Generation, Growth and Propagation of Waves 



107 



sea T F and upon the decay distance The results were given in the form of 

 dimensionless parameters which can be checked against the observations. 

 The conclusions drawn confirm what had been expected from qualitative 

 considerations: For a given wave period T F and a decay distance D the 

 increase of the period and the decrease of the height of a swell are the greater 

 the shorter is the fetch. These conclusions are more comprehensive than 

 those of Sverdrup and Munk, who investigated only the influence of 

 T F and D. Besides, the graphs show that the theoretical results fit the ob- 

 servations only in part, which is not surprising if one regards the simultaneous 

 influence of so many factors. 



Pierson, Neumann and James (1952, 1953) have treated this problem 

 in an entirely different way. Based on the energy spectrum of short-crested 

 wind generated waves, they try to solve the influence of dispersion and of 

 lateral angular spreading. For the case of a line-shaped source of wave 

 generation, having a width B, Fig. 46 b gives the quantities used. T x designates 



Wmdfieid 



Fig. 46b. Registration of a swell filter in a linear area of wave origin. P point of observa- 

 tion of swell. 



the period of those waves which have just passed the point of observation P 

 at the time t D , T 2 the period of the waves which just reach P at the time t D . 

 d x and d 2 are the angles of propagation of those waves which just pass "above" 

 and "below" P. Using the group velocity for each period, T x can be computed 

 from the duration of the emission of such waves from the source, 6 X and 2 

 from the width B. The wave periods and directions existing in P at the time 

 t D are between T x and T 2 and X and 6 2 , respectively. The formerly broad 

 energy spectrum is contracted into a narrow spectral band of the swell in P 

 at the time t D . The entire process is similar to the effect of a filter. The period 

 range of the swell can be determined by applying this method to the energy 



