This article reviews the literature on the theory of wall turbulence and the correlation of data from the viewpoint of composite expansions. As an interpretive tool, composite expansions have been used explicitly since the time of the introduction of the wake law. Nevertheless, the articles of the pioneer turbulence researchers, Prandtl and von Ka´rma´n for example, can be interpreted in this more contemporary light. Although the review begins with the work of the founding fathers, it is comprehensive and includes the modern high-quality experiments, “direct numerical simulations,” and analyses that have been published in this century. Additionally, this review organizes and consolidates the theory as it offers a unifying way to think about wall turbulence. There are 119 reference cited.

Issue Section:
Review Articles
Keywords:
boundary layer turbulence, flow simulation, wakes, pipe flow, channel flow, numerical analysis, reviews
Topics:
Boundary layers, Composite materials, Reynolds number, Stress, Turbulence, Wakes, Pipe flow, Flow (Dynamics), Pipes, Channel flow, Pressure
1.
Prandtl, L., 1976, Aerodynamic Theory, Durand, W. F. ed., Peter Smith, Gloucester, MA, Vol. III.
2.
1976, Aerodynamic Theory, Durand, W. F. ed., Peter Smith, Gloucester, MA, Vol. III.
3.
Rotta, J., 1950, Uber die Theorie der turbulenten Grenzschichten, Mitt. Max-Plank-Inst., Go¨ttingen, No. 1; translated as; “On the Theory of Turbulent Boundary Layers,” NACA TM No. 1344, 1953.
4.
Clauser
,
F. H.
,
1956
, “
The Turbulent Boundary Layer
,”
Adv. Appl. Mech.
,
4
, pp.
1
–
51
.
5.
Coles, D., and Hirst, 1968, Proceedings; Computation of Turbulent Boundary Layers-1968 AFOSR-IFP-Stanford Conference, Vol. II, Mechanical Engineering Department, Stanford University, CA.
1.
Yaglom
,
A.
,
1979
, “
Similarity Laws for Constant-Pressure and Pressure-Gradient Turbulent Wall Flows
,”
Annu. Rev. Fluid Mech.
,
11
, pp.
505
–
540
;
2.
2001, Course 1 in “New Trends in Turbulence,” M. Lesieur, A. Yaglom, and F. David, eds., Springer-Verlag, Berlin.
1.
Gad-el-Hak
,
M.
, and
Bandyophadhyay
,
P.
,
1994
, “
Reynolds Number Effects in Wall Bounded Turbulent Flows
,”
Appl. Mech. Rev.
,
47
, p.
307
307
.
2.
Fernholtz
,
H. H.
, and
Findley
,
J. P.
,
1996
, “
The Incompressible Zero-Pressure-Gradient Turbulent Boundary Layer: An Assessment of the Data
,”
Prog. Aerosp. Sci.
,
32
, pp.
245
–
311
.
3.
Isakson
,
A.
,
1937
, “
On the Formula for the Velocity Distribution Near Walls
,”
Zh. Eksp. Teor. Fiz.
,
7
, p.
919
919
.
4.
Millikan, C. B., 1938, “A Critical Discussion of Turbulent Flows in Channels and Circular Tubes,” Proceedings Fifth Int. Conference Appl. Mech., Cambridge MA, p. 386.
5.
Mellor
,
G. L.
, and
Gibson
,
D. M.
,
1966
, “
Equilibrium Turbulent Boundary Layers
,”
J. Fluid Mech.
,
24
, pp.
225
–
253
.
6.
Busch
,
W. B.
, and
Fendel
,
F. E.
,
1972
, “
Asymptotic Analysis of Turbulent Channel and Boundary Layer Flow
,”
J. Fluid Mech.
,
56
, p.
657
657
.
7.
Deriat
,
E.
, and
Guiraud
,
J.-P.
,
1986
, “
On the Asymptotic Description of Turbulent Boundary Layers
,”
J. Mec. Theor. Appl.
,
5
, pp.
109
–
140
.
8.
Walker, J. D. A., 1998, “Turbulent Boundary Layers II, Further Developments,” in Recent Advances in Boundary Layer Theory, A. Kluwick, ed., Springer, New York, pp. 145–161.
9.
Bjorgum, O., 1961, “On the Application of Asymptotic Expansions to Turbulent Shear Flow,” Mat. Naturv. Serie 1960, No. 18, Arbok University Press, Bergen, Norway.
10.
Tennekes
,
H.
,
1968
, “
Outline of a Second-Order Theory of Turbulent Pipe Flow
,”
AIAA J.
,
6
, pp.
1735
–
1740
.
11.
Yajnik
,
K. S.
,
1970
, “
Asymptotic Theory of Turbulent Shear Flows
,”
J. Fluid Mech.
,
42
, pp.
411
–
427
.
12.
Mellor
,
G. L.
,
1972
, “
The Large Reynolds Number, Asymptotic Theory of Turbulent Boundary Layers
,”
J. Fluid Mech.
,
10
, pp.
851
–
873
.
13.
Afzal
,
N.
,
1976
, “
Millikan’s Argument at Moderately Large Reynolds Numbers
,”
Phys. Fluids
,
19
, pp.
600
–
602
.
14.
Buschmann
,
M.
, and
Gad-el-Hak
,
M.
,
2003
, “
The Generalized Logarithmic Law and Its Consequences
,”
AIAA J.
,
41
, p.
40
40
.
15.
Tennekes, H., and Lumley, J. L., 1972, A First Course in Turbulence, MIT Press, Cambridge, MA.
16.
Gersten, K., 1987, “Some Contributions to the Asymptotic Theory for Turbulent Flows,” Proc. 2nd Int. Symposium. on Transport Phenomena in Turbulent Shear Flows, Toyko, pp. 201–214.
17.
Gersten, K., and Herwig, H., 1992, Stro¨mungsmechanik, Verlag Vieweg, Wiesbaden.
18.
Schlichting, H., and Gersten, K., 2000, Boundary Layer Theory, 8th ed., McGraw-Hill, New York.
19.
Barenblatt, G. I., 1979, Similarity, Self Similarity, and Intermediate Asymptotics, Plenum Press, New York.
20.
Barenblatt
,
G. I.
,
1993a
, “
Scaling Laws for Fully Developed Turbulent Shear Flows. Part 1: Basic Hypothesis and Analysis
,”
J. Fluid Mech.
,
248
, p.
513
513
.
21.
Barenblatt
,
G. I.
, and
Prostokishin
,
V. M.
,
1993
, “
Scaling Laws for Fully Developed Turbulent Shear Flows. Part 2: Processing Experimental Data
,”
J. Fluid Mech.
,
248
, p.
521
521
.
22.
Barenblatt, G. I., 1996, Scaling, Self Similarity, and Intermediate Asymptotics, Revised ed., Cambridge University Press, Cambridge.
23.
Barenblatt
,
G. I.
,
Chorin
,
A. J.
, and
Prostokishin
V. M.
,
1997a
, “
Scaling Laws for Fully Developed Turbulent Flow in Pipes: Discussion of Experimental Data
,”
Proc. Natl. Acad. Sci. U.S.A.
,
94
, p.
773
773
.
24.
Barenblatt
,
G. I.
,
Chorin
,
A. J.
, and
Prostokishin
,
V. M.
,
1997b
, “
Scaling Laws in Fully Developed Turbulent Pipe Flow
,”
Appl. Mech. Rev.
,
50
, p.
413
413
.
25.
Barenblatt
,
G. I.
,
Chorin
,
A. J.
,
Hald
,
O. H.
, and
Prostokishin
,
V. M.
,
1997c
, “
Structure of the Zero-Pressure-Gradient Turbulent Boundary Layer
,”
Proc. Natl. Acad. Sci. U.S.A.
,
94
, p.
7817
7817
.
26.
Barenblatt, G. I., Chorin, A. J., and Prostokishin, V. M., 2000a, “Analysis of Experimental Investigations of Self-Similar Intermediate Structures in Zero-Pressure-Gradient Boundary Layers at Large Reynolds Numbers,” UC Berkeley, Center for Pure and Applied Math, Report PAM 777, January 2000.
27.
Barenblatt
,
G. I.
,
Chorin
,
A. J.
, and
Prostokishin
,
V. M.
,
2000b
, “
Self-Similar Intermediate Structures in Turbulent Boundary Layers at Large Reynolds Numbers
,”
J. Fluid Mech.
,
410
, p.
263
263
.
28.
Barenblatt
,
G. I.
,
Chorin
,
A. J.
, and
Prostokishin
,
V. M.
,
2000c
, “
A Note on the Intermediate Region in Turbulent Boundary Layers
,”
Phys. Fluids
,
12
(
9
), p.
2159
2159
.
29.
George, W. K., Knecht, P., and Castillo, L., 1992, “Zero-Pressure-Gradient Turbulent Boundary Layer Revisited,” Proceedings of the Thirteenth Biennial Symposium on Turbulence, Rolla MO.
30.
George
,
W. K.
, and
Castillo
,
L.
,
1997
, “
Zero-Pressure-Gradient Turbulent Boundary Layer
,”
Appl. Mech. Rev.
,
50
, pp.
689
–
729
.
31.
George, W. K., Castillo, L., and Wosnik, M., 1997, “A-Theory for Turbulent Pipe and Channel Flows,” TAM Report No. 872 UILU-ENG-6033, University of Illinois, November 1997.
32.
Wosnik
,
M.
,
Castillo
,
L.
, and
George
,
W.
,
2000
, “
A Theory for Turbulent Pipe and Channel Flows
,”
J. Fluid Mech.
,
421
, p.
521
521
.
33.
von Ka´rma´n, T., 1930, Mechanische Aehnlichkeit und Turbulenz, Nachr. Ges. Wiss. Goettingen, p. 68.
34.
Schlichting, H., 1979, Boundary Layer Theory, McGraw-Hill, New York.
35.
Stanton
,
T. E.
, and
Pannel
,
J. R.
,
1914
, “
Similarity of Motion in Relation to the Surface Friction of Fluids
,”
Philos. Trans. R. Soc. London, Ser. A
,
214
, p.
199
199
.
36.
Coles
,
D.
,
1956
, “
The Law of the Wake in a Turbulent Boundary Layer
,”
J. Fluid Mech.
,
1
, pp.
191
–
226
.
37.
Oberlack
,
M.
,
2001
, “
A Unified Approach for Symmetries in Plane Parallel Turbulent Shear Flows
,”
J. Fluid Mech.
,
427
, pp.
299
–
328
.
38.
Lindgren, B., O¨sterlund, J. M., and Johansson, A. V., 2002, “Evaluation of Scaling Laws Derived From Lie Group Symmetries in Turbulent Boundary Layers,” AIAA Pap. 2002-1103.
39.
Van Dyke, M., 1975, Perturbation Methods in Fluid Mechanics, Parabolic Press, Stanford, CA.
40.
Hinch, E. J., 1991, Perturbation Methods, Cambridge University Press, Cambridge.
41.
Lagerstrom, P. A., 1989, “Matched Asymptotic Expansions,” Applied Mathematical Sciences, Springer-Verlag, Berlin, p. 76.
42.
Eckhaus, W., 1979, Asymptotic Analysis of Singular Perturbations, North-Holland, Amsterdam.
43.
Mauss
,
J.
, and
Cousteix
,
J.
,
2002
, “
Uniformly Valid Approximation for Singular Perturbation Problems and Matching Principle
,”
Comptes Rendus Me´canique
,
330
, p.
697
697
.
44.
Latta, G. E., 1951, “Singular Perturbation Problems,” Doctoral thesis, California Inistitute of Technology, Pasadena.
45.
Monkewitz, P., et al., 2001, Bulletin of the American Physical Society, Division Fluid Dynamics Meeting 2001.
46.
Cole, J. D., 1968, Perturbation Methods in Applied Mathematics, Ginn/Blaidsdell, Waltham MA.
47.
Zagarola
,
M. V.
, and
Smits
,
A. J.
,
1998
, “
Mean Flow Scaling of Turbulent Pipe Flow
,”
J. Fluid Mech.
,
373
, pp.
33
–
79
.
48.
Zagarola
,
M. V.
, and
Smits
,
A. J.
,
1997
, “
Scaling of the Mean Velocity Profile for Turbulent Pipe Flow
,”
Phys. Rev. Lett.
,
78
, p.
239
239
.
49.
Perry
,
A. E.
,
Hafez
,
S.
, and
Chong
,
M. S.
,
2001
, “
A Possible Reinterpretation on the Princeton Superpipe Data
,”
J. Fluid Mech.
,
439
, pp.
395
–
401
.
50.
Panton, R. L., 1996, “Incompressible Flow,” 2nd ed., Wiley-Interscience, New York.
51.
Panton
,
R. L.
,
1997
, “
A Reynolds Stress Function for Wall Layers
,”
ASME J. Fluids Eng.
,
119
, p.
325
325
.
52.
Musker
,
A. J.
,
1979
, “
Explicit Expression for the Smooth Wall Velocity Distribution in a Turbulent Boundary Layer
,”
AIAA J.
,
17
, p.
655
655
.
53.
Clauser
,
F. H.
,
1954
, “
Turbulent Boundary Layers in Adverse Pressure Gradients
,”
J. Aeronaut. Sci.
,
21
, pp.
91
–
108
.
54.
O¨sterlund, J. M., 1999, “Experimental Studies of Zero-Pressure-Gradient Turbulent Boundary Layer Flows,” Doctoral thesis, Royal Institute of Technology, Stockholm.
55.
Lewkowicz
,
A. K.
,
1982
, “
An Improved Universal Wake Function for Turbulent Boundary Layers and Some of Its Consequences
,”
Z. Flugwiss. Weltraumforsch.
,
6
, pp.
261
–
266
.
56.
Ludwieg, H., 1949, “Ein Gera¨t zur Messung der Wandschubspannung turbulenten Reibungsschichten,” Ing.-Arch. 17,288; translated as “Instrument for Measuring the Wall Shearing Stress of Turbulent Boundary Layer,” NACA TM 1284 (1950).
57.
Ludwieg, H., and Tillmann, W., 1949, “Untersuchungen u¨ber die Wandschubspannung in Turbulenten Reibungsschichten,” Ing.-Arch. 17,288-299; translated as “Investigations of the Wall Shearing Stress in Turbulent Boundary Layer,” NACS TM 1285 (1950).
58.
Townsend, A. A., 1956, The Structure of Turbulent Shear Flow, 2nd ed., Cambridge University Press, Cambridge.
59.
Townsend
,
A. A.
,
1961
, “
Equilibrium Layers and Wall Turbulence
,”
J. Fluid Mech.
,
11
, p.
97
97
.
60.
O¨sterlund
,
J. M.
,
Johansson
,
A. V.
,
Nagib
,
H. M.
, and
Hites
,
M. H.
,
2000
, “
A Note on the Intermediate Region in Turbulent Boundary Layers
,”
Phys. Fluids
,
12
, p.
2159
2159
.
61.
Ross
,
D.
, and
Roberson
,
J. M.
,
1951
, “
A Superposition Analysis of the Turbulent Boundary Layer in an Adverse Pressure Gradient
,”
ASME J. Appl. Mech.
,
18
, p.
95
95
.
62.
Finley
,
P. J.
,
Phoe
,
K. C.
, and
Poh
,
C. J.
,
1966
, “
Velocity Measurements in a Thin Turbulent Layer
,”
Houille Blanche
,
21
, p.
713
713
.
63.
Spalart
,
P. R.
,
1988
, “
Direct Numerical Simulation of a Turbulent Boundary Layer up to ReΘ=1410,
”
J. Fluid Mech.
,
187
, p.
61
61
.
64.
Wilcox, D. C., 1998, Turbulence Modeling for CFD, 2nd ed., DCW Industries, La Can˜ada, CA.
65.
Bradshaw
,
P.
,
1967b
, “
The Turbulence Structure of Equilibrium Boundary Layers
,”
J. Fluid Mech.
,
29
, p.
625
625
.
66.
East, L. F., Sawyer, W. G., and Nash, C. R., 1979, “An Investigation of the Structure of Equilibrium Turbulent Boundary Layers,” Royal Aircraft Establishment, Tech. Report 79040, April 1979.
67.
Skare
,
P. E.
, and
Krogstad
,
P.
,
1994
, “
A Turbulent Equilibrium Boundary Layer Near Separation
,”
J. Fluid Mech.
,
272
, p.
319
319
.
68.
DeGraff
,
D. B.
, and
Eaton
,
J. K.
,
2000
, “
Reynolds Number Scaling of the Flat Plate Turbulent Boundary Layer
,”
J. Fluid Mech.
,
422
, pp.
319
–
346
.
69.
Panton, R. L., 2001, “The Law-of-the-Wake for the Reynolds Stress in a Boundary Layer,” Proceedings Turbulence and Shear Flow Phenomena 2, KTH Stockholm, June 2001.
70.
Panton, R. L., 2002a, “Reynolds Number Effect for the Reynolds Stress in a Boundary Layer,” AIAA Pap. 2002-1105.
71.
Bradshaw
,
P.
, and
Koh
,
Y. M.
,
1981
, “
A Note on Poisson’s Equation for Pressure in a Turbulent Flow
,”
Phys. Fluids
,
24
, p.
777
777
.
72.
Lilley, G. M., and Hodgson, T. H., 1960, AGARD Report No. 276.
73.
Bradshaw
,
P.
,
1967a
, “
Irrotational Fluctuations Near a Turbulent Boundary Layer
,”
J. Fluid Mech.
,
27
, p.
209
209
.
74.
Panton
,
R. L.
,
Goldman
,
A. L.
,
Lowery
R. L.
, and
Reischman
,
M. M.
,
1980
, “
Low-Frequency Pressure Fluctuations in Axisymmetric Turbulent Boundary Layers
,”
J. Fluid Mech.
,
97
, pp.
299
–
319
.
75.
Farabee
,
T. M.
, and
Casarella
,
M. J.
,
1991
, “
Spectral Features of Wall Pressure Fluctuations Beneath Turbulent Boundary Layers
,”
Phys. Fluids
,
3
, pp.
2410
–
2420
.
76.
Lofdahl
,
L.
,
Kalvesten
,
E.
, and
Stemm
,
G.
,
1996
, “
Small Silicon Pressure Transducers for Space-Time Correlation Measurements in a Flat Plate Boundary Layer
,”
ASME J. Fluids Eng.
,
118
, pp.
457
–
463
.
77.
Naguib
,
A. M.
,
Gravante
,
S. P.
, and
Wark
,
C. E.
,
1996
, “
Extraction of Turbulent Wall-Pressure Time Series Using Optimal Filtering
,”
Exp. Fluids
,
22
, pp.
14
–
22
.
78.
Klewicki, J. C., and Miner, H., 2002, “Wall Pressure Structure at High Reynolds Number,” Bulletin of the American Physical Society, Division Fluid Dynamics Meeting 2002, FH 001.
79.
Bradshaw
,
P.
,
1967c
, “
Inactive’ Motion and Pressure Fluctuations in Turbulent Boundary Layers
,”
J. Fluid Mech.
,
30
, p.
241
241
.
80.
Willmarth
,
W. W.
,
1975a
, “
Structure of Turbulent Boundary Layers
,”
Adv. Appl. Mech.
,
15
, pp.
159
–
254
.
81.
Willmarth
,
W. W.
,
1975b
, “
Pressure Fluctuations Beneath Turbulent Boundary Layers
,”
Annu. Rev. Fluid Mech.
,
7
, p.
13
13
.
82.
Willmarth
,
W. W.
, and
Yang
,
C. S.
,
1970
, “
Wall-Pressure Fluctuations Beneath Turbulent Boundary Layers on a Flat Plate and a Cylinder
,”
J. Fluid Mech.
,
11
, pp.
47
–
80
.
83.
Karangelen, C. C., Casarella, M. J., and Farabee, T. M., 1991b, “Wavenumber-Frequency Spectra of Turbulent Wall Pressure Fluctuations,” American Society of Mechanical Engineers Winter Annual Meeting, NCA-Vol. 11/FED-Vol. 130, pp. 37–44.
84.
Wills
,
J. A. B.
,
1970
, “
Measurements of the Wavenumber/Phase Velocity Spectrum of Wall Pressure Beneath a Turbulent Boundary Layer
,”
J. Fluid Mech.
,
45
, pp.
65
–
90
.
85.
Panton
,
R. L.
, and
Linebarger
,
J. H.
,
1974
, “
Wall Pressure Spectra Calculations for Equilibrium Boundary Layers
,”
J. Fluid Mech.
,
65
, pp.
261
–
287
.
86.
Panton, R. L., 1989, “Inner-Outer Structure of Wall-Pressure Correlation Function,” Near Wall Turbulence, Kline, S. J. and Afgan, N. H., eds., Hemisphere Press, New York, pp. 381–396.
87.
Panton
,
R. L.
, and
Robert
,
G.
,
1994
, “
The Wavenumber-Phase Velocity Representation for the Turbulent Wall-Pressure Spectrum
,”
ASME J. Fluids Eng.
,
116
, pp.
477
–
483
.
88.
O¨sterlund, J. M., and Johansson, A. V., 2001, “Turbulence Statistics of Zero Pressure Gradient Turbulent Boundary Layers” (unpublished).
89.
Nagib, H. M., and Hites, M. H., 1995, AIAA Pap. 95-0786.
90.
Hinze, J. O., 1975, Turbulence, McGraw-Hill, New York.
91.
Kaplan, S., 1967, Fluid Mechanics and Singular Perturbations: Collected Papers by Saul Kaplan, P. A. Lageerstrom, L. N. Howard, and C.-H. Liu, eds., Academic Press, New York.
92.
Zanoun, E., Nagib, H., Durst, F., and Monkewitz, P., 2002, “Higher Reynolds Number Channel Data and Their Comparison to Recent Asymptotic Theory,” AIAA Pap. 2002-1102.
93.
Smith, D. W., and Walker, J. H., 1958, “Skin-Friction Measurements in Incompressible Flow,” NACA TN 4231, March 1958.
94.
Winter, K. G., and Gaudet, L., 1973, “Turbulent Boundary Layer Studies at High Reynolds Numbers and Mach Numbers Between 0.2 and 2.8,” Aeronautical Research Council R & M No. 3712.
95.
Kim
,
J.
,
Moin
,
P.
, and
Moser
,
R. D.
,
1987
, “
Turbulence Statistics in Fully Developed Channel Flow at Low Reynolds Number
,”
J. Fluid Mech.
,
177
, pp.
133
–
139
.
96.
Moser
,
R. D.
,
Kim
,
J.
, and
Mansour
,
N. N.
,
1999
, “
Direct Numerical Simulation of Turbulent Channel Flow Up to Re_Tau=590
,”
Phys. Fluids
,
11
, p.
943
943
.
97.
Comte-Bellot, G., 1965, “Ecoulement Turbulent Entre Deux Parois Paralle`les,” Pub. Scient. et Tech. du Minist. de l’Air No. 419.
98.
den Toonder, J. M., and Nieuwstadt, F., 1997, “Reynolds Number Effects in a Pipe Flow for Low and Moderate Re,” Phys. Fluids, 1, p. 3398.
99.
O¨sterlund
,
J. M.
,
Johansson
,
A. V.
, and
Nagib
,
H. M.
,
2000
, “
Comment on a Note on the Intermediate Region in Turbulent Boundary Layers Phys. Fluids, 12, p. 2159”
,
Phys. Fluids
,
12
, p.
2360
2360
.
100.
Panton
,
R. L.
,
2002
, “
Evaluation of the Barenblatt-Chorin-Prostokishin Power Law for Turbulent Boundary Layers
,”
Phys. Fluids
,
14
, pp.
1806
–
1808
.
101.
Long
,
R. R.
, and
Chen
,
T.-C.
,
1981
, “
Experimental Evidence for the Existence of a Mesolater in Turbulent Systems
,”
J. Fluid Mech.
,
105
, pp.
19
–
59
.
102.
Afzal
,
N.
, and
Bush
,
W. B.
,
1985
, “
A Three-Layer Asymptotic Analysis of Turbulent Channel Flow
,”
Proc. Indian Acad. Sci.
,
94
, pp.
135
–
148
.
103.
Sreenivasan, K. R., and Sahay, A., 1997, in Self-Sustaining Mechanisms of Wall Turbulence, Panton, Ronald, L., ed., Computational Mechanics Publications, Southhampton, UK, Chap. 11.
104.
Antonia
,
R. A.
,
Teitel
,
M.
,
Kim
,
J.
, and
Browne
,
L. W. B.
,
1992
, “
Low Reynolds-Number Effects in a Fully Developed Turbulent Channel Flow
,”
J. Fluid Mech.
,
236
, pp.
579
–
605
.
105.
Harder
,
K. J.
, and
Tiederman
,
W. G.
,
1991
, “
Drag Reduction and Turbulent Structure in Two-Dimensional Channel Flow
,”
Philos. Trans. R. Soc. London, Ser. A
,
336
, pp.
19
–
28
.
106.
Wei
,
T.
, and
Willmarth
,
W. W.
,
1989
, “
Reynolds Number Effects on the Structure of a Turbulent Channel Flow
,”
J. Fluid Mech.
,
204
, pp.
57
–
64
.
1.
Kuroda, A., Kasagi, N., and Hirata, M., 1989, “A Direct Numerical Simulation of the Fully Developed Turbulent Channel Flow,” International Symposium on Computational Fluid Dynamics, Nagoya, pp. 1174–1179;
2.
also in 1990, Numerical Methods in Fluid Dynamics, M. Yasuhara et al., eds., Jap. Soc. Comp. Fluid Dyn., Vol. 2, pp. 1012–1017.
1.
Kuroda, A., Kasagi, N., and Hirata, M., 1990a, “A Direct Numerical Simulation of the Turbulent Flow Between Two Parallel Walls: Turbulence Characteristics Near the Wall Without Mean Shear,” 5th Symposium on Numerical Simulation of Turbulence, IIS of the University of Tokyo, pp. 1–5.
2.
Kasagi, N., Horiuti, K., Miyake, Y., Miyauchi, T., and Nagano, Y., 1992, “Direct Numerical Simulation Database of Turbulent Transport Phenomena,” by the Ministry of Education, Science and Culture, The University of Tokyo, Bunkyo-ku, Tokyo 113: http://www.thtlab.t.u-tokyo.ac.jp/.
3.
Andersson
,
H. I.
, and
Kristoffersen
,
R.
,
1992
, “
Statistics of Numerically Generated Turbulence
,”
Acta Appl. Math.
,
26
, pp.
293
–
314
.
4.
Gilbert, N., and Kleiser, L., 1991, “Turbulence Model Testing Withthe Aid of Direct Numerical Simulation Results,” Proc. of 8th Symposium on Turbulent Shear Flows, Paper 26-1, Munich, Sept. 9–11.
5.
Eggels
,
J. G. M.
,
Unger
,
F.
,
Weiss
,
M. H.
,
Westerweel
,
J.
,
Adrian
,
R. J.
,
Friedrich
,
R.
, and
Nieuwstadt
,
F. T. M.
,
1994
, “
Fully Developed Turbulent Pipe Flow: A Comparison Between Direct Numerical Simulation and Experiment
,”
J. Fluid Mech.
,
268
, pp.
175
–
209
.
6.
Eggels
,
J. G. M.
,
Westerweel
,
J.
,
Nieuwstadt
,
F. T. M.
, and
Adrian
,
R. J.
,
1993
, “
Direct Numerical Simulation of Turbulent Pipe Flow: A Comparison Between Simulation and Experiment at Low Re-Number
,”
Appl. Sci. Res.
,
51
, pp.
319
–
324
.
Copyright © 2005
 by ASME
You do not currently have access to this content.