Recent experimental and direct numerical simulation data of two-dimensional, isothermal wall-bounded incompressible turbulent flows indicate that Reynolds-number effects are not only present in the outer layer but are also quite noticeable in the inner layer. The effects are most apparent when the turbulence statistics are plotted in terms of inner variables. With recent advances made in Reynolds-stress and near-wall modeling, a near-wall Reynolds-stress closure based on a recently proposed quasi-linear model for the pressure strain tensor is used to analyse wall-bounded flows over a wide range of Reynolds numbers. The Reynolds number varies from a low of 180, based on the friction velocity and pipe radius/channel half-width, to 15406, based on momentum thickness and free stream velocity. In all the flow cases examined, the model replicates the turbulence statistics, including the Reynolds-number effects observed in the inner and outer layers, quite well. Furthermore, the model reproduces the correlation proposed for the location of the peak shear stress and an appropriately defined Reynolds number, and the variations of the near-wall asymptotes with Reynolds numbers. It is conjectured that the ability of the model to replicate the asymptotic behavior of the near-wall flow is most responsible for the correct prediction of the Reynolds-number effects.

1.
Anderson, E. C., and Lewis, C. H., 1971, “Laminar or Turbulent Boundary Layer Flows of Perfect Gases or Reacting Gas Mixtures in Chemical Equilibrium,” NASA Contractor Report 1893.
2.
Andreopoulos, J., Durst, F., Jovanovic, J. and Zaric, Z., 1984, “Influence of Reynolds Number on Characteristics of Turbulent Wall Boundary Layers,” Experiments in Fluids, Vol. 2, 7–16.
3.
Bandyopadhyay
P. R.
and
Gad-el-Hak
M.
,
1994
, “
Reynolds Number Effects in Wall-Bounded Turbulent Flows
,”
Applied Mechanics Review
, Vol.
47
,
307
365
.
4.
Coles, D. E., 1962, The Turbulent Boundary Layer in a Compressible Fluid, Report R-403-PR, Rand Corporation, Santa Monica, CA.
5.
Demuren
A. O.
and
Sarkar
S.
,
1993
, “
Perspective: Systematic Study of Reynolds Stress Closure Models in the Computations of Plane Channel Flows
,”
ASME JOURNAL OF FLUIDS ENGINEERING
, Vol.
115
, pp.
5
12
.
6.
Durst, F., Jovanovic, J., and Sender, J., 1993, “Detailed Measurements of the Near Wall Region of Turbulent Pipe Flows,” Proceedings of the 9th Symposium on Turbulent Shear Flows, Kyoto, Japan, Paper No. 2.2.
7.
Huser
A.
and
Biringen
S.
,
1993
, “
Direct Numerical Simulation of Turbulent Flow in a Square Duct
,”
Journal of Fluid Mechanics
, Vol.
257
, pp.
65
95
.
8.
Karniadakis
E. G.
and
Orszag
S. A.
,
1993
, “
Nodes, Modes, and Flow Codes
,”
Physics Today
Vol.
46
, No.
3
,
34
42
.
9.
Karlsson, R. I. and Johansson, T. G., 1988, “LDV Measurements of Higher Order Moments of Velocity Fluctuations in a Turbulent Boundary Layer,” Laser Anemometry in Fluid Mechanics, D. F. G. Durao et al., eds., Ladoan-Instituto Superior Tecnico, Portugal, pp. 273–289.
10.
Kim
J.
,
1989
, “
On the Structure of Pressure Fluctuations in Simulated Turbulent Channel Flow
,”
Journal of Fluid Mechanics
, Vol.
205
, pp.
421
451
.
11.
Kim, J., 1991, Private communication.
12.
Kim
J.
,
Moin
P.
, and
Moser
R. D.
,
1987
, “
Turbulence Statistics in Fully Developed Channel Flow at Low Reynolds Number
,”
Journal of Fluid Mechanics
, Vol.
177
, pp.
133
186
.
13.
Klebanoff, P. S., 1955, Characteristics of Turbulence in a Boundary Layer with Zero Pressure Gradient, NACA Report 1247.
14.
Kolmogorov, A. N., 1941, “The Local Structure of Turbulence in an Incompressible Viscous Fluid for Very Large Reynolds Numbers,” Comptes Rendus Academy of Science, U.S.S.R. 30, 301–305 (Translation, Turbulence, Classic Papers on Statistical Theory, S. K. Friedlander & L. Topper, Interscience, 1961).
15.
Kristoffersen
R.
,
Bech
K. H.
and
Andersson
H. I.
,
1993
, “
Numerical Study of Turbulent Plane Couette Flow at Low Reynolds Number
,”
Applied Scientific Research
, Vol.
51
, pp.
337
343
.
16.
Lai
Y. G.
, and
So
R. M. C.
,
1990
, “
On Near-Wall Turbulent Flow Modeling
.”
Journal of Fluid Mechanics
, Vol.
221
, pp.
641
673
.
17.
Laufer, J., 1954, “The Structure of Turbulence in Fully-Developed Pipe Flow,” NACA Report 1174.
18.
Launder
B. E.
,
Reece
G. J.
, and
Rodi
W.
,
1975
, “
Progress in the Development of a Reynolds Stress Turbulence Closure
,”
Journal of Fluid Mechanics
, Vol.
68
, pp.
537
566
.
19.
Launder
B. E.
and
Reynolds
W. C.
,
1983
, “
Asymptotic Near-Wall Stress Dissipation Rates in a Turbulent Flow
,”
Physics of Fluids
, Vol.
26
, pp.
1157
1158
.
20.
Mellor
G. L.
and
Gibson
D. M.
,
1966
, “
Equilibrium Turbulent Boundary Layers
,”
Journal of Fluid Mechanics
, Vol.
24
, pp.
225
253
.
21.
Millikan, C. B., 1939, “A Critical Discussion of Turbulent Flow in Channels and Circular Pipes,” Proceedings of the Fifth International Congress on Applied Mechanics, Wiley, New York, pp. 386–392.
22.
Moser
R. D.
and
Moin
P.
,
1987
, “
The Effects of Curvature in Wall-Bounded Turbulent Flows
,”
Journal of Fluid Mechanics
, Vol.
175
, pp.
479
510
.
23.
Perry
A. E.
and
Abell
C. J.
,
1975
, “
Scaling Laws for Pipe-Flow Turbulence
,”
Journal of Fluid Mechanics
, Vol.
67
, pp.
257
271
.
24.
Purtell
L. P.
,
Klebanoff
P. S.
and
Buckley
F. T.
,
1981
, “
Turbulent Boundary Layer at Low Reynolds Number
,”
The Physics of Fluids
, Vol.
24
, pp.
802
811
.
25.
Schildknecht
M.
,
Miller
J. A.
and
Meier
G. E. A.
,
1979
, “
The Influence of Suction on the Structure of Turbulence in Fully-Developed Pipe Flow
,”
Journal of Fluid Mechanics
, Vol.
90
, pp.
67
107
.
26.
Simpson
R. L.
,
1970
, “
Characteristics of Turbulent Boundary Layers at Low Reynolds Numbers With and Without Transpiration
,”
Journal of Fluid Mechanics
, Vol.
42
, pp.
769
802
.
27.
So, R. M. C., Aksoy, H., Sommer, T. P. and Yuan, S. P., 1994a, “Development of a Near-Wall Reynolds-Stress Closure Based on the SSG Model for the Pressure Strain,” NASA Contractor Report 4618.
28.
So
R. M. C.
,
Zhang
H. S.
,
Gatski
T. B.
and
Speziale
C. G.
,
1994
b, “
On Logarithmic Laws for Compressible Turbulent Boundary Layers
,”
AIAA Journal
, Vol.
32
, pp.
2162
2168
.
29.
Spalart
P. R.
,
1988
, “
Direct Simulation of a Turbulent Boundary Layer up to Rθ = 1410
,”
Journal of Fluid Mechanics
, Vol.
187
, pp.
61
98
.
30.
Speziale
C. G.
,
Sarkar
S.
, and
Gatski
T. B.
,
1991
, “
Modeling the Pressure-Strain Correlation of Turbulence: An Invariant Dynamical Systems Approach
,”
Journal of Fluid Mechanics
, Vol.
227
, pp.
245
272
.
31.
Sreenivasan, K. R., 1988, “A Unified View of the Origin and Morphology of the Turbulent Boundary Layer Structure,” Turbulence Management and Relaminarization, eds., H. W. Liepmann and R. Narasimha, Springer-Verlag, pp. 37–61.
32.
Wei
T.
and
Willmarth
W. W.
,
1989
, “
Reynolds-Number Effects on the Structure of a Turbulent Channel Flow
,”
Journal of Fluid Mechanics
, Vol.
204
, pp.
57
95
.
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