TM No. 377 



Discounting the group of primed sevens in the °"u. plot (figure V-27), the 

 average slope of the envelope of variances for each velocity component is very 

 similar. Further, if one considers the slopes of those variances associated with 

 comparable wind speeds (i.e., for speeds of 5, 6, 7 and 8 m sec"l in each plot), 

 the abscissa and ordinate intercepts are quite similar in each case - roughly 

 11-12 meters and U00-800 cm 2 sec~2 ? respectively. 



It is of interest to compare the measured variances with the theoretical 

 values obtained from the vertical velocity function of a classical trochoidal wave 

 (see, for example, Proudman, 1953). This function is given as a third order approxi- 

 mation of a trochoidal wave: 



u+toi,*). - f^jj-i i^f] z^m<H; 



(V-I2) 



where iOr ( *»; % */ is the deviation of the theoretical vertical velocity component 

 about a zero mean, A is the amplitude of the wave, T is the period, and L is the 

 wave length. The coordinate Xo is a constant, indicating that the measurements 

 are being made at a fixed horizontal position but at various depths Z. 



A trochoidal wave is preferable to the traditional sinusoidal type wave, 

 since the former is perhaps more representative of actual ocean waves. Also, the 

 trochoidal system is derived by assuming a realistic ratio of wave amplitude to 

 wave length, whereas the sinusoidal wave is derived by assuming a vani shingly 

 small amplitude. 



The theoretical variance function is defined as: 



2- _ 



u>; = 



<r , -=.- 



/% 



SMT277 



\ 



(M9 



(V-13) 



where 



ft 



.^(i-ioewvp 



(V-lU) 



119 



