REYNOLDS STRESS STRUCTURE IN TURBULENT BOUNDARY LAYER 293
u , -= 0 with negative slope was greatly increased. A correction in the location of the center of the sampling window was made to account for the
approximately constant time lag introduced in the signal u , by the low pass
filter. An example of the data we obtained in this way can be found in
Willmarth and Lu (1972, Fig. 6). Here, we proceed to the next refinement
before presenting the results of thc sampling measumment8.
3.2. Conditionally Sampled and Sorted Measurements
of Reynolds Stress Contributions
The next improvement in the sampled date was made by sorting the
samples we obtained at a given value of u, and positive or negative slope
into four categories depending upon the quadrant of the u-v plane in which
the signal uu occurred. In order to dedcribe the procedure, define h,(r) where
1
for any time I that the point (u, u) is in
the ith quadrant in the u-v plane,
[ 0 otherwise,
(1)
hi@) =
for i = 1.2, 3,4. The averaged values of the portions of the uu signal in each
quadrant are
N
1- 1
( U U J = N - c [ h , ( T ) ~ W I . /
t
(2)
where N is the total number of samples and 5 iS the time relative to the
beginning of the “window” in a given sample. In the measurements to be
described below ( uoz) comes from the second quadrant in the u-v plane and
is associated with the outflow, bunt, of low speed fluid, while (uu4) comes
from fourth quadrant and is aeeocietcd with the i - ,
weeps, of high speed
fluid. (uuI) and ( w 3 ) am the other interactions.
Figure 3 shows results of measurements of t b aatrrgled, sorted contributions to Reynolds strew aa expomrscd ia Eq. (2) in whioh the x wire is a
distance yt ! = 30 from the wall dirpctly above the u, wire at a distance
y + ‘Y 15 from the wall. In the measurement the crit#ioa is that u, = -u&
with negative slope, here the prime denotes thc root-man9quare value. The
use of this criterion in addition to sorting the uv signal mutts in detection of
large contribution to the Rcynokb stress cawed by truptions or bursts at
the time when the sampling criterion is met at tbe ccntcr of the sampliag
window.
Figure 4 shows similar results of measurements as expressed in Eq. (2)
with the hot wire probes in the same position as Fig 3 but with the criterion
that u, = U; with positive slope. In this case the detection criteria show the
occurrence of sweeps (uu4) at the center of the sampling window when the
criterion is satisfied.
u , -= 0 with negative slope was greatly increased. A correction in the location of the center of the sampling window was made to account for the
approximately constant time lag introduced in the signal u , by the low pass
filter. An example of the data we obtained in this way can be found in
Willmarth and Lu (1972, Fig. 6). Here, we proceed to the next refinement
before presenting the results of thc sampling measumment8.
3.2. Conditionally Sampled and Sorted Measurements
of Reynolds Stress Contributions
The next improvement in the sampled date was made by sorting the
samples we obtained at a given value of u, and positive or negative slope
into four categories depending upon the quadrant of the u-v plane in which
the signal uu occurred. In order to dedcribe the procedure, define h,(r) where
1
for any time I that the point (u, u) is in
the ith quadrant in the u-v plane,
[ 0 otherwise,
(1)
hi@) =
for i = 1.2, 3,4. The averaged values of the portions of the uu signal in each
quadrant are
N
1- 1
( U U J = N - c [ h , ( T ) ~ W I . /
t
(2)
where N is the total number of samples and 5 iS the time relative to the
beginning of the “window” in a given sample. In the measurements to be
described below ( uoz) comes from the second quadrant in the u-v plane and
is associated with the outflow, bunt, of low speed fluid, while (uu4) comes
from fourth quadrant and is aeeocietcd with the i - ,
weeps, of high speed
fluid. (uuI) and ( w 3 ) am the other interactions.
Figure 3 shows results of measurements of t b aatrrgled, sorted contributions to Reynolds strew aa expomrscd ia Eq. (2) in whioh the x wire is a
distance yt ! = 30 from the wall dirpctly above the u, wire at a distance
y + ‘Y 15 from the wall. In the measurement the crit#ioa is that u, = -u&
with negative slope, here the prime denotes thc root-man9quare value. The
use of this criterion in addition to sorting the uv signal mutts in detection of
large contribution to the Rcynokb stress cawed by truptions or bursts at
the time when the sampling criterion is met at tbe ccntcr of the sampliag
window.
Figure 4 shows similar results of measurements as expressed in Eq. (2)
with the hot wire probes in the same position as Fig 3 but with the criterion
that u, = U; with positive slope. In this case the detection criteria show the
occurrence of sweeps (uu4) at the center of the sampling window when the
criterion is satisfied.