Generation, Growth and Propagation of Waves 81 



Apart from these first effects of the wind, one can observe a continuous 

 action of the wind in well-developed wave trains. When an air current blows 

 over the wave crests, phenomena appear which are similar to those when 

 wind flows over a fixed obstacle. Only when the flow of air is small compared 

 to the wave velocity, the streamlines of the air motion join the wave profile. 

 The pressure exerted on the windward side of the wave will be greater than 

 that on the lee side. Air pockets will develop in the wave troughs and on 

 the lee side. When the wind becomes much stronger, lee eddies are formed, 

 which, with large wave heights, become characteristic for the wind dis- 

 tribution above the water. Weickmann has experimented in 1930, during 

 the "Meteor" Expedition in the waters of Iceland-Greenland, with small 

 balloons floating just above the water, and the results showed clearly the 

 streamlines of the air above the wave profile, as described by Defant 

 (1929, p. 165). Despite the difficulties of this experiment, the air movements 

 on a small scale were similar to those occurring on a large scale above dunes 

 and which are used by gliders. Apparently there must be an excess pressure 

 on the windward slopes of the waves and a pressure deficit at the leeside, 

 which try to increase the wave height for such a time until the loss of energy 

 by friction is compensated by the work done by the pressure forces. 



Motzfeld (1937, p. 193) and Stanton (1932) have measured in a wind 

 tunnel the pressure distribution on models of water waves in order to test 

 the distribution of pressure caused by wind on a wavy surface. These models 

 consisted of (1) a train of three sine waves with a wave length I = 300 mm 

 and a height 2^4 = 15 and 30 mm respectively; (2) a train of six waves with 

 a trochoid profile with I = 150 mm and 2 A = 14-5 mm, and finally (3) a train 

 of six waves with sharp crests (crest angle 120°) with X = 150 mm and 

 2A = 20 mm. 



Figures 40 and 41 show for the second and the third case the streamlines 

 of the air motion over the wave-shaped surface and the total pressure on 

 the streamlines. Where the crests are rounded, the streamlines hug to the 

 wave profile, being more crowded over the crests than over the wave troughs. 

 The wave profile with sharp crests shows the strong air current upward at 

 the windward slope of the wave, whereas on the leeside an eddy reaches 

 from the crest to the bottom of the trough. The wave shape of the streamlines 

 has shifted a distance of approximately one-fourth of the wave length in 

 the direction of the wind with reference to the profile of the wave. Consider- 

 ing the total pressure on the streamlines, it shows that behind the wave crests 

 at the lower stramlines there is a loss of energy which then reaches the inside 

 of the current more downstream. With decreasing static pressure the energy 

 on the lower streamlines increases again. This energy increase has its origin 

 inside the current, because there is here a continuous decrease of the total 

 pressure on the streamlines. During these tests, the air resistance (pressure 

 resistance) of the waves W d was measured and it was found according to 



