106 Generation, Growth and Propagation of Waves 



drup and Munk were but sparse and unreliable, but in the main they confirm 

 the theoretical results. The theory clearly shows that, while the swell waves 

 travel from the storm area, the period, wave length and velocity of propagation 

 increase and the wave height decreases. Later on, Sverdrup (1947a) com- 

 pleted his theory. Assuming that swell generally has the same characteristics 

 as the waves in the generating area, it is shown that the air resistance which 

 the swell encounters leads to a selective dissipation. The energy associated 

 with the shorter period waves is dissipated more rapidly than that of longer 

 period waves, and consequently the energy maximum shifts toward longer 

 periods, that is, the period of the significant waves increases. The effect is 

 modified by following or opposing winds. Numerical examples are in satis- 

 factory agreement with results from the formerly semi-empirical graphs. 



This result was fully confirmed by Darbyshire (1952). Using his wave 

 spectrum and introducing a coefficient of friction proportional to the wave 

 steepness (see p. 87), he explained the transformation of swell waves by 

 the different extinction of the spectral components progressing independently 

 of one another. This extinction is due to the air resistance. Groen and 

 Dorrestein (1950), and later Bowden (1950), give a completely different 

 explanation for the energy loss of swell waves. The former regard the 

 turbulence friction as the main cause of the loss of energy, and take the 

 turbulence coefficients to be proportional to the 4/3 power of the wave length 

 (after von Weizsacker, vol. I no. 1), while Bowden takes them to be pro- 

 portional to the velocity and amplitude of the waves. Both assumptions 

 are capable of explaining completely the transformation of swell waves. It was 

 not possible to decide whether this transformation is due more to air resistance 

 or to turbulence friction. This fact will not be changed by the application 

 of a refined method by Groen (1954). It was also possible to prove that 

 the tidal currents exercise an influence on the swell waves (Deacon, 1949; 

 Darbyshire, 1952). 



Hitherto, only the influence of air resistance and of turbulent friction 

 has been discussed. We shall now deal with the influence of dispersion on 

 the transformation of swell waves. Since long waves progress faster than 

 shorter waves, the wave spectrum of a wave pack will gradually change. 

 The apparent wave period of the swell must increase with time with increasing 

 fetch whereas at a fixed point the period decreases. At the same time the 

 dispersion requires a decrease in wave energy. This leads to a reduction of 

 the heights of significant waves. The first study of the transformation of 

 swell waves on the basis of the effect of dispersion was made by Breit- 

 schneider (1952), who started out from the wave values of significant waves. 

 He wants to determine, on the one hand, the dependence of the wave heights 

 of a swell H D upon the fetch F, upon the height of the wind-sea at the end 

 of the wind-field and upon the decay distance, and, on the other hand, the 

 dependence of the period T D upon the fetch, upon the period of the wind- 



