consider each narrow band of directions and frequencies separately. A change 

 in wave energy depends on the advection of energy into and out of a region; 

 transformation of the wind's kinetic energy into the energy of water waves; 

 dissipation of wave energy into turbulence by friction, viscosity, and 

 breaking; and transformation of wave energy at one frequency into wave energy 

 at other frequencies. 



Phillips (1957) showed that the turbulence associated with the flow of 

 wind near the water would create traveling pressure pulses. These pulses 

 generate waves traveling at a speed appropriate to the dimensions of the 

 pressure pulse. Wave growth by this process is most rapid when the waves are 

 short and when their speed is identical with the component of the wind 

 velocity in the direction of wave travel. The empirical data analyzed by 

 Inoue (1966, 1967) indicates that the effect of turbulent pressure pulses is 

 real, but it is only about one-twentieth as large as the original theory 

 indicated. 



Miles (1957) showed that the waves on the sea surface must be matched by 

 waves on the bottom surface of the atmosphere. The speed of air and water 

 must be equal at the water surface. Under most meteorological conditions, the 

 airspeed increases from near to 60-90 percent of the free air value within 

 20 meters (66 feet) of the water surface. Within a shear zone of this type, 

 energy is extracted from the mean flow of the wind and transferred to the 

 waves. The magnitude of this transfer at any frequency is proportional to the 

 wave energy already present at that frequency. Growth is normally most rapid 

 at high frequencies. The energy transfer is also a complex function of the 

 wind profile, the turbulence of the airstream, and the vector difference 

 between wind and wave velocities. 



The theories of Miles and Phillips predict that waves grow most rapidly 

 when the component of the windspeed in the direction of wave propagation is 

 equal to the speed of wave propagation. 



The wave generation process discussed by Phillips is very sensitive to the 

 structure of the turbulence. This is affected significantly by any existing 

 waves and the temperature gradient in the air near the water surface. The 

 turbulence structure in an offshore wind is also affected by land surface 

 roughness near the shore. 



The wave generation process discussed by Miles is very sensitive to the 



vertical profile of the wind. This is determined largely by turbulence in the 



windstream, the temperature profile in the air, and by the roughness of the 

 sea surface. 



Measurements of the rate of wave growth due to Miles' mechanism indicated 

 that only about 20 percent of the growth could be accounted for by direct wind 

 input to waves. Hasselmann (1962) suggested a mechanism by which the wave 

 field could shift energy within itself. He proposed that resonant inter- 

 actions among waves of different frequencies and directions could lead to an 

 energy transfer from the region of the spectrum just above the peak frequency 

 to both lower and higher frequencies. The wave energy transferred to low fre- 

 quencies is seen as wave growth, and the energy input is generally larger than 

 the energy contributed to those frequencies directly by the wind. Measure- 

 ments of the wave-wave interactions are in reasonable agreement with 

 theoretical values (Hasselmann et al., 1973). 



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