The present work aims at expanding the set of buoyancy-driven unstable reference flows—a critical ingredient in the development of turbulence models—by considering the recently introduced “Unstably Stratified Homogeneous Turbulence” (USHT) in both its self-similar and transient regimes. The previously established accuracy of an anisotropic Eddy-Damped Quasi-Normal Markovian Model (EDQNM) on the USHT has allowed us to: (i) build a data set of well defined transient flows from Homogeneous Isotropic Turbulence (HIT) to late-time self-similar USHT and (ii) on this basis, calibrate, validate, and compare three common Reynolds-Averaged Navier–Stokes (RANS) mixing models (two-equation, Reynolds stress, and two-fluid). The model calibrations were performed on the self-similar flows constrained by predefined long range correlations (Saffman or Batchelor type). Then, with fixed constants, validations were carried out over the various transients defined by the initial Froude number and mixing intensity. Significant differences between the models are observed, but none of them can accurately capture all of the transient regimes at once. Closer inspection of the various model responses hints at possible routes for their improvement.

References

1.
Godeferd
,
F. S.
, and
Cambon
,
C.
,
1994
, “
Detailed Investigation of Energy Transfers in Homogeneous Stratified Turbulence
,”
Phys. Fluids
,
6
(
6
), pp.
2084
2100
.
2.
Griffond
,
J.
,
Gréa
,
B. J.
, and
Soulard
,
O.
,
2014
, “
Unstably Stratified Homogeneous Turbulence as a Tool for Turbulent Mixing Modeling
,”
ASME J. Fluids Eng.
,
136
(
9
), p.
091201
.
3.
Batchelor
,
G. K.
,
Canuto
, V
. M.
, and
Chasnov
,
J. R.
,
1992
, “
Homogeneous Buoyancy-Generated Turbulence
,”
J. Fluid Mech.
,
235
(
2
), pp.
349
378
.
4.
Livescu
,
D.
, and
Ristorcelli
,
J. R.
,
2007
, “
Buoyancy-Driven Variable-Density Turbulence
,”
J. Fluid Mech.
,
591
(
11
), pp.
43
71
.
5.
Chung
,
D.
, and
Pullin
,
D.
,
2009
, “
Direct Numerical Simulation and Large-Eddy Simulation of Stationary Buoyancy-Driven Turbulence
,”
J. Fluid Mech.
,
643
, pp.
279
308
.
6.
Lazier
,
J.
,
Hendry
,
R.
,
Clarke
,
A.
,
Yashayaev
,
I.
, and
Rhines
,
P.
,
2002
, “
Convection and Restratification in the Labrador Sea, 1990–2000
,”
Deep Sea Res. Part I: Oceanogr. Res. Pap.
,
49
(
10
), pp.
1819
1835
.
7.
Soulard
,
O.
,
Griffond
,
J.
, and
Gréa
,
B.-J.
,
2014
, “
Large-Scale Analysis of Self-Similar Unstably Stratified Homogeneous Turbulence
,”
Phys. Fluids
,
26
(
1
), p. 015110.
8.
Burlot
,
A.
,
Gréa
,
B.-J.
,
Godeferd
,
F. S.
,
Cambon
,
C.
, and
Soulard
,
O.
,
2015
, “
Large Reynolds Number Self-Similar States of Unstably Stratified Homogeneous Turbulence
,”
Phys. Fluids
,
27
(
6
), p.
065114
.
9.
Thoroddsen
,
S. T.
,
Van Atta
,
C. W.
, and
Yampolsky
,
J. S.
,
1998
, “
Experiments on Homogeneous Turbulence in an Unstably Stratified Fluid
,”
Phys. Fluids
,
10
(
12
), pp.
3155
3167
.
10.
Batchelor
,
G. K.
,
1949
, “
The Role of Big Eddies in Homogeneous Turbulence
,”
Proc. R. Soc. London, Ser. A
,
195
(
1043
), pp.
513
532
.
11.
Llor
,
A.
,
2011
, “
Langevin Equation of Big Structure Dynamics in Turbulence: Landaus Invariant in the Decay of Homogeneous Isotropic Turbulence
,”
Eur. J. Mech. B/Fluids
,
30
(
5
), pp.
480
504
.
12.
Poujade
,
O.
, and
Peybernes
,
M.
,
2010
, “
Growth Rate of Rayleigh–Taylor Turbulent Mixing Layers With the Foliation Approach
,”
Phys. Rev. E
,
81
(
1
), p.
016316
.
13.
Youngs
,
D. L.
,
1984
, “
Numerical Simulation of Turbulent Mixing by Rayleigh–Taylor Instability
,”
Physica D
,
12
(
13
), pp.
32
44
.
14.
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
.
15.
Livescu
,
D.
,
Wei
,
T.
, and
Peterson
,
M. R.
,
2011
, “
Direct Numerical Simulations of Rayleigh–Taylor Instability
,”
J. Phys.: Conf. Ser.
,
318
(
082007
), pp.
1
10
.
16.
Youngs
,
D. L.
,
2013
, “
The Density Ratio Dependence of Self-Similar Rayleigh–Taylor Mixing
,”
Philos. Trans. R. Soc. London, Ser. A
,
371
(
2003
), pp.
1
15
.
17.
Dimonte
,
G.
,
2000
, “
Spanwise Homogeneous Buoyancy-Drag Model for Rayleigh–Taylor Mixing and Experimental Evaluation
,”
Phys. Plasma
,
7
(
6
), pp.
2255
2269
.
18.
Dimonte
,
G.
,
Ramaprabhu
,
P.
, and
Andrews
,
M.
,
2007
, “
Rayleigh–Taylor Instability With Complex Acceleration History
,”
Phys. Rev. E
,
76
(
4
), p.
046313
.
19.
Ramaprabhu
,
P.
,
Karkhanis
,
V.
, and
Lawrie
,
A. G. W.
,
2013
, “
The Rayleigh–Taylor Instability Driven by an Accel-Decel-Accel Profile
,”
Phys. Fluids
,
25
(
11
), pp.
1
33
.
20.
Burlot
,
A.
,
Gréa
,
B.-J.
,
Godeferd
,
F. S.
,
Cambon
,
C.
, and
Griffond
,
J.
,
2015
, “
Spectral Modelling of High Reynolds Number Unstably Stratified Homogeneous Turbulence
,”
J. Fluid Mech.
,
765
, pp.
17
44
.
21.
Gauthier
,
S.
, and
Bonnet
,
M.
,
1990
, “
A k–ε Model for Turbulent Mixing in Shock-Tube Flows Induced by Rayleigh–Taylor Instability
,”
Phys. Fluids A
,
2
(
9
), pp.
1685
1694
.
22.
Grégoire
,
O.
,
Souffland
,
D.
, and
Gauthier
,
S.
,
2005
, “
A Second-Order Turbulence Model for Gaseous Mixtures Induced by Richtmyer–Meshkov Instability
,”
J. Turbul.
,
6
(
29
), pp.
1
20
.
23.
Llor
,
A.
, and
Bailly
,
P.
,
2003
, “
A New Turbulent Two-Field Concept for Modeling Rayleigh–Taylor, Richmyers–Meshkov, and Kelvin–Helmholtz Mixing Layers
,”
Laser Part. Beams
,
21
(
7
), pp.
311
315
.
24.
Griffond
,
J.
,
Gréa
,
B.-J.
, and
Soulard
,
O.
,
2015
, “
Numerical Investigation of Self-Similar Unstably Stratified Homogeneous Turbulence
,”
ASME J. Turbul.
,
16
(
2
), pp.
167
183
.
25.
Grinstein
,
F. F.
,
Margolin
,
L. G.
, and
Rider
,
W. J.
,
2007
,
Implicit Large Eddy Simulation: Computing Turbulent Fluid Dynamics
,
Cambridge University
, Cambridge, UK.
26.
Zhou
,
Y.
,
2010
, “
Renormalization Group Theory for Fluid and Plasma Turbulence
,”
Phys. Rep.
,
488
(
1
), pp.
1
49
.
27.
Lesieur
,
M.
,
2008
,
Turbulence in Fluids
, Fluid Mechanics and Its Applications Series,
Springer
, Berlin.
28.
Chen
,
S.
,
Doolen
,
G.
,
Herring
,
J. R.
,
Kraichnan
,
R. H.
,
Orszag
,
S. A.
, and
She
,
Z. S.
,
1993
, “
Far-Dissipation Range of Turbulence
,”
Phys. Rev. Lett.
,
70
(
20
), pp.
3051
3054
.
29.
Canuto
,
V. M.
,
Dubovikov
,
M. S.
, and
Dienstfrey
,
A.
,
1997
, “
A Dynamical Model for Turbulence. IV. Buoyancy-Driven Flows
,”
Phys. Fluids
,
9
(
7
), pp.
2118
2131
.
30.
Zhou
,
Y.
,
Robey
,
H. F.
, and
Buckingham
,
A. C.
,
2003
, “
Onset of Turbulence in Accelerated High-Reynolds-Number Flow
,”
Phys. Rev. E
,
67
(
5
), p.
056305
.
31.
Hanazaki
,
H.
, and
Hunt
,
J. C. R.
,
1996
, “
Linear Processes in Unsteady Stably Stratified Turbulence
,”
J. Fluid Mech.
,
318
(
6
), pp.
303
337
.
32.
Gréa
,
B.-J.
,
2013
, “
The Rapid Acceleration Model and the Growth Rate of a Turbulent Mixing Zone Induced by Rayleigh–Taylor Instability
,”
Phys. Fluids
,
25
(
1
), p.
015118
.
33.
Johnson
,
B. M.
, and
Schilling
,
O.
,
2011
, “
Reynolds‐Averaged Navier–Stokes Model Predictions of Linear Instability. i: Buoyancy- and Shear-Driven Flows
,”
J. Turbul.
,
12
(36), pp.
1
38
.
34.
Mueschke
,
N. J.
, and
Schilling
,
O.
,
2009
, “
Investigation of Rayleigh–Taylor Turbulence and Mixing Using Direct Numerical Simulation With Experimentally Measured Initial Conditions. II. Dynamics of Transitional Flow and Mixing Statistics
,”
Phys. Fluids
,
21
(
1
), p. 014107.
35.
Schilling
,
O.
,
2010
, “
Rayleigh–Taylor Turbulent Mixing: Synergy Between Simulations, Experiments, and Modeling
,”
12th International Workshop on the Physics of Compressible Turbulent Mixing
, Moscow.
36.
Schilling
,
O.
, and
Mueschke
,
N. J.
,
2010
, “
Analysis of Turbulent Transport and Mixing in Transitional Rayleigh–Taylor Unstable Flow Using Direct Numerical Simulation Data
,”
Phys. Fluids
,
22
(
10
), p. 105102.
37.
Souffland
,
D.
,
Soulard
,
O.
, and
Griffond
,
J.
,
2014
, “
Modeling of Reynolds Stress Models for Diffusion Fluxes Inside Shock Waves
,”
ASME J. Fluids Eng.
,
136
(
9
), p. 091102.
38.
Schwarzkopf
,
J. D.
,
Livescu
,
D.
,
Gore
,
R. A.
,
Rauenzahn
,
R. M.
, and
Ristorcelli
,
J. R.
,
2011
, “
Application of a Second-Moment Closure Model to Mixing Processes Involving Multicomponent Miscible Fluids
,”
ASME J. Turbul.
,
12
(
49
), pp.
1
35
.
39.
Watteaux
,
R.
,
2012
, “
Détection des grandes structures turbulentes dans les couches de mélange de type Rayleigh–Taylor en vue de la validation de modèles statistiques turbulents bi-structure
,” Ph.D. thesis, Thèse de doctorat en Science de l'Ecole Normale Supérieure de Cachan, Cachan.
40.
Gréa
,
B.-J.
,
2015
, “
The Dynamics of the k ε Mix Model Toward its Self-Similar Rayleigh–Taylor Solution
,”
ASME J. Turbul.
,
16
(
2
), pp.
184
202
.
41.
Schiestel
,
R.
,
2008
,
Modeling and Simulation of Turbulent Flows
,
Wiley
, New York.
42.
Banerjee
,
A.
,
Gore
,
R. A.
, and
Andrews
,
M. J.
,
2010
, “
Development and Validation of a Turbulent-Mix Model for Variable-Density and Compressible Flows
,”
Phys. Rev. E
,
82
(
4
), p.
046309
.
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