(9) Instructions for formation of power spectra from cosine transforms 

 of auto-correlated terms (equation (7)). 



(10) Instructions for formation of co- and quad-spectra from cosine 

 transforms of sums and differences of cross-correlated terms 

 (equations (II) and (12)). 



(11) Instructions for writing the processed series on a system output 

 tape in a form suitable for plotting curves of the required 

 functions. 



The information on the output tape may be used at any time to plot 

 rough graphs on a printer, or for drawing smooth curves on an X-Y plotter. 

 Figure 14 is a reproduction of several curves drawn by a plotter. 



Section V EXAMPLES OF FIELD AND LABORATORY tNSTRUIvlENTATI ON 



The multi-channel input feature of the data acquisition system permits 

 several sensors to be arranged as needed and then sampled simultaneously 

 resulting in a mu I t i-dimensJona I data pattern. The sensor arrangements 

 described here have been employed in the study of nearshore phenomena. 



I . Array of Digital Wave Staffs for Longshore Component of Wave Power 



The simultaneous recording of one or more arrays of wave staffs is 

 necessary if the directional properties of waves are to be measured. A sche- 

 matic arrangement of two arrays of four digital wave staffs and a vibrating- 

 wire pressure sensor is shown in Figure 16. The plan here is to economize 

 the number of required wave staffs by employing the optimum irregular spacing 

 sequence and to obtain measurements in and outside of the surf zone from a 

 single installation during the low and high stands of the tide. 



A very simple one-dimensional array of four staffs with spacings of I, 

 3, and 2 units will give correlations of the regular array (uniformly spaced) 

 of I, 2, 3, 4, 5 and 6 units (Barber, 1962). For maximum efficiency one 

 unit of spacing should be approximately one-quarter wave length. The use 

 of two arrays of four each, as illustrated in Figure 16 should provide good 

 measures of the direction of incident energy flux associated with incoming 

 waves, as we I I as an assessment of the modes of trapped energy in the form 

 of edge waves, or other waves such as surf beat and seiche. 



Successful field measurements from two sensors of a simple array have 

 been obtained and are shown in Figure 15 on page 28. Comparison of the power 

 spectra for the two digital wave staffs shows that the sea-breeze waves and 

 the breaking waves both have power spectra peaked at 2.63 sec. (frequency 

 0.380 cps) and that the spectrum for the seaward staff has a somewhat broader 

 peak. Also, the general background noise is greater at all frequencies for 

 the seaward staff. A series of minor spectral peaks, with frequencies less 

 than that of the principal peak, occurs in both spectra. These minor spectral 

 peaks, with only one exception, occur at approximately the same frequency in 

 both analyses. They do not appear to result from aliasing or side band beat 



30 



