22 



Theory of Short and Long Waves 



The mean value for a wave length is 



vE 



log Ac 2 = \Ec 



(11.146) 



This equation can therefore be interpreted that either the entire energy is 

 propagated at half the wave velocity or half the energy at full wave velocity. 

 The latter interpretation appears to be the better one, because, according 

 to the above expression for P, rE = cP, which means that the potential 

 energy is transmitted with the wave velocity. To satisfy (II. 14), P = hE. It should 

 be observed that the potential energy is a periodical function, which advances 

 in phase with the deformation of the surface, whereas the kinetic energy 

 is evenly distributed along the entire wave and is independent of the position 

 or the velocity (Sverdrup and Munk, 1947) with which the surface de- 

 formation advances. See Fig. 1 1 . 



Fig. 11. Variation of the potential and kinetic energy along a wave length of a progressive 



wave over a great depth. 



2. Further Development of the Stokes Wave Theory 



The wave theory developed so far has as a condition that the wave height 

 must be small compared to the wave length. The profile of the wave was 

 a simple-harmonic. This condition is fulfilled at the beginning of the de- 

 velopment of a wave. But with the increase of the wave amplitude this 

 restriction should be abandoned. The determination of the wave-forms which 

 satisfy the conditions of uniform propagation without change of type, when 



