TM No. 377 



bias in the covariances. Moreover, for an effective artificial stress to "be 

 observed, the phase lag or response time of the u and w channels must be 

 different. If, in equation (V-^4-5), an identical A(p occurred in both the u* 

 and w* functions, the resulting covariances would be identically zero. 



What is the possibility of there being consistent differences in the response 

 of the u and w sensors? Table II-U lists estimated response times for each of the 

 u and w impellers of the OMDUM III system (in both flow directions). The average 

 response time T r is 66.5 milliseconds with a standard deviation of Q"Z "8*3 milli- 

 seconds. 



Again, assuming a sinusoidal wave with a k- second period as the dominant 

 motional contribution to the covariance, the resultant maximum phase shift of one 

 meter (with respect to the other) would be: 



±(JZ+2± e 'V° " 3 x2Tr = ±fr& e . 



4»o 



The corresponding virtual stresses (from figure V-^5) are ±2, ±5, ±8, ±lU dynes 

 cm for particle velocity amplitudes of 20, 30, UO and 50 cm sec _ l, respectively. 

 These estimates in table II-U are only approximate, since only five observations 

 of T r were made; and the T r values appear to have relatively wide random scatter. 

 Specifically, the two values obtained for +u are as different from each other as 

 they are from other channels. The scatter may therefore be caused by the errors 

 of the experiment, and the actual response times of the two impellers (in either 

 direction) could be closely identical. There is also a possibility that the 

 covariance model in equation (V-U7) may be over-simplified. 



A phase shift could possibly result from an inadvertent shifting of the 

 time axis of one of the velocity pairs (u,w), with respect to the other, during 

 the data processing (particularly during the reading of the data strip charts, as 

 discussed in chapter III). Note that the direction of the accidental time axis 

 shift would control the sign of the covariance (see equation (V-*+7))« A rigorous 

 attempt was made to preserve the simultaneity of the time scales of u and w. 

 However, the checking was not fail-safe; and it is possible that the few 

 excessively large (and seemingly spurious) covariances appearing in table V-4 

 could have been caused by such accidental time axis shifting in the data abstrac- 

 tion procedure. 



Effect of Wave Meter Motion - Another possible effect of instrument bias is 

 associated with the dynamic reaction of the suspended wave meter to the oscilla- 

 tory wave forces. The pyramidal guy wire suspension (discussed in chapter IV") 

 appeared from visual observations to hold the OMDUM III system virtually rigid 

 at all depths, except when it was at the immediate trough level. With the 

 passage of large waves, the maximum horizontal deflection of the wave meter was 

 about 10 cm. The vertical damping appeared to be complete, as was expected 

 because of the heavy counterweights (see figure V-15). 



152 



