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 meteoro- 

 logical conditions, the air speed increases from near to 60 - 90 percent 

 of the free air value within 66 feet (20 meters) 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 air stream, 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 wind speed 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 wind stream, the temperature profile in the air, and by the rough- 

 ness of the sea surface. 



Shorter waves grow most rapidly. Those waves which propagate obliquely 

 to the wind are favored, for they are better matched to the component of 

 the wind velocity in the direction of wave propagation than those moving 

 parallel to the wind. Thus, the first wave pattern to appear for short 

 fetches and durations consists of two wave trains forming a rhombic 

 pattern with one diagonal along the direction of the mean wind. 



There is a limit to the steepness to which a wave can grow without 

 breaking. Shorter waves reach their limiting growth rather quickly; 

 longer waves, which grow more slowly but can obtain greater heights, 

 then become more prominent. Thus, the apparent direction of propagation 

 of the two wave trains tends to coalesce with increasing fetch and duration. 

 The length of the region in which a rhombic pattern is apparent may extend 

 from a few meters to a few kilometers depending on the width of the basin, 

 the wind speed, and previously existing waves. 



Wave growth is significantly affected by any preexisting waves. The 

 empirical data analyzed by Inoue (1966, 1967) indicated that the magnitude 

 of the effect of seas already present is about eight times the value given 

 in the original Miles (1957) theory. Neglecting this effect in early wave 

 prediction theories has led to large errors in computing the duration 

 required for a fully arisen sea. There are many situations in which the 

 largest waves and the waves growing most rapidly are not being propagated 

 in the wind direction. 



3-16 



