TM No. 377 



inequality between the amplitude of fluctuations of the u and w components 

 (<j- 2 = 22.3 cm 2 sec" 2 , as opposed to 62.9 cm 2 sec"" for CT^ 2 )* The reason for 



this inequality is not clear, since one might expect that the variances of the 

 vertical and the horizontal velocity components would be approximately equal for 

 "deep water" waves, the motions of which suggest quasi-circular orbits (see 

 equations (II-9) and (II-10)). 



In examining the OMDUM velocity data from the first few observations from the 

 BBELS, it was found that the same disproportion between variances generally occurred, 

 A comparison of the variances of u and w for the various measurements is provided 

 by table V-l. The table lists the ratios and square roots of the ratios of the 

 variances of the u and w components (the latter being equivalent to the ratio of 

 the standard deviations of the amplitudes of the velocity fluctuations). Also 

 listed are: the mean horizontal velocity u; the sea state judged from visual 

 estimates of wave structure, using the definitions in table II-2; the instruments 

 used; and the method of support of the instruments (see chapter IV) . 



It is evident that the more stable the suspension system, the more nearly 

 equal the variances become (ratio <T U /0~w approaches unity). One might conclude 

 that the wave forces upon the meters bias the measurement of the relative magni- 

 tudes of the two velocities „ Note also that the OMDUM III instrument has about 

 one-half the cross-sectional area of OMDUM II, which would reduce drag. Hence, it 

 appears that as the waves pass the suspended instrument, the u measurement tends 

 to be biased by oscillation of the meter in the x direction. 



It appears from table V-l that, during higher mean horizontal velocity u 

 (absolute value), the ratio % tends to be smaller, suggesting that the mean 

 current flow may be a counteracting phenomenon tending to dampen the instrument 

 response to fluctuations of u. However, maximum value of % is O.978, and most 

 of the values are well below 0.8. Also, the Narragansett Bay measurements (rigid 

 suspension system) and those from BBELS-lU and lb (most stable suspension system) 

 do not produce exceptionally high ratios. 



This disproportion between the amplitudes of u and w was somewhat dis- 

 couraging when the first observations were analyzed, since it seemed to cast 

 doubts on all data obtained with the wave meters. Further examination of the 

 spectra of the data indicated that, although the accuracy of the u data was 

 rendered somewhat questionable by the non-rigid mounting of the instruments, 

 other explanations of the unequal variances were plausible, and that the two- 

 dimensional motions seemed, in general, to be well portrayed. 



There is no a priori evidence that one must obtain equal variances for 

 observed component wave motions. Some insight into the potential differences 

 that might be expected in the statistics of u and w can be obtained by examining 

 factors which may be used to distinguish horizontal from vertical motions. 



Eckart (1955), in discussing fluid motion, defined a "random oscillation" 

 flow as distinct from a "random drift". To visualize this, let L be the time 



