RI%NOl.l)S STRESS STRUCTURE IN TURBULENT BOUNDARY LAYER
301
the ' * hole " are the other four regions. The size of the hole is determined by
the curves 1 uvI = constant. Introduce the parameter H and let I ucl
= Hu'c'. where u' and I*' are the local root mean square values of u and c
signals. The parameter H is called the hole size. With this scheme, large
contributors to ur relative to u'c' from each quadrant can be extracted
leaving the smaller fluctuating uu sighal in the hole. The contribution to iiF
from the hole would mean the contribution during the more quiescent periods, while the second quadrant represents the burstlike events and the
fourth quadrant the sweeplike events.
The contributions to ii3 from the four quadrants were computed from the
equations
& ( H )
1 . 1
= -_ Iim
ua(t)Si(r, H ) dt,
i = 1,2, 3, 4,
111;
b t f l T- T ~ C J
(3)
t
where the subscript i refers to the ith quadrant and
1
0
otherwise.
if I uu(r) I > Hu'I~' and the point (u, c) in
the u-c plane is in the ith quadrant.
(4)
Si(t. H ) =
Contributions to uii from the hole region were obtained using Eq. (3) but
with Si replaced by Sh where
1
( 5 )
Sh = 10
otherwise.
These five contributions, uvi and utj,, are all functions of the hole size H, and
if I uu(t) I < Hu'v',
= 1.
U;,(H)
+
liU,(H)
-
, F; l
*
u u
Typical rcsults of the measurements at low speed at various distances
from the wall are shown in Figs. 12-14. There was only one measurement for
the case of high speed flow which was made at a distance of y + = 265 from
the wall. This result is shown in Fig. 15. The results were very similar for
both high and low Reynolds number measurements and regardless of the x
wire probe location in the turbulent boundary layer. In Figs. 12-15 curves
representing the fraction of total time that uu signal spent in the hole region
are also included.
For a large portion of the time, I uu I is very small. Stated in another way,
U P has an intermittency factor of 0.55 since in Figs. 12-15 99% of the
contribution to u-t occurs during 55 of the time. As a matter of fact, these
two curves, i.e., the fraction of the total time in the hole and the contribution
to Oij from the hole region, can be derived from the assumption of joint
301
the ' * hole " are the other four regions. The size of the hole is determined by
the curves 1 uvI = constant. Introduce the parameter H and let I ucl
= Hu'c'. where u' and I*' are the local root mean square values of u and c
signals. The parameter H is called the hole size. With this scheme, large
contributors to ur relative to u'c' from each quadrant can be extracted
leaving the smaller fluctuating uu sighal in the hole. The contribution to iiF
from the hole would mean the contribution during the more quiescent periods, while the second quadrant represents the burstlike events and the
fourth quadrant the sweeplike events.
The contributions to ii3 from the four quadrants were computed from the
equations
& ( H )
1 . 1
= -_ Iim
ua(t)Si(r, H ) dt,
i = 1,2, 3, 4,
111;
b t f l T- T ~ C J
(3)
t
where the subscript i refers to the ith quadrant and
1
0
otherwise.
if I uu(r) I > Hu'I~' and the point (u, c) in
the u-c plane is in the ith quadrant.
(4)
Si(t. H ) =
Contributions to uii from the hole region were obtained using Eq. (3) but
with Si replaced by Sh where
1
( 5 )
Sh = 10
otherwise.
These five contributions, uvi and utj,, are all functions of the hole size H, and
if I uu(t) I < Hu'v',
= 1.
U;,(H)
+
liU,(H)
-
, F; l
*
u u
Typical rcsults of the measurements at low speed at various distances
from the wall are shown in Figs. 12-14. There was only one measurement for
the case of high speed flow which was made at a distance of y + = 265 from
the wall. This result is shown in Fig. 15. The results were very similar for
both high and low Reynolds number measurements and regardless of the x
wire probe location in the turbulent boundary layer. In Figs. 12-15 curves
representing the fraction of total time that uu signal spent in the hole region
are also included.
For a large portion of the time, I uu I is very small. Stated in another way,
U P has an intermittency factor of 0.55 since in Figs. 12-15 99% of the
contribution to u-t occurs during 55 of the time. As a matter of fact, these
two curves, i.e., the fraction of the total time in the hole and the contribution
to Oij from the hole region, can be derived from the assumption of joint