TR No. 22 
The sources of error in the digitized velocity data have been dis-= 
cussed previously; 
1, Sensitivity of the current meter of *0,25% of mean velocity 
corresponding to an error of 11 cm-sec™1, 
2. Analog to digital conversion rate resulting in an error of 
ti em-sec7l, The total expected error, then, is of the order 
Orne cm=-sec”, which agrees well with the observed noise 
levels for the energy spectra. 
Figure 28 is a plot of the sample variance as a function of the es- 
timated downstream distance, x', of the sample from the channel buoys. 
Because of the large amount of variation it was not possible to determine 
the change in variance with respect to x’. According to Batchelor (1) 
the change in variance is 
SU > Re 
oe i 
27 (32) 
where A is a number of the order cf one and Xp is the wave number at which 
the maximum in the energy spectrum is located, Applying the Taylor 
hypothesis, this is 
2 
2H ls i 1S 
D x ay PT 
(33) 
An order of magnitude estimate of the change in variance with respect 
to x' can be obtained from this. The average value of the variance for 
34 samples is 55.6 cm?-sec~* +25,0 (standard error), (The variances from 
the third and fourth samples from run No. 4 and the first sample from 
run No. 7 were not included in the average since the values are excessively 
large, probably caused by motion of the boat.) The average value of the 
variance derived from the energy spectra is 3.2 x 1073 or less. Then 
ay 
BU LESS oy ayo 
ax 400 ZoDE 
= aa —2 
s £9 210 Cm-s5ee 
22 
