The Texas A&M water channel experiment is modified to examine the effect of single-mode initial conditions on the development of buoyancy-driven mixing (Rayleigh-Taylor) with small density differences (low-Atwood number). Two separated stratified streams of ~5°C difference are convected and unified at the end of a splitter plate outfitted with a servo-controlled flapper. The top (cold) stream is dyed with Nigrosine and density is measured optically through the Beer-Lambert law. Quantification of the subtle differences between different initial conditions required the optical measurement uncertainties to be significantly reduced. Modifications include a near-uniform backlighting provided through quality, repeatable, professional studio flashes impinging on a white-diffusive surface. Also, a black, absorptive shroud isolates the experiment and the optical path from reflections. Furthermore, only the red channel is used in the Nikon D90 CCD camera where Nigrosine optical scatterring is lower. This new optical setup results in less than 1% uncertainty in density measurements, and 2.5% uncertainty in convective velocity. With the Atwood uncertainty reduced to 4% using a densitometer, the overall mixing height and time uncertainty was reduced to 5% and 3.5%, respectively. Initial single-mode wavelengths of 2, 3, 4, 6, and 8 cm were examined as well as the baseline case where no perturbations were imposed. All non-baseline cases commence with a constant velocity that then slows, eventually approaching the baseline case. Larger wavelengths grow faster, as well as homogenize the flow at a faster rate. The mixing width growth rates were shown to be dependent on initial conditions, slightly outside of experimental uncertainty.

References

References
1.
Duggleby
,
A.
,
Ball
,
K. S.
, and
Schwaenen
,
M.
, 2009, “
Structure and Dynamics of Low Reynolds Number Turbulent Pipe Flow
,”
Phil. Trans. Roy. Soc. A.
,
347
, pp.
473
488
.
2.
Knost
,
D. G.
,
Thole
,
K. A.
, and
Duggleby
,
A.
, 2009, “
Evaluating a Slot Design for the Combustor-Turbine Interface
,” ASME Int. Gas Turb. Conf. GT2009-60168.
3.
Dimotakis
,
P. E.
, 2005, “
Turbulent Mixing
,”
Annu. Rev. Fluid Mech.
,
37
(
1
), pp.
329
356
.
4.
Kolmogorov
,
A. N.
, 1941, “
Local Structure of Turbulence in an Incompressible Fluid at Very High Reynolds Numbers
,”
Doklady AN SSSR
,
30
(
4
), pp.
29
303
.
5.
Batchelor
,
G. K.
, and
Townsend
,
A. A.
, 1949, “
The Nature of Turbulent Motion at Large Wave-Numbers
,”
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
,
199
(
1057
), pp.
238
255
.
6.
Townsend
,
A. A.
, 1961, “
Equilibrium Layers and Wall Turbulence
,”
J. Fluid Mech.
,
11
(
1
), pp.
97
120
.
7.
Youngs
,
D. L.
, 1984, “
Numerical Simulation of Turbulent Mixing by Rayleigh-Taylor Tnstability
,”
Physica D.
,
12
, p.
32
44
.
8.
Guala
,
M.
,
Hommena
,
S.
, and
Adrian
,
R.
, 2007, “
Large-Scale and Very-Large-Scale Motions in Turbulent Pipe Flow
,”
Phil. Trans. R. Soc. A.
,
365
, pp.
521
542
.
9.
Monty
,
J. P.
,
Hutchins
,
N.
,
Ng
,
H. C. H.
,
Marusic
,
I.
, and
Chong
,
M. S.
, 2009, “
A Comparison of Turbulent Pipe, Channel and Boundary Layer Flows
,”
J. Fluid Mech.
,
632
, pp.
431
442
.
10.
Balakumar
,
B. J.
, and
Adrian
,
R. J.
, 2007, “
Large- and Very-Large-Scale Motions in Channel and Boundary-Layer Flows
,”
Phil. Trans. Roy. Soc.
,
365
(
1852
), pp.
665
681
.
11.
Yoshimatsu
,
K.
,
Okamoto
,
N.
,
Schneider
,
K.
,
Kaneda
,
Y.
, and
Farge
,
M.
, 2009, “
Intermittency and Scale-Dependent Statistics in Fully Developed Turbulence
,”
Phys. Rev. E
,
79
(
2
), p.
026303
.
12.
Dimonte
,
G.
,
Youngs
,
D. L.
,
Dimits
,
A.
,
Weber
,
S.
,
Marinak
,
M.
,
Wunsch
,
S.
,
Garasi
,
C.
,
Robinson
,
A.
,
Andrews
,
M. J.
,
Ramaprabhu
,
P.
,
Calder
,
A. C.
,
Fryxell
,
B.
,
Biello
,
J.
,
Dursi
,
L.
,
MacNeice
,
P.
,
Olson
,
K.
,
Ricker
,
P.
,
Rosner
,
R.
,
Timmes
,
F.
,
Tufo
,
H.
,
Young
,
Y.-N.
, and
Zingale
,
M.
, 2004, “
A Comparative Study of the Turbulent Rayleigh-Taylor Instability Using High-Resolution Three-Dimensional Numerical Simulations: The Alpha-Group Collaboration
,”
Phys. Fluids.
,
16
(
5
), pp.
1668
1693
.
13.
Ristorcelli
,
J. R.
, and
Clark
,
T. T.
, 2004, “
Rayleigh-Taylor Turbulence: Self-Similar Analysis and Direct Numerical Simulations
,”
J. Fluid Mech.
,
507
, pp.
213
253
.
14.
Banerjee
,
A.
, and
Andrews
,
M. J.
, 2006, “
Statistically Steady Measurements of Rayleigh-Taylor Mixing in a Gas Channel
,”
Phys. Fluids
,
18
(
035104
), pp.
1
13
.
15.
Ramaprabhu
,
P.
,
Dumonte
,
G.
, and
Andrews
,
M. J.
, 2005, “
A Numerical Study of the Influence of Initial Perturbations on the Turbulent Rayleigh-Taylor instability
,”
J. Fluid Mech.
,
536
(
1
), pp.
285
319
.
16.
Olson
,
D. H.
, and
Jacobs
,
J. W.
, 2009, “
Experimental Study of Rayleigh-Taylor Instability With a Complex Initial Perturbation
,”
Phys. Fluids
,
21
(
3
), p.
034103
.
17.
Rayleigh
,
L.
, 1884, “
Investigation of the Equilibrium of an Incompressible Heavy Fluid of Variable Density
,”
Proc. Lond. Math. Soc.
,
14
, pp.
170
177
.
18.
Taylor
,
G. I.
, 1950, “
The Instability of Liquid Surfaces When Accelerated in a Direction Perpendicular to Their Planes
,”
Proc. R. Soc. Lond.
,
201
, pp.
192
-
196
.
19.
Cabot
,
W. H.
, and
Cook
,
A. W.
, 2006, “
Reynolds Number Effects on Rayleigh-Taylor Instability With Possible Implications for Type-Ia Supernovae
,”
Nat. Phys.
,
2
(
8
), pp.
562
568
.
20.
Rahmstorf
,
S.
, 2003, “
The Current Climate
,”
Nature
,
421
, p.
691
.
21.
Golabek
,
G. J.
,
Schmeling
,
H.
, and
Tackley
,
P. J.
, 2008, “
Earth’s Core Formation Aided by Flow Channelling Instabilities Induced by Iron Diapirs
,”
Earth Planet. Sci. Lett.
,
271
(
1–4
), pp.
24
33
.
22.
Lindl
,
J. D.
, and
Mead
,
W. C.
, 1975, “
Two-Dimensional Simulation of Fluid Instability in Laser-Fusion Pellets
,”
Phys. Rev. Lett.
,
34
(
20
), pp.
1273
1276
.
23.
Banerjee
,
A.
, and
Andrews
,
M. J.
, 2006, “
Statistically Steady Measurements of Rayleigh-Taylor Mixing in a Gas Channel
,”
Phys. Fluids
,
18
, pp.
192
196
.
24.
Betti
,
R.
, 2009,
“Hot Spot Dynamics and Hydrodynamic Instabilities,”
High Energy Density Physics Summer School
.
25.
Lobatchev
,
V.
, and
Betti
,
R.
, 2000, “
Ablative Stabilization of the Deceleration Phase Rayleigh-Taylor Instability
,”
Phys. Rev. Lett.
,
85
(
21
), pp.
4522
4525
.
26.
Petersen
,
M. R.
, 2006, “
Baroclinic Vorticity Production in Protoplanetary Disks Part II: Vortex Growth and Longevity
,”
Astrophys. J.
,
658
, pp.
192
196
.
27.
Chandrasekhar
,
S.
, 1961,
Hydrodynamic and Hydromagnetic Stability
,
Cambridge University Press
,
London
.
28.
Dimonte
,
G.
,
Ramaprabhu
,
P.
,
Youngs
,
D.
,
Andrews
,
M. J.
, and
Rosner
,
R.
, 2005, “
Recent Advances in the Turbulent Rayleigh-Taylor Instability
,”
Phys. Plasmas
,
12
(
056301
), pp.
1
6
.
29.
Snider
,
D. M.
, and
Andrews
,
M. J.
, 1994, “
Rayleigh-Taylor and Shear-Driven Mixing with an Unstable Thermal Stratification
,”
Phys. Fluids
,
6
(
10
), pp.
3324
3334
.
30.
Ramaprabhu
,
P.
, and
Andrews
,
M.
, 2004, “
Experimental Investigation of Rayleigh-Taylor Mixing at Small Atwood Numbers
,”
J. Fluid Mech.
,
502
, (Mar 10), pp.
233
271
.
31.
Mueschke
,
N. J.
,
Andrews
,
M. J.
, and
Schilling
,
O.
, 2006, “
Experimental Characterization of Initial Conditions and Spatio-Temporal Evolution of a Small-Atwood-Number Rayleigh-Taylor Mixing Layer
,”
J. Fluid Mech.
,
567
, (Nov 25), pp.
27
63
.
32.
Schlichting
,
H.
, and
Gersten
,
K.
, 2000,
Boundary Layer Theory
,
Springer
,
Berlin
.
33.
Hollas
,
J.
, 2004,
Modern Spectroscopy
,
4th ed
.
Wiley
,
New York
.
34.
Barrow
,
G. M.
, 1962,
Introduction to Molecular Spectroscopy
,
McGraw-Hill
,
New York.
35.
Kline
,
S. J.
, and
McClintock
,
F. A.
, 1953, “
Describing Uncertainties in Single-Sample Experiments
,”
Mech. Eng.
,
75
, pp.
3
8
.
You do not currently have access to this content.