TM Wo. 377 



The auto-spectra ^^ and ^ui of each model are shown in figure 

 V-48. Again, the random model (RBM) shows no dominant peaks, whereas the sine- 

 like systems display relatively strong, well-defined pedestals at a frequency of 

 about 0.5 cps or a period of 2.0 seconds. Note that this is the period of the 

 auto-covariance oscillation for the sine functions (SUM and SBM) . Figure V-^9 

 shows the co-spectra C uw and the qua-spectra Qu W for the three models. The co- 

 spectrum scale is l/20 the qua-spectrum scale. 



The qua-spectrum Qq W for the RBM shows no significant energy peaks, whereas 

 strong peaks occur for both the SUM and SBM at the wave frequency of 0.5 cps. 

 These strong qua- spectral peaks are to be expected (see equations (V-39) and (V-Uo)), 

 since the fundamental sine and cosine functions are exactly out-of -phase (i.e., by 

 TT/2). 



Examination of the co-spectral functions shows that the areas between the 

 0^ curves and the zero axes are equivalent to the value of the covariance u'w' 

 (which for all three cases is negative). The co-spectra of the three models are 

 the most interesting, since they are indicative of the sensitivity of the corre- 

 lation phenomena. The Cuw for the RBM is highly random and (noting the difference 

 in scaling of the C U w an< i Quw axes) is similar over the whole frequency range to 

 Quw- 



The co-spectrum of the SUM is relatively flat with a slight disturbance 

 indicated at about 0.5 cps. On the other hand, the co-spectrum for the SBM shows 

 a very pronounced negative peak precisely at the wave frequencies. This indicates 

 that, by altering the magnitude of the values of the u component by about 5 per- 

 cent over small intervals near the wave peaks, the covariance obtained shows a 

 strong negative peak at a frequency associated with the waves themselves. 



A very real problem in measurement exists, since the instrumentation 

 measuring the actual wave motions could provide an artificial correlation in the 

 recorded data, in addition to the real correlation provided by the true motions 

 themselves. It is therefore pertinent to ask to what extent the wave meter 

 systems can bias the records. 



Instrument Problems 



In this study a new and relatively crude instrument was developed to 

 examine wave motions. In spite of some obvious drawbacks in the wave meter, 

 associated with limited calibration techniques and imperfect mounting methods, 

 a good deal of plausible and probably valuable information was obtained about 

 the gross properties of surface wind-wave motions. These results have been 

 discussed in the preceding sections of this chapter. This section, which treats 

 the observed time correlative properties of the wave motions, deals with more 

 speculative interpretations of the observed data. It can be argued that much 

 of the covariance information provided by the instrument is spurious. This 

 possibility is acknowledged and examined in the light of the mechanism of such 

 correlation discussed in the previous section. There are also four (not 

 necessarily independent) effects which can be attributed to the OMDUM system, 



