The development of a continuous turbulence model that is suitable for representing both the subgrid scale stresses in large eddy simulation and the Reynolds stresses in the Reynolds averaged Navier-Stokes formulation is described. A recursion approach is used to bridge the length scale disparity from the cutoff wave number to those in the energy-containing range. The proposed model is analyzed in conjunction with direct numerical simulations of Kolmogorov flows.

1.
Speziale
,
C. G.
, 1991, “
Analytical Methods for the Development of Reynolds Stress Closures in Turbulence
,”
Annu. Rev. Fluid Mech.
0066-4189,
23
, pp.
107
157
.
2.
Yakhot
,
V.
,
Orszag
,
S. A.
,
Thangam
,
S.
,
Gatski
,
T. B.
, and
Speziale
,
C. G.
, 1992, “
Development of Turbulence Models for Shear Flows by a Double-Expansion Technique
,”
Phys. Fluids A
0899-8213,
4
, pp.
1510
1524
.
3.
Gatski
,
T. B.
, and
Speziale
,
C. G.
, 1993, “
On Explicit Algebraic Stress Models for Complex Turbulent Flows
,”
J. Fluid Mech.
0022-1120,
254
, pp.
59
78
.
4.
Zhou
,
Y.
,
Vahala
,
G.
, and
Thangam
,
S.
, 1994, “
Development of a Turbulence Model Based on Recursion Renormalization Group Theory
, ”
Phys. Rev. E
1063-651X,
49
, pp.
5195
5206
.
5.
Thangam
,
S.
,
Wang
,
X.
, and
Zhou
,
Y.
, 1999, “
Development of a Turbulence Model Based on the Energy Spectrum for Flows Involving Rotation
,”
Phys. Fluids
1070-6631,
11
, pp.
2225
2234
.
6.
Smagorinsky
,
J.
, 1963, “
General Circulation Experiments With the Primitive Equations, Part I: The Basic Experiment
,”
Mon. Weather Rev.
0027-0644,
91
, pp.
99
164
.
7.
Bardina
,
J.
,
Ferziger
,
J. H.
, and
Reynolds
,
W. C.
, 1983, “
Improved Turbulence Models Based on Large Eddy Simulations Homogeneous, Incompressible Turbulent Flows
,” Stanford University Technical Report TF-19.
8.
Germano
,
M.
,
Piomelli
,
U.
,
Moin
,
P.
, and
Cabot
,
W. H.
, 1991, “
A Dynamic Subgrid-Scale Eddy Viscosity Model
,”
Phys. Fluids A
0899-8213,
3
, pp.
1760
1765
.
9.
Hussaini
,
M. Y.
, 1998, “
On Large Eddy Simulation of Compressible Flows
,” AIAA Paper 98-2802, 29th Fluid Dynamics Conference, Albuquerque, NM.
10.
Speziale
,
C. G.
, 1998a, “
Turbulence Modeling for Time-Dependent RANS and VLES: A Review
,”
AIAA J.
0001-1452,
36
, pp.
173
184
.
11.
Speziale
,
C. G.
, 1998b, “
A Combined Large-Eddy Simulation and Time-Dependent RANS Capability for High-Speed Compressible Flows
,”
J. Sci. Comput.
0885-7474,
13
, pp.
253
274
.
12.
Hussaini
,
M. Y.
,
Speziale
,
C. G.
, and
Woodruff
,
S. L.
, 2002, “
Continuous Models: Variants of LES
,” 14th US Natl. Congress Theor. App. Mech., Blacksburg, VA.
13.
Woodruff
,
S. L.
,
Seiner
,
J. M.
, and
Hussaini
,
M. Y.
, 2000, “
Grid-Size Dependence Considerations for Subgrid-Scale Models for LES of Kolmogorov flows
,”
AIAA J.
0001-1452,
38
, pp.
600
604
.
14.
Borue
,
V.
, and
Orszag
,
S. A.
, 1996, “
Numerical Study of Three-Dimensional Kolmogorov Flow at High Reynolds Numbers
,”
J. Fluid Mech.
0022-1120,
306
, pp.
293
314
.
15.
Shebalin
,
J. V.
, and
Woodruff
,
S. L.
, 1997, “
Kolmogorov Flow in Three Dimensions
,”
Phys. Fluids
1070-6631,
9
, pp.
164
170
.
16.
Speziale
,
C. G.
, 1987, “
On Nonlinear K‐l and K‐ε Models of Turbulence
,”
J. Fluid Mech.
0022-1120,
178
, pp.
459
475
.
17.
Hur
,
N.
,
Thangam
,
S.
, and
Speziale
,
C. G.
, 1990, “
Numerical Study of Turbulent Secondary Flows in Curved Ducts
,”
ASME J. Fluids Eng.
0098-2202,
112
, pp.
205
211
.
18.
Zhou
,
Y.
,
Vahala
,
G.
, and
Hossain
,
M.
, 1988, “
Renormalization Group for Eddy Viscosity in Subgrid Modeling
,”
Phys. Rev. A
1050-2947,
73
, pp.
2590
2598
.
19.
Zhou
,
Y.
, and
Vahals
,
G.
, 1993, “
Renormalization-Group Estimates of Transport Coefficients in the Advection of a Passive Scalar by Incompressible Turbulence
,”
Phys. Rev. E
1063-651X,
48
, pp.
4387
4398
.
20.
Kraichnan
,
R. H.
, 1976, “
Eddy Viscosity in Two and Three Dimensions
,”
J. Atmos. Sci.
0022-4928,
33
, pp.
1521
1536
.
21.
Kraichnan
,
R. H.
, 1987a, “
Kolmogorov’s Constant and Local Interactions
,”
Phys. Fluids
0031-9171,
30
, pp.
1583
1585
.
22.
Kraichnan
,
R. H.
, 1987b, “
An Interpretation of the Yakhot-Orszag Turbulence Theory
,”
Phys. Fluids
0031-9171,
30
, pp.
2400
2405
.
23.
Yoshizawa
,
A.
, 1984, “
Statistical Analysis of the Derivation of the Reynolds Stress From Its Eddy-Viscosity Representation
,”
Phys. Fluids
0031-9171,
27
, pp.
1377
1387
.
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