J.
Fluid
Mech.
(1976),
vol.
78,
part
3,
pp.
535-560
Printed
in
Great
Britain
535
The
mixing
€ayer at
high
Reynolds number:
large-structure dynamics and entrainment
By PAUL
E.
DIMOTAKIS
AND
GARRY
L.
BROWN?
Graduate Aeronautical Laboratories, California
Institute of Technology, Pasadena
(Received
7
November
1975
and
in
revised
form
19
March
1976)
A
turbulent mixing layer in
a
water channel was observed
at
Reynolds numbers up
to
3
x
los.
Flow visualization with dyes revealed (once more) large coherent
structures and showed their role in the entrainment process; observation
of
the
reaction of
a
base and an acid indicator injected on the two sides
of
the layer,
respectively, gave some indication
of
where molecular mixing occurs. Auto-
correlations of streamwise velocity fluctuations, using
a
laser-Doppler veloci-
meter (LDV) revealed
a
fundamental periodicity associated with the large
structures. The surprisingly long correlation times suggest time scales much
longer than had been supposed;
it
is
argued that the mixing-layer dynamics
at
any point
are
coupled to the large structure further downstream, and some
possible consequences regarding the effects
of
initial conditions and of the
influence of apparatus geometry are discussed.
1.
Introduction
It
is becoming increasingly evident that the classical picture
of
turbulence,
as
a
state
of
flow in which the properties
of
the various dynamic variables can
only be determined in
a
stochastic sense,
is
not quite complete. Experimental
results in the last few years indicate that within the obvious randomness of
turbulence there exist flow patterns and large-scale structures that appear to be
dominant in determining the overall characteristics
of
such
flows.
A notable
example is the discovery that the turbulent mixing layer is inhabited by
a
more
or
less organized large structure (Brown
&
Roshko
1971).
Large-scale vortices and instabilities at very high Reynolds number had been
found in other flows. Yet the apparent quasi-regularity that
is
manifest in the
photographs and high-speed motion pictures of Brown
&
Roshko
(1971, 1974)
was not expected.
It
was unexpected because such well-defined structure
is
far
from random a.nd appears inconsistent with the classical picture
of
turbulence.
Even though such apparent inconsistencies are probably adequately explained,
in terms of the irregularity and jitter in the formation, amalgamation and
spacing of these large structures (Brown
&
Roshko
1974),
important questions
remain to
be
answered.
It
becomes important,
for
example, to establish whether
t
Permanent address: University
of
Adelaide, Australia.
536
P.
E.
Dimotakis
and
G.
L.
Brown
these large structures persist
at
even higher Reynolds numbers
or
whether they
are
a
curious transition from the well-defined periodicity of the laminar in-
stability region (Sato
1956)
to
a
state-of complete randomness
at
infmite Reynolds
number. In addition, the question of persistence of the mechanism of vortex
pairing, well documented
at
relatively low Reynolds number (Winant
&
Browand
1974),
arises, especially since
this
mechanism is not
so
apparent in the photo-
graphs and motion pictures of Brown
&
Roshko, taken
at
much higher Reynolds
numbers.
With these questions in mind, the experiment described here was undertaken.
It
was decided to use the
GALCIT
50
x
50
cm Free Surface Water Tunnel, which
has
a
test
section
2.4
m
(8
ft) long and in which
a
test-section velocity
of
7.6
m/s
can be reached. To generate the shear layer, an insert was designed for the
test
section, yielding
a
velocity ratio between the two streams of
5:
1.
Water offers several attractive features
as
the flowing medium. The most
important
of
these, for our purposes, was the high Reynolds number per
unit
length and velocity. In addition, and as
a
consequence of the relatively low
velocities required, flow visualization by dye injection is particularly simple.
Lastly,
it
was possible
to
take advantage of the high accuracy and high
spatial and temporal resolution of
a
newly developed single-particle laser-
Doppler velocimeter, water being an ideal medium for this measurement
technique.
By injecting dye for flow visualization, we were able to observe and photo-
graph the large structure and follow the process of entrainment by direct observa-
tion and motion pictures.
By
replacing the dye by an acid containing
a
pH
indicator on one side and by
a
base on the other side of the layer, we obtained
photographs
as
well
as
a
motion picture in which the chemical reaction between
the two,
as
they were entrained and mixed in the layer, was qualitatively marked
by the change
in
colour of the indicator.
The flow-visualization evidence for the existence of the large structure
at
a
high Reynolds number
(3
x
106)
is
unmistakable and its dominant role in the
entrainment process is manifest.
The autocorrelation function of the streamwise velocity fluctuations revealed
a
fundamental periodicity which was found to be consistent with the expected
similarity scaling. Other features of the
data,
however, cannot be explained
quite
so
simply and
it
now appears that similarity in the broad sense does not
account for much of the observed behaviour. More complicated processes which
cannot be explained in terms of local phenomena seem
to
govern the dynamics
of the flow. Mechanisms for coupling the whole shear layer
are
required and
suggest that such factors
as
initial conditions may always be important.
These experiments are the
&st
part
of
a
larger investigation and perhaps raise
more questions than they can answer. Nevertheless, we feel that the results
presented here are of sufficient interest in themselves and important in that
they do raise these questions.
The mixing layer at high Reynolds
number
537
2.
Apparatus and resulting
flow
fluid
The high Reynolds numbers which may be achieved in the
50
x
50
cm GALCIT
Free
Surface Water Tunnel made this facility
a
logical choice for the experiment.
This tunnel is capable of
a
maximum velocity, without
a
model in the 2.4m
working section, of
7.6
m/s.
It
was decided to modify this facility in such
a
way
as
to
generate
a
well-defined, two-dimensional shear layer with
a
high aspect
ratio. Unfortunately, to obtain
a
shear layer with
a
large velocity ratio in two
separate streams within the
test
section of
a
conventional wind
or
water tunnel
is by no means straightforward. This
is
especially true if it is not feasible to
divide the flow into two parts within the tunnel contraction. In several other
attempts to establish two streams of different velocity in
a
tunnel
test
section
by dividing the flow and placing flow resistance on the low-speed side, there
appear to have been difficulties with flow separation and flow non-uniformity
as the velocity ratio became large. Having
a
velocity of zero on the low-speed
side may appear
to
avoid these problems but, in the GALCIT Water Tunnel at
least, to satisfy the entrainment requirements while maintaining a low-turbulence
high-quality flow would render this choice an even more difficult problem.
Consequently, we decided to design an insert that would produce
a
shear layer
with
a
non-zero
U,
within the water-tunnel
test
section, taking special pre-
cautions
to
minimize the possibility of separation. The outcome is shown in
figure
1
and the manner in which it is placed in the working section is shown in
figure 2. The resulting apparatus proved to be very satisfactory and the basis
for the design of the insert possibly merits
a
brief description. In order to avoid
separation
at
the leading edge of the flow divider,
it
is
desirable to design the
two flow paths to have exactly the same pressure drop for
a
given inlet velocity.
For
an
area
contraction ratio of
Ain/Aout
=
C,
on the high-speed side and
a
corresponding expansion of
l/C,
on the low-speed side, matched inlet and exit
pressures and uniform flow
at
the two inlets ensure that the velocity ratio
r
=
UJU.
is equal
to
PA.
The flow resistance on the low-speed side must match
the Bernoulli pressure drop on the high-speed side. The flow must also be re-
directed within the expansion
to
avoid separation. The two perforated plates
shown in figure
1
(50
yo
open) were accordingly placed where separation might
otherwise have occurred. The plates were curved (rolled
as
segments
of
a
circle)
so
as
to be approximately perpendicular to the streamlines of an inviscid flow
through the expansion. Adjustment was provided by allowing movement of the
lower edge of the plate upstream and the upper edge downstream
or
vice versa
so
that the flow could be directed more towards the lower
or
upper boundary.
Fine control and adjustment of the pressure drop were achieved by placing an
identical perforated sheet on
top
of the
&st.
Sliding one vertically relative to the
other changed the percentage open area. This, of course, had some
effect
on the
flow direction after the plate, which had to be offset,
as
required, by tilting the
plate. Finally, the resulting turbulence on the low-speed side was reduced in
scale and amplitude and the flow made even more uniform by the
40
mesh,
50
yo
open screen placed
at
the exit of the expansion. The percentage open areas
(solidities) of the plates and the
screen
as well
as
their locations were chosen to
538
P.
E. Dimotakis
and
G.
L.
Brown
FIUURE
1.
Insert
for
the shear layer with velocity ratio
5:
1.
.
L..I*LI,
1.
L.1
FIUURE
2.
Test section with insert and top installed.
provide the requisite total pressure coefficient. Handbook
data
were used to
compute the individual pressure drops. Perforated plates were chosen to provide
the flow resistance because the pressure drop across them
is
very nearly Reynolds
number independent and because they have sufficient thickness to provide
in-plane forces that tend to give an exit flow velocity that is perpendicular to the
surface of the plate (hence the curved shape).
In
addition to this insert,
a
lucite
top 150cm long was installed
in
the remainder of the
test
section to remove
free-surface effects of various kinds (see figure
2).
Just downstream of the insert, the flow on the low-velocity side was found to
be uniform to within
1
yo
of the velocity of the faster stream over the full
35
cm
The mixing
layer
at
high Reynolds number
539
l.O
t
0.8
1
V
OA
I
I
-
0.2
-0.1
0
0.1 0.2
1,
71
=
(Y-Yo)/@-%)
FIGURE
3.
Similarity mean velocity
profiles.
x
,
m
=
15.24cm;
0,
m
=
30.48cm;
A,
x
=
60.96cm;
V,
z
=
91.44cm.
mo
=
3.05cm. Free-stream velocity
on
high-speed side
U,
=
165cmls.
width of the flow. The measured velocity ratio
r
=
U&
was
0.21
with
U,
=
165
cmls.
At the first measuring station, 15 em downstream from the end
of
the splitter
plate, the root-mean-square fluctuation of the velocity measurements in the
free
stream on the high-speed side was less than
0.5%
of
U,
(no attempt was
made
to
distinguish low frequency velocity fluctuations, turbulence and electronic
noise: this
is
then an upper bound for the turbulence level). On the low-speed
side
it
was less than
2
%
of
U,,
which, since
U,
is
much less than
V,,
is
also very
small compared with the relevant velocity
U,-
U,.
In general, the whole flow
was very steady (less than
I
yo
long-term variation in free-stream velocity) over
many hours of operation, except for some small low frequency fluctuations in
free-stream velocity, observed
at
the measuring station furthest downstream,
probably owing to surface waves downstream of the
150
ern lucite top.
At
a
free-stream velocity on the high-speed side of 165cm/s, the boundary
layer was found to be transitional (occasional turbulent spots), with
a
momentum
thickness of the order of
0.4
mm. The maximum slope thickness,
12
mm down-
stream of the splitter plate’s trailing edge, was
2
mm. The mean velocity profiles
at
a
high-speed free-stream velocity of 165 cm/s,
at
which most of the data were
taken, are plotted in similarity co-ordinates in figure 3. They represent measure-
ments 15cm, 30cm, 60cm and 90cm downstream of the splitter plate. Each
point is the time-averaged velocity computed from several records consisting of
1024
discrete measurements, in
a
manner described in
$4.
No
quantitative
velocity
data
were recorded any further downstream in order to restrict the data
to
an aspect ratio for the large structure (ratio of span to vorticity thickness)
as
large
as
possible. From the flow-visualization
data,
however,
it
was clear that,
at
least qualitatively, the same basic two-dimensional large structure persisted