TR No. 22 
RESULTS AND DISCUSSION 
Figures 13 through 17 are graphs of the digitized velocity data 
for several typical samples. The autocovariance series corresponding 
to the samples are shown in figures 18 through 22. Thirty-seven useful 
samples were obtained from seven runs. It is not necessary to show the 
autocovariance series and energy spectra for the individual samples; the 
autocovariance series shown in figures 18 through 22 and the energy spectra 
given in figures 23 through 27 are representative of the results. The 
results from the 37 samples are tabulated numerically in appendix C. The 
values of the energy spectra have been divided by the corresponding sample 
variances previous to being plotted. Before proceeding to a discussion of 
the results it is appropriate to consider the deficiencies in the data 
and/or measurements which are apparent in the autocovariance series and 
the energy spectra. 
Noise 
The energy spectra do not continue to decrease for wave numbers 
greater than around K= 0.06 cm71 as expected but approach a constant 
value of the order of orf K) = 20 cm3-sec72, with considerable variation 
among samples. This can be shown to result from random error in the 
digitized velocity data. If, for a sample consisting of N equally spaced 
values of velocity the ®¥ror which the ith value, u!, is subject ot is ei» 
then the ee error in the kth value Ore (BS autocovariance series 
1s 
! aes \ ( 
Nets NEI fL Peee ll Hel Sa, 
J | dap 
ele [-I< N-K 
= nee uly! Alle WE jg * u! (ee 
Nea! Jtk Pree J Eee stk J 
| (25) 
F Nk J Gj +c ~ N-k4 Uy rk y), 
N-k JA N-K Je | KEK 
Ree. | iN y \ 
ey eee “Si * Wk ed Ak nko I IFK 
s = 
20 
