of considerable practical importance, but that they could not account 

 for the generation of the highest and longest waves observed in nature. 

 For this purpose it is necessary to consider the transfer of energy and 

 jnomentum from short waves to longer waves by nonlinear processes. The 

 earliest technical discussions of the transformation of energy between 

 wave components with different frequencies appear to have been Phillips 

 (1960), Hasselmann (1962), and Longuet-Higgins (1962). The theory has 

 been extended by these and other authors and is reviewed in the nomo- 

 graphs discussed previously. Hasselmann, et al. (1973) discussed the 

 interaction of all prominent mechanisms involved in the generation of 

 waves and provided the results of one of the most extensive programs 

 for recording wave generation ever conducted in the field. Hasselmann, 

 et al. (1973) found that the form of representation used in Figure 4 

 showed much less scatter when only modem high-quality data are used. 

 Hasselmann, et al. (1976) suggested that the dimensionless parameters rep- 

 resentation should be adequate for applications in which the detailed 

 structure of the wave spectrum is not important. A few exceptional 

 situations which may require more consideration are identified in this 

 s tudy . 



2. Boundary Layer Theory . 



When fluid flows parallel to a plane rigid boundary the fluid mol- 

 ecules in contact with the boundary are motionless. Most of the velocity 

 shear between the boundary and the free fluid is confined to a thin layer 

 of fluid called the boundary layer. Flow within this region is domina- 

 ted by the shear at the fluid boundary and the diffusion of momentum from 

 the interior of the fluid toward the boundary. The laws which approximately 

 describe flow within this region of boundary shear are known as boundary 

 layer theory. Boundary layer theory must be considered to explain the 

 variability of Cj (Fig. 3) and to establish relations between the wind 

 shear on water in a laboratory facility and wind shear on water at pro- 

 totype scale. 



In this section the boundary is considered to be a horizontal plane. 

 The fluid is considered to be homogeneous. The mean flow, averaged over 

 some finite time, is a horizontal current, u(z) , in the x-direction. 

 Deviations between the instantaneous horizontal current and the mean value 

 are denoted by u' ; the instantaneous vertical current is denoted by 

 w'. Within this system, the fluid stress in a vertical plane is described 

 by: 



8u 



T = P[v H - (u'w-)] , (4) 



where p is the density, and v the kinemat ic molecular viscosity 

 coefficient for the fluid. The term (u'w') represents the contribution 

 of turbulence to the effective viscosity. Very near the boundary, w' 

 must vanish and the entire stress must be expressed by: 



T = pv 3u/8z . (5) 



22 



