TM Nc. 377 



V.UJ =. 





r T 1 



(v-38) 



This integration is represented graphically in figure V-U3A (u pper diagram). A.s 

 shown by the shaded area beneath the time variable curve of "u 'w', the value of 

 u'w' is zero when averaged over an integral number of wave periods or for a long 

 record. 



In the case of intermediate or shallow water waves 3 the orbits are elliptical, 

 with the semi -minor and semi -major axes parallel to the Z and X axes, respectively. 

 However, both the elliptical and the circular velocity functions have sere co- 

 variances. Thus, the classical progressive wave, according to equation (V-30), 

 has associated with it a zero Reynolds stress. 



Turning now to consider a slightly different model, suppose that orthogonal 

 wave motion components, measured at a fixed point, can be described by: 



1C =■ Au, CQS<T--t > 



(v-39) 



and 



U/ s Ato &>AJ (<T6-h A 4>) 



(v-to) 



Here ^(^ is a small phase shift between the orthogonal velocity components. 

 The new covariance is given by: 



14' 5 £±h> 





- T >2. 



Using trigonometric identities, this becomes: 



(V-Ui) 



T) « AuA<4 



r r ti 



u!uj 



IT 



jj5^(2(T-hA4>) -hi^A^JcIt , 



-T* 



(V-k2) 



1U2 



