Spectral analysis. Spectral analysis was performed using a standard Fast 

 Fourier Transform (Press et al. 1989). Data were divided into blocks of 

 4,096 points and the spectrum was calculated for each block. The total 

 number of blocks per run was determined by the run length (20-min run = 

 4 blocks, 40-min run = 8 blocks, and 70-min run = 15 blocks). The average 

 spectrum for each run was calculated by averaging the spectra over all blocks 

 within the run. The confidence bands for each spectrum become tighter as the 

 number of averages increases. The degrees of freedom (DOF) for the spectra 

 are approximately twice the number of averages (20-min run = 8 DOF, 

 40-min run = 16 DOF, and 70-min run = 30 DOF). 



Figure 3-2. 



Period response of the low-pass filter for cutoff period 

 6 sec 



Although most runs were 20, 40, or 70 min in length, shorter runs were 

 also made. For 10-min runs, blocks of 4,096 points with two averages were 

 used and for 5-min runs, blocks of 2,048 points with no averages were used. 

 Runs of 1 to 3 min that were conducted to investigate sediment suspension 

 (Runs A2908B through A3017B) were not analyzed for this report. The 

 spectral parameters calculated for the resistance wave staffs are: 



a. Setup and setdown or mean water elevation (relative to the still-water 

 elevation) 



if = 5(0) ( 3_1 ) 



where 5(0) is the energy density of the discrete water surface spectrum 

 at the frequency / equal to zero. 



b. Spectral estimate of the standard deviation of the water surface 



62 



Chapter 3 SUPERTANK Hydrodynamics 



