complicated interference patterns produce a higher and longer sea 

 than that which would be the normal state with respect to the wind 

 conditions in the middle and southern parts of the fetch. Perhaps 

 it may give the impression that the (local) waves have been de- 

 veloped to larger size at the utmost end of the fetch as a result of 

 increasing. On the growth of the sea under the action of wind, 

 see Chapter II. 



In the following, an attempt is made to explain some strik- 

 ing features of complex wave motion by principles of interference, 

 considering at first steady-state conditions at the end of a fetch 

 over which a steady wind is blowing and assiunlng infinitely wide 

 waves. 



Let A,, A 2, A ^ be the wave lengths of the three character- 

 istic waves mentioned in Chapter II, CTj^, (T2i C5% their velocities 

 of propagation, and a,, a2j a^ the amplitudes of these waves. As- 

 suming sine wave profiles with first approximation, we have 



CTnt - X (Tot - X <T-.t - X 



y = anSinairC — *—. ) + a^sinairC r ) + aoSin2Tr( — ^ ). 



^ Al '^ A2 ^ A3 



This equation contains both of the variables, the time t and the 

 fetch X. We chose x = and t = so that at this place and time 

 all three waves have the same phase and y = 0. With regard to an 

 observer at sea, who is measuring the waves at a fixed locality as 

 a function of time, we consider the variations of the resulting 

 wave motion at a given place x = const. 



Let us take as an example a wind velocity of 16 m/sec. There 

 we have to expect the following wave lengths, periods, wave velo- 

 cities and heights, supposing the wave motion is fully developed 



27 



