TM No. 3U2 



output of an accelerometer attached to the meters o The frequency response 

 of the impellers was shown to he greater than 10 cps. This rapid response 

 permits accurate sensing of perturbations of the time scales of wind waves 

 of the period from O.p to 8 seconds. 



It is realized th^t there must be a limiting size of eddy or oscillatory 

 configuration for which the volume dimensions of the meter alter or inter- 

 fere with the inherent motions of the eddies. The effect of decreasing 

 orbital size upon flow sensing is to be determined by measuring the meter 

 response of the ducted meters in a wave generating flume system at the 

 Coastal Engineering Laboratory in Washington^ D. C. 



THREE HYPOTHETICAL WAVE MODELS 



A comprehensive understanding of the analysis and synthesis of the Tiikey 

 spectral estimates is essential for drai-Tlng valid conclusions and making 

 interpretations regarding the nature of wave motions as derived from their 

 statistical properties. To best assess the application of the spectral 

 analysis upon the two component velocity time-series data, three sets of 

 hypothetical \m.ve data were constructed and analyzed. These sets of data 

 depicted three different wave models: one whose particle motions are (a) 

 quasi-random with an induced bias to give U' W' < with no preferred fre- 

 quency in the covariance spectra; (b) quasi-ideal sinusoidal particle motions 

 with no intentional bias giving U' W a-»0; and (c) sinusoidal velocity fluc- 

 tuations with a bias rendering U' W ^ and having a preferred frequency in 

 the covariance spectra equivalent to the frequency of the quasi-sinusoidal 

 velocity functions. 



The three sets of data each contained 60O pairs consisting of the hori- 

 zontal velocity coniponent IL and the vertical velocity component Wp. The 



subscript n indicates the n"th data point where n = 1, 2, 3^ N;, and 



W being the total number of data pieces equally spaced at time intervals of 

 At. Thus, the total period of sampling, T, is equal to N ^ t. For the 

 three time series T is I80 seconds . The amplitude or half range of the 

 velocity components for all three data sets was about 10 cm sec"l. Table 1 

 lists the pertinent statistical parameters of the three data ensembles . A 

 description of the three models follows . 



Biased Random Wave Model (BR) 



The first hypothetical wave model can be envisaged as a siorface wave 

 field where the particle motion is quasi-random produced by many oscil- 

 latory progressive waves moving in many directions. The term "quasi-random" 

 is used for two reasons: (l) the values of time series data were arbitrarily 

 chosen without u^e of tables of random numbers and (2) about 5^ of actual 

 values of data points were altered to give a slight negative correlation 

 fimction, i.e., a value of the covariance function at zero lag (U* W* ) less 



