Generation, Growth and Propagation of Waves 



99 



group velocity c g = \c and grow by wind. One of the main results of Darby- 

 shire's is that the wave spectrum is fully arisen already after a fetch of 200- 

 300 nm, with the longest wave period of the spectrum being, in sec, \v g , 

 where v g means the maximum gradient wind speed. The period of the highest 

 waves is T max = \v g and the steepness of the higher waves <5 max ~l/j/ v 

 All results are summarized in an amplitude spectrum containing the stages 

 of generation and the fully arisen waves 



[h(o)Y = —-r- exp 



xp{- 



20 





4 6(1 + 1 25 x 10- 4 F)(l-e-° 23 ^) 



(IV. 43) 



In this equation v g is the gradient wind speed and F the fetch in nm. For 

 great values of F the equation gives the simple energy spectrum of the fully 

 arisen sea, the wind speed v at the sea surface is 0-667 v g . The constant C 

 was found to be 22 cm 2 sec -2 . In general, the theory of Darbyshire seems 

 to be verified by the observations. In some cases there will be differences 

 in the results gained from Neumann's and Darbyshire's theories. The reason 

 for these differences will probably be the fact that each theory assumes an 

 entirely different mechanism of wave generation by wind. As mentioned 

 above, in Darbyshire's theory each component of the wave spectrum grows 

 independently of the other components present; whereas Neumann assumes 

 that after the beginning of wind action short-period steep waves develop 

 from the initial waves which soon break up, that is, become unstable. They 

 are run under by the longer waves and in part give their kinetic and potential 

 energy to the longer waves. After this stage and with sufficiently long duration 

 and fetch long waves develop, which progress with the wind speed. After 

 Neumann, the longer waves will appear and grow only after the shorter 

 ones are fully arisen. These discrepancies between the two conceptions will 

 be settled only by further research. 



7. Swell, Observations and Theory 



(a) Observations on the Propagation of Swell 



A strong wave motion, generated by a storm of long duration, travels 

 from the generating area with a great velocity. Alteration of the wave profile 

 transforms the wind-sea into a swell. As soon as the wind decreases in force, 

 the waves change their shape quite characteristically. The irregularities in 

 form in the wave profile smooth out, the shorter wave disturbances vanish 

 first and only the waves of greater height and length remain. This is the swell, 

 where the waves are not any longer subjected to action of the wind (U < c). 

 In a system of waves of different lengths, the waves of greater wave length 

 move with a greater velocity than the shorter ones. One can observe how 

 these smaller waves apparently climb backwards to the crests of the large 

 waves. Finally, only the large waves remain and the wave trains acquire shapes 



7* 



