For thermal and magnetic convection at very high Rayleigh and Hartman numbers, which are inaccessible to the conventional large eddy simulation, we propose a time-dependent Reynolds-average-Navier-Stokes (T-RANS) approach in which the large-scale deterministic motion is fully resolved by time and space solution, whereas the unresolved stochastic motion is modeled by a “subscale” model for which an one-point RANS closure is used. The resolved and modeled contributions to the turbulence moments are of the same order of magnitude and in the near-wall regions the modeled heat transport becomes dominant, emphasizing the role of the subscale model. This T-RANS approach, with an algebraic stress/flux subscale model, verified earlier in comparison with direct numerical simulation and experiments in classic Rayleigh-Bénard convection, is now expanded to simulate Rayleigh-Bénard (RB) convection at very high Ra numbers—at present up to O(1016)—and to magnetic convection in strong uniform magnetic fields. The simulations reproduce the convective cell structure and its reorganization caused by an increase in Ra number and effects of the magnetic field. The T-RANS simulations of classic RB indicate expected thinning of both the thermal and hydraulic wall boundary layer with an increase in the Ra number and an increase in the exponent of the NuRan correlation in accord with recent experimental findings and Kraichnan asymptotic theory.

1.
Ha Minh
,
H.
, and
Kourta
,
A.
, 1993, “
Semi-Deterministic Turbulence Modelling for Flows Dominated by Strong Organized Structures
,”
Proceedings of the Ninth International Symposium on Turbulent Shear Flows
,
Kyoto
, Japan, pp.
10.5
-1–10.5-
6
.
2.
Aubrun
,
S.
,
Kao
,
P. L.
,
Ha Minh
,
H.
, and
Boisson
,
H.
, 1999, “
The Semi-Deterministic Approach as Way to Study Coherent Structures: Case of a Turbulent Flow Behind a Backward-Facing Step
,”
Engineering Turbulence Modelling and Experiments
,
W.
Rodi
and
D.
Laurence
, eds.,
Elsevier Science
,
Amsterdam
, pp.
491
499
.
3.
Speziale
,
C. G.
, 1998, “
Turbulence Modeling for Time-Dependent RANS and VLES: A Review
,”
AIAA J.
0001-1452,
36
(
2
), pp.
173
184
.
4.
Spalart
,
P. R.
, 1999, “
Strategies for Turbulence Modelling and Simulations
,”
Engineering Turbulence Modelling and Experiments 4
,
W.
Rodi
and
D.
Laurence
, eds.,
Elsevier Science
,
Amsterdam
, pp.
3
17
.
5.
Travin
,
A.
,
Shur
,
M.
,
Strelets
,
M.
, and
Spalart
,
P.
, 1999, “
Detached-Eddy Simulations Past a Circular Cylinder
,”
Flow, Turbul. Combust.
1386-6184,
63
, pp.
293
313
.
6.
Nikitin
,
N. V.
,
Nicoud
,
F.
,
Wasistho
,
B.
,
Squires
,
K. D.
, and
Spalart
,
P. R.
, 2000, “
An Approach to Wall Modeling in Large-Eddy Simulations
,”
Phys. Fluids
1070-6631,
12
(
7
), pp.
1629
1632
.
7.
Kenjereš
,
S.
, and
Hanjalić
,
K.
, 1999a, “
Transient Analysis of Rayleigh-Bénard Convection with a RANS Model
,”
Int. J. Heat Fluid Flow
0142-727X,
20
, pp.
329
340
.
8.
Kenjereš
,
S.
, and
Hanjalić
,
K.
, 2000a, “
Convective Rolls and Heat Transfer in Finite-Length Rayleigh-Bénard Convection: A Two-Dimensional Study
,”
Phys. Rev. E
1063-651X,
62
(
2
), pp.
7987
7998
.
9.
Kenjereš
,
S.
, and
Hanjalić
,
K.
, 2002, “
A Numerical Insight into Flow Structure in Ultra-Turbulent Thermal Convection
,”
Phys. Rev. E
1063-651X,
66
(
3
), pp.
036307
.
10.
Hanjalić
,
K.
, and
Kenjereš
,
S.
, 2000a, “
T-RANS Simulation of Deterministic Eddy Structure in Flows Driven by Thermal Buoyancy and Lorentz Force
,”
Flow, Turbul. Combust.
1386-6184,
66
, pp.
427
451
.
11.
Hanjalić
,
K.
, and
Kenjereš
,
S.
, 2000b, “
Reorganization of Turbulence Structure in Magnetic Rayleigh-Bénard Convection: A T-RANS Study
,”
J. Turbul.
1468-5248,
1
(
8
), pp.
1
22
.
12.
Hanjalić
,
K.
, and
Kenjereš
,
S.
, 2001, “
VLES of Flows Driven by Buoyancy and Magnetic Field
,”
Modern Simulation Strategies for Turbulent Flows
,
B. G.
Geurts
, eds.,
Edwards
,
Philadelphia
, pp.
223
246
.
13.
Hanjalić
,
K.
, and
Kenjereš
,
S.
, 2002, “
Simulation of Coherent Structures in Buoyancy-Driven Flows with Single-Point Turbulence Closure Models
,”
Closure Strategies for Turbulent and Transitional Flows
,
B. E.
Launder
and
N.
Sandham
, eds.,
Cambridge University Press
,
Cambridge, UK
, pp.
659
684
.
14.
Cioni
,
S.
,
Ciliberto
,
S.
, and
Sommeria
,
J.
, 1997, “
Strongly Turbulent Rayleigh-Bénard Convection in Mercury: Comparison with Results at Moderate Prandtl Number
,”
J. Fluid Mech.
0022-1120,
335
, pp.
111
140
.
15.
Eidson
,
T. M.
, 1985, “
Numerical Simulation of the Turbulent Rayleigh-Bénard Problem Using Subgrid Model
,”
J. Fluid Mech.
0022-1120,
158
, pp.
245
268
.
16.
Hanjalić
,
K.
,
Hadžiabdić
,
M.
,
Temmerman
,
L.
, and
Leschziner
,
M.
, 2004, “
Merging LES and RANS Strategies: Zonal or Seamless Coupling?
,”
Direct and Large-Eddy Simulations V
,
R.
Friedrich
,
B.
Geurts
, and
O.
Métais
, eds.,
Kluwer Academic
,
Dordrecht, The Netherlands
, pp.
451
464
.
17.
Kenjereš
,
S.
, and
Hanjalić
,
K.
, 2000b, “
On the Implementation of Lorentz Force in Turbulence Closure Models
,”
Int. J. Heat Fluid Flow
0142-727X,
21
(
3
), pp.
329
337
.
18.
Kerr
,
M. R.
, 1996, “
Rayleigh Number Scaling in Numerical Convection
,”
J. Fluid Mech.
0022-1120,
310
, pp.
139
179
.
19.
Wörner
,
M.
, 1994, “
Direkte Simulation Turbulenter Rayleigh-Bénard Konvektion in Flussigem Natrium
,” Dissertation, University of Karlsruhe, KfK 5228, Kernforschungszentrum Karlsruhe.
20.
Grötzbach
,
G.
, 1983, “
Spatial Resolution Requirement for Direct Numerical Simulation of Rayleigh-Bénard Convection
,”
J. Comput. Phys.
0021-9991,
49
, pp.
241
264
.
21.
Kenjereš
,
S.
, and
Hanjalić
,
K.
, 1999b, “
Identification and Visualization of Coherent Structures in Rayleigh-Bénard Convection with a Time-Dependent RANS
,”
J. Visualization
1343-8875,
2
(
2
), pp.
169
176
.
22.
Chavanne
,
X.
,
Chilla
,
F.
,
Castaing
,
B.
,
Hebral
,
B.
,
Chabaud
,
B.
, and
Chaussy
,
J.
, 1997, “
Observation of the Ultimate Regime in Rayleigh-Benard Convection
,”
Phys. Rev. Lett.
0031-9007,
79
(
19
), pp.
3648
3651
.
23.
Chavanne
,
X.
,
Chilla
,
F.
,
Chabaud
,
B.
,
Castaing
,
B.
, and
Hebral
,
B.
, 2001, “
Turbulent Rayleigh-Benard Convection in Gaseous and Liquid He
,”
Phys. Fluids
1070-6631,
13
(
5
), pp.
1300
1320
.
24.
Roche
,
P. E.
,
Castaing
,
B.
,
Chabaud
,
B.
, and
Hebral
,
B.
, 2001, “
Observation of the 1∕2 Power Law in Rayleigh-Benard Convection
,”
Phys. Rev. E
1063-651X,
63
(
4
), pp.
045303
.
25.
Glazier
,
J. A.
,
Segawa
,
T.
,
Naert
,
A.
, and
Sano
,
M.
, 1999, “
Evidence Against ‘Ultrahard’ Thermal Turbulence at Very High Rayleigh Numbers
,”
Nature (London)
0028-0836,
398
(
6725
), pp.
307
310
.
26.
Niemela
,
J. J.
,
Skrbek
,
L.
,
Srenivassan
,
K. R.
, and
Donnely
,
R. J.
, 2000, “
Turbulent Convection at Very High Rayleigh Numbers
,”
Nature (London)
0028-0836,
404
(
6780
), pp.
837
840
.
27.
Theerthan
,
S. A.
, and
Arakeri
,
J. H.
, 1998, “
A Model for Near-Wall Dynamics in Turbulent Rayleigh-Bénard Convection
,”
J. Fluid Mech.
0022-1120,
373
, pp.
221
253
.
28.
Siggia
,
E. D.
, 1994, “
High Rayleigh Number Convection
,”
Annu. Rev. Fluid Mech.
0066-4189,
26
, pp.
137
168
.
29.
Kerr
,
R. M.
, and
Herring
,
J. R.
, 2000, “
Prandtl Number Dependence of Nusselt Number in Direct Numerical Simulations
,”
J. Fluid Mech.
0022-1120,
419
, pp.
325
344
.
30.
Belmonte
,
A.
,
Tilgner
,
A.
, and
Libchaber
,
A.
, 1994, “
Temperature and Velocity Boundary-Layers in Turbulent Convection
,”
Phys. Rev. E
1063-651X,
50
(
1
), pp.
269
275
.
31.
Xin
,
Y. B.
, and
Xia
,
K Q
, 1997, “
Boundary Layer Length Scales in Convective Turbulence
,”
Phys. Rev. E
1063-651X,
56
(
3
), pp.
3010
3015
.
32.
Zhou
,
S. Q.
, and
Xia
,
K. Q.
, 2001, “
Spatially Correlated Temperature Fluctuations in Turbulent Convection
,”
Phys. Rev. E
1063-651X,
63
(
4
), pp.
046308
.
33.
Cioni
,
S.
,
Chaumat
,
S.
, and
Sommeria
,
J.
, 2000, “
Effect of a Vertical Magnetic Field on Turbulent Rayleigh-Bénard Convection
,”
Phys. Rev. E
1063-651X,
62
(
4
), pp.
R4520
.
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