Generation, Growth and Propagation of Waves 

 Table 1 1 . Distribution of energy in a short wave train 



73 



in a wave train starting at a source and propagating in undisturbed water 

 is obtained through the elegant solution of the differential equation (IV.8), 

 as given by Sverdrup and Munk (1947). It is superfluous to go into these 

 mathematical developments here; an example computed for n = 900 will 

 show the most important results, and is present in Fig. 37. It gives the change 



100 



99 



-50 



200 



400 

 a\, wavelengths 



600 



800 



Fig. 37. Change of wave height with increasing distance from source region in a wave 

 train advancing through water originally at rest. Deep water waves (Sverdrup and Munk). 



of wave height with increasing distance from the source (indicated by m in 

 wave lengths) when it is assumed that the deep water waves produced are 

 uniform and are advancing through water originally at rest. The ratio of 

 the energy E' of a certain wave to the wave with maximum energy E drops 

 from 90 to 10% of the maximum value over a small wave range (in Fig. 37 

 from m = 485 to in = 435; centre wave m = 4505) in the vicinity of the 

 centre wave. This region of sharpest decrease in energy is at the same time 

 the region of sharpest decrease in wave height, as the latter is proportional 

 to the square root of energy. The region of sharpest decrease in wave height 

 travels with the group velocity C. The height of the waves in front of this 



