RESEARCH· ·1970·

BENNETT AND McQUIVEY
turbulence in open-channel flow, the bulk of the energy
occurs at much lower :frequencies (below 10Hz) than it
does in air. For this reason, the power spectral densities
of this study were obtained by digital-cmnputer methods,
wherein the low-frequency resolution is limited
only by t,he length of record which can be processed.
.Data processing by digital methods could not be accomplished
in the field, so the output voltages from the
1nensuring systems were recorded on n~agnctic tape for
later n .. nalysis. The output :from the hot-fihn anemometer
was recorded directly; that from the propeller flowmeter
1neasuring syst01n had to be amplified before it
could be recorded. '"!"he a-c amplifier used had n. lowfrequency
cutoff of 1 II~.
In addition to measurements of power specti·al
density, several measurements were made in which only
longitudinal turbulence intensities, 1~', were obtained.
The voltage intensity for substitution into equa.tion 6
was obtn .. ined frotn an analog root-mean-square (rms)
voltage meter or, when a..va,ilable, from the output of the
computation program :for power spectral density. The
analog rms meter had a low-frequency cutoff of 0.5 l-Iz,
and 11 high-frequency-response flat well beyond the
ra.nge of frequencies o:f interest. The 0.5-Ilz cutoff prevents
the rms 1neter from n1ensur.ing all the turbulence
energy eontained in the velocity fluctuations having frequencies
o:f less than 0.5 l-Iz.
Because the output of the hot-f-ilm anemometer could
be corrected for drift, and because the hot-film anemometer
:is free of inertial and spatial averaging problems,
the results of :the hot-iihn measurements have been used
as stanclnrcls for judging the perfonnance of the propeller
flown1eter.
MEASUREMENT OF POWER SPECTRAL DENSITY
B259
Power spectral densities, S 00
(.f), obtained from the
propeller output for the measurements in the Atrisco
Feeder Canal are given in figure 5, where y is the distanee
above the bed and } 7 the total depth of flow. The
broken curves on this figure a.re the power spectral
densities after they have been corrected for the system
.function. Owing to the differences in roughness height
a .. nd spaeing between the Atrisco channel and the artificially
roughened ehannel in which Bennett (1968)
1neasured the efficiency of spatial resolution (fig. 4), it
was felt that the '1 (f)'s of figure 4 should not be used as
corrections for the field da;ta. (In any ca.se, the Lx/U's of
figu:_e 5 are, except for 5D, all outside the range of
La:!U of figure 4.) Thus no corrections for the efficiency
of spatial resolution could be 1nade; '1 (f) was assumed to
be 1.0. Power spectral densities obtained frmn the hotfilm
anemon1eter over the same relative d~pth range are
presented in figure 6.
The effect of the spatial averaging of the propeller
on the power spectral density of tlie turbulence ·can be
seen in figure 7. In this figure, the power spectral densities
corrected for the system function of the propel~er
as shown in figure 5 have been plotted along with those
of the hot-film anemometer frmn figure 6 for the nearest
available relative depth. The spectra of figures 5,
6, and 7 have been computed using a digital version of
equation 2. Thus those spectra are normalized. Owing to
the normalizing procedure, there is a vertical positioning
difference between the propeller curves and the
hot-film eurves of figure 7. This is due not only to
propeller characteristics but to the exclusion from the
Ill
0
z
0
u
100
10-1
U.J
Ill 10- 2
~
.....
...
VI
A
10- 3 1:-:0.34 ·-~
iJ = 1.68 feet
per second
f :0.94
\ B
' ' .,
' '
\
..' \ \
.. \
~=0.21
u
\
.
\
\
\
10-·
1 10 10
.!:..!.::0.22 •
iJ
c
.!!._ :::0.31
L~
a ==1.67 feet
per second
f :0.67
10
f,IN HERTZ
.
d •
T,. =0.35
D
iJ =1.68 feet
per second
f :::0.66
E
\
\
\
., \
\
\
\
\
\
\
10 10
\
\
\
\
l!'roum~ 5.-Power spectral densities S(f) as functions of frequency t~· propeller output (solid line) corrected for
propeller frequency response (broken line). Measurements made in Atrisco Feeder Canal.