computation of other wave characteristics such as total wave energy, 

 significant wave height, and period of maximum energy. The equilibrium state 

 between wind and waves rarely occurs in the ocean and may never occur for 

 higher windspeeds. 



A more general model may be constructed by assuming that the sea is calm 

 when the wind begins to blow. Integration of the equations governing wave 

 growth then permits the consideration of changes in the shape of the spectrum 

 with increasing fetch and duration. If enough wave and wind records are 

 available, empirical data may be analyzed to provide similar information. 

 Pierson, Neumann, and James (1955) introduced this type of wave prediction 

 scheme based almost entirely on empirical data. Inoue (1966, 1967) repeated 

 this exercise in a manner more consistent with the Miles-Phillips theory, 

 using a differential equation for wave growth. Inoue was a member of 

 Pierson' s group when this work, was carried out, and his prediction scheme may 

 be regarded as a replacement for the earlier Pier son-Neuman- James (PNJ) wave 

 prediction model. The topic has been extended by Silvester and 

 Vongvisessomjai (1971) and others. 



These simplified wave prediction schemes are based on the implicit 

 assumption that the waves being considered are due entirely to a wind blowing 

 at a constant speed and direction and for a given duration. 



In principle it would be possible to consider some effects of variable 

 wind velocity by tracing each wave train. Once waves leave a generating area 

 and become swell, the wave energy is then propagated according to the group 

 velocity. The total energy at a point and the square of the significant wave 

 height could be obtained by adding contributions from individual wave 

 trains. Without a computer, this procedure is too laborious and theoretically 

 inaccurate. 



A more practical procedure is to relax the restrictions implied by 

 derivation of these schemes. Thus wind direction may be considered constant 

 if it varies from the mean by less than some finite value, say 30°. Windspeed 

 may be considered constant if it varies from the mean by less than ± 5 knots 

 (±2.5 meters per second) or V2 barb on the weather map. (The uncertainty 

 inherent in this assumption is not much greater than the uncertainty inherent 

 in wind reports from ships.) In this procedure, average values are used and 

 are assumed constant over the fetch area and for a particular duration. 



Hasselmann et al. (1973) have demonstrated that the spectrum of an 

 actively growing wind sea can be reasonably well represented by one family of 

 spectral shapes. The shape of the wind sea spectrum is given by 



E(f) = " g\ ^ e^ Y^ (3-32) 



(2ti)^ f^ 

 where 



a = - 



4 \f 



3-43 



