficiently long fetch 

 a stationary final state, corresponding to the given wind speed, would be 

 reached ("fully arisen sea"), and everywhere the energy supplied by the wind 

 would equal the energy dissipation. In this case all wave values would be 

 independent of the time at all places, even though simultaneous local dif- 

 ferences may exist. This ideal case may occur in small sea areas if the wind 

 duration is long enough. If, however, the sea region affected by a homogeneous 

 wind field is unlimited, the structure of the wind sea is determined by the 

 wind speed and wind duration. Also in this instance the stationary state 

 of a "fully arisen sea" is reached after a certain wind duration. There are 

 no local differences in this ideal case, but uniform time variations at all places. 

 This case will occur on the ocean most easily with a short wind duration 

 (Roll 1957). The theory of Sverdrup and Munk takes full account of the 

 differences in time and space of the wind sea, in other words, here the ocean 

 waves are not "conservative" and do not maintain their identity during 

 propagation. 



