long as there is a positive amount of energy A - D left, the 

 waves will grow further even when reaching the state 6(1) , But 

 they cannot exceed the maximum steepness given by (63), and there- 

 fore they will grow by increasing their wave length. Later on, we 

 shall see that the further development of waves beyond the state 

 p(l), 6(1) , manifests itself in an increase of wave length, where- 

 as the height remains nearly the same. Thus, the longer waves 

 (p* -waves) rather soon increase in length, and attain propagation 

 velocities that exceed the wind velocity. With this newly generated 

 waviness the normal pressure components of wind force are out of 

 phase by the phase difference u. The further development of the 

 waves therefore will be increasingly delayed, the more their wave 

 lengths increase and the faster these waves travel. Finally the state 

 A = D will be reached approximately when the longer waves travel 

 with a phase velocity of <3' * = 1.37v, The work done by these nor- 

 mal pressure forces, which act with a negative sign at the long 

 B *-waves, together with the dissipation, balance the work done by 

 tangential stresses on complex wave motion in this state. 



It is to be expected that with increasing height of the p(l)- 

 waves, interference phenomena appear between these waves and the 

 3 -waves, which depend upon the wind velocity and upon the state of 

 development of the p(l)-waves. As a consequence, from time to time, 

 particularly high waves with considerable steepness will occur, 

 forming higher and more spacious "breakers" :han in the preceding 

 stages of wave development. These increasing breakers imply an 

 eddying of more extended and deeper water masses of the surface 

 layer, and therefore will be succeeded by an increase of the 



91 



