SECT. 5] WIND WAVES 669 



From a knowledge of E'{a) the "significant wave height" and "significant 

 wave period" used by engineers can be derived. For studies of ship motion, the 

 two-dimensional spectrum E'{a, 6) is required. 



3. Theories of Wave Generation by Wind 



Several mechanisms have been suggested by which the wind can generate 

 waves on water, but at the present time work is concentrated on two of these 

 which between them can probably account adequately for the generation of 

 waves at sea, and these will be discussed here. The reader is referred to a 

 review of the subject by Ursell (1956) for an account of the other possibilities. 



The two mechanisms are : 



(a) The deflexion of the wind as it blows over the wave-profile causing 

 dynamic pressure differences which can feed energy into the waves. 



(b) The turbulence in the wind causing a moving pattern of pressure fluctua- 

 tions which can generate waves without reaction of the weaves on the wind. 



If a simple long-crested wave train is travelling over a water surface with no 

 wind blowing, the pressure difference in the air between crest and trough can 

 be shown theoretically to be twice the static pressure difference. The simplest 

 way of looking at this is as follows. In the water, the dynamic pressure changes 

 just cancel the static ones, to give constant pressure at the surface (neglecting 

 the pressure differences in the air, which are small compared to those in the 

 water). The motion of the air particles follows a similar pattern to that of 

 the water j^articles, but "upside-down", so that the dynamic pressure differences 

 add to the static pressure differences. When the wind blows over the waves, a 

 further set of dynamic pressure differences is introduced. 



If the flow^ were laminar and friction-free, it is evident that all these pressure 

 differences would be in phase with the wave profile and therefore feed no 

 energy into the wave system : every place where a pressure is acting on a down- 

 ward moving surface is balanced by a corresponding area where the same 

 pressure acts on a surface moving upward. However, in the presence of viscosity 

 or turbulence, out-of-phase pressure differences are introduced which can put 

 energy into the waves. From the observed rate of growth of waves under a 

 wind, it is possible to estimate that the magnitude of the out-of-phase pressures 

 should be approximately -g^ of the amplitude of the in-phase pressures. This 

 means that the amplitude of the resultant pressures is very nearly that of the 

 in-phase component, but that the phase of the pattern is changed by about 2° 

 relative to the wave profile. The measurement of the amount of energy fed into 

 the waves therefore presents a severe instrumentation problem which has not 

 so far been solved, though such a measurement has been attempted (Longuet- 

 Higgins, Cartwright and Smith, in press). 



Jeffreys (1925) was the first to attempt to calculate this energy transfer. He 

 assumed an eddy on the lee side of the waves, so that by the theory of turbulent 

 flows, pressure differences proportional to {V-C)^ will be set up between 



