Generation, Growth and Propagation of Waves 105 



After the waves have left the generating area, they travel through a region 

 of calm, where the wind velocity is small compared to the wave velocity. 

 The waves receive no energy by normal pressures but, on the contrary, air 

 resistance causes a loss of energy. According to the equation (IV. 256), this 

 loss of energy per unit area equals 



R N = -|.W= - S ff-H*c-\ (IV. 43) 



the transfer of energy due to tangential stress of the wind can be neglected 

 (R T = 0). 



A KH F ,T F ,t F \ 



,P(H ,T D .t D ) 



Fig. 46a. Registration of swell. 



The swell composed of different wave systems can now be explained by 

 means of the significant waves. The theory of Sverdrup and Munk for the 

 decay of waves is closely related to the theory of the growth of waves and 

 thus explains for the first time, on a general physical basis, this important 

 phenomenon of ocean waves. The differential equation for the change of 

 wave velocity with propagation of the wave is simplified and can be solved 

 without introducing other hypotheses and constants. The most important 

 results is that the period of the waves increases with increasing distance 

 from the end of the fetch, whereas the wave height decreases simultaneously. 

 The distance is called the distance of decay D. The theory shows that the 

 ratio between the period at the end of the decay distance and the period at 

 the end of the fetch T D :T F , and the ratio between the corresponding wave 

 heights H D :H F , as well as the ratio between the travel time and the period 

 at the end of the fetch t D :T F can be represented as functions of the same 

 non-dimensional parameter D/gT F . The observations then available to Sver- 



