WIND CURRENTS AND WIND WAVES 143 



The energy of the waves is transmitted to them by the wind, and, 

 according to Jeffreys, the processes that lead to the generation of waves 

 are also of fundamental importance to their further development. When 

 the wind velocity increases, the pressure exerted on the windward side 

 of the wave will be greater than that on the lee side. Consequently, 

 the waves will increase in height and their energy will increase also. 

 The energy considerations do not lead to any limit of height to which the 

 waves can grow, but the wave theory itself, as developed by Michell 

 (see p. 137), shows that the height cannot exceed about one seventh 

 of the wave length. Thus, if the wind constantly imparts energy to the 

 waves, and if there is no increase in the wave length, the crests will merely 

 break and the sea will become covered by whitecaps. However, the 

 longer the wave the greater the height it can reach, and thus the greater 

 the amount of energy it can absorb from the wind. The wind is able to 

 produce waves of different length, but the longer will continue to grow 

 for a longer time. Jeffreys therefore concludes: ''When the waves have 

 traveled a long distance, with the wind blowing them all the time, the 

 longest waves will tend to predominate, simply because they can store 

 more energy.'^ 



However, there is also a limit to the length that waves can attain, 

 because the velocity of progress of the waves increases with increasing 

 wave length and because the wind cannot impart further energy to the 

 waves if they travel at a speed that is greater than the wind velocity. At 

 a given wind velocity the longest possible waves will therefore be those 

 that travel at a velocity somewhat below the wind velocity. According 

 to Cornish the speed of the fully developed waves, on an average, is 

 eight tenths of the speed of the wind, but it should be borne in mind that 

 the observed wind velocity depends upon the height at which the velocity 

 is measured. Information is still lacking as to the relation between the 

 velocity of the wind directly over the sea surface and the velocity of the 

 waves. 



It also follows that the greatest wave velocity cannot exceed the 

 velocity of the wind that has created the waves, assuming that a surface 

 wave continues at a constant speed after leaving a region of strong 

 winds. Theories developed by Poisson and Cauchy, however, lead to 

 the conclusion that the wave length — and therefore the velocity of prog- 

 ress and the period — of a surface wave increases in course of time. The 

 velocity of the swell reaching the coast, according to these theories, 

 should be greater than the velocity of the waves that were directly 

 created by the wind. Kriimmel quotes a single observation that may 

 support these conclusions, whereas Cornish emphasizes the fact that 

 no breakers have been observed whose velocity of progress in deep 

 water exceeded observed wind velocities. In the case of breakers with a 

 period of 20 sec, corresponding to a velocity of progress of about 30 m/sec, 



