Starting from the basic conservation laws of fluid flow, we investigated transition and breakdown to turbulence of a laminar flat plate boundary layer exposed to small, statistically stationary, two-component, three-dimensional disturbances. The derived equations for the statistical properties of the disturbances are closed using the two-point correlation technique and invariant theory. By considering the equilibrium solutions of the modeled equations, the transition criterion is formulated in terms of a Reynolds number based on the intensity and the length scale of the disturbances. The deduced transition criterion determines conditions that guarantee maintenance of the local equilibrium between the production and the viscous dissipation of the disturbances and therefore the laminar flow regime in the flat plate boundary layer. The experimental and numerical databases for fully developed turbulent channel and pipe flows at different Reynolds numbers were utilized to demonstrate the validity of the derived transition criterion for the estimation of the onset of turbulence in wall-bounded flows.
Issue Section:
Additional Technical Papers
1.
Hinze, J. O., 1975, “Turbulence,” 2nd ed., McGraw-Hill, New York.
2.
Kline
, S. J.
, Reynolds
, W. C.
, Schraub
, F. A.
, and Runstadler
, P. W.
, 1967
, “The Structure of Turbulent Boundary Layers
,” J. Fluid Mech.
, 30
, pp. 741
–773
.3.
Kim
, H. T.
, Kline
, S. J.
, and Reynolds
, W. C.
, 1971
, “The Production of Turbulence Near Smooth Wall in a Turbulent Boundary Layer
,” J. Fluid Mech.
, 50
, pp. 133
–160
.4.
Falco, R. E., 1978, “The Role of Outer Flow Coherent Motions in the Production of Turbulence Near a Wall,” In Coherent Structure of Turbulent Boundary Layer (ed. by C. R. Smith and D. E. Abbott), AFOSR/Lehigh University, pp. 448–461.
5.
Laufer
, J.
, 1975
, “New Trends in Experimental Turbulence Research
,” Annu. Rev. Fluid Mech.
, 7
, pp. 307
–326
.6.
Laufer, J., 1982, “Flow Instability and Turbulence,” In Structure of Turbulence in Heat and Mass Transfer, Ed. by Z. Zaric´, Hemisphere.
7.
Fischer
, M.
, Jovanovic´
, J.
, and Durst
, F.
, 2000
, “Near-Wall Behavior of Statistical Properties in Turbulent Flows
,” Int. J. Heat Fluid Flow
, 21
, pp. 471
–479
.8.
Fischer, M., 1999, “Turbulente wandbebundene Stro¨mungen bei kleinen Reynoldszhalen,” Ph.D. Thesis, Universita¨t Erlangen-Nu¨rnberg, pp. 63–65.
9.
Chou
, P. Y.
, 1945
, “On the Velocity Correlation and the Solution of the Equation of Turbulent Fluctuation
,” Q. Appl. Math.
, 3
, pp. 38
–54
.10.
Lumley
, J. L.
, and Newman
, G.
, 1977
, “The Return to Isotropy of Homogeneous Turbulence
,” J. Fluid Mech.
, 82
, pp. 161
–178
.11.
Kolovandin
, B. A.
, and Vatutin
, I. A.
, 1972
, “Statistical Transfer Theory in Nonhomogeneous Turbulence
,” Int. J. Heat Mass Transfer
, 15
, pp. 2371
–2383
.12.
Jovanovic´
, J.
, Ye
, Q.-Y.
, and Durst
, F.
, 1995
, “Statistical Interpretation of the Turbulent Dissipation Rate in Wall-Bounded Flows
,” J. Fluid Mech.
, 293
, pp. 321
–347
.13.
Jovanovic´, J., Ye, Q.-Y., and Durst, F., 1992, “Refinement of the Equation for the Determination of Turbulent Micro-Scale,” Universita¨t Erlangen-Nu¨rnberg Rep., LSTM 349/T/92.
14.
Jovanovic´
, J.
, Otic´
, I.
, and Bradshaw
, P.
, 2003
, “On the Anisotropy of Axisymmetric Strained Turbulence in the Dissipation Range
,” J. Fluids Eng.
, 125
, pp. 401
–413
.15.
Tennekes, H., and Lumley, J. L., 1972, “A First Course in Turbulence,” MIT Press, Cambridge, MA.
16.
Fischer
, M.
, Jovanovic´
, J.
, and Durst
, F.
, 2001
, “Reynolds Number Effects in the Near-Wall Region of Turbulent Channel Flows
,” Phys. Fluids
, 13
, pp. 1755
–1767
.17.
Jovanovic´, J., 2004, “The Statistical Dynamics of Turbulence,” Springer-Verlag, Berlin.
18.
Lumley
, J. L.
, 1978
, “Computational Modeling of Turbulent Flows
,” Adv. Appl. Mech.
, 18
, pp. 123
–176
.19.
Jovanovic´
, J.
, and Otic´
, I.
, 2000
, “On the Constitutive Relation for the Reynolds Stresses and the Prandtl-Kolmogorov Hypothesis of Effective Viscosity in Axisymmetric Strained Turbulence
,” J. Fluids Eng.
, 122
, pp. 48
–50
.20.
Schumann
, U.
, 1977
, “Realizability of Reynolds Stress Turbulence Models
,” Phys. Fluids
, 20
, pp. 721
–725
.21.
Taylor
, G. I.
, 1936
, “Statistical Theory of Turbulence. Part V. Effects of Turbulence on Boundary Layer. Theoretical Discussion of Relationship Between Scale of Turbulence and Critical Resistance of Spheres
,” Proc. R. Soc. London, Ser. A
, 156
, pp. 307
–317
.22.
Schlichting, H., 1968, Boundary-Layer Theory, 6th edn., McGraw-Hill, New York.
23.
Becker, S., 1999, personal communication.
24.
Kolmogorov
, A. N.
, 1941
, “On Degeneration of Isotropic Turbulence in an Incompressible Viscous Liquid
,” Dokl. Akad. Nauk SSSR
, 6
, pp. 538
–540
.25.
Moser
, R. D.
, Kim
, J.
, and Mansour
, N. N.
, 1999
, “Direct Numerical Simulation of Turbulent Channel Flow up to Reτ=590,
” Phys. Fluids
, 11
, pp. 943
–945
.26.
Antonia
, R. A.
, Teitel
, M.
, Kim
, J.
, and Browne
, L. W. B.
, 1992
, “Low-Reynolds Number Effects in a Fully Developed Channel Flow
,” J. Fluid Mech.
, 236
, pp. 579
–605
.27.
Kim
, J.
, Moin
, P.
, and Moser
, R. D.
, 1987
, “Turbulence Statistics in a Fully Developed Channel Flow at Low Reynolds Numbers
,” J. Fluid Mech.
, 177
, pp. 133
–166
.28.
Kuroda, A., Kasagi, N., and Hirata, M., 1993, “Direct Numerical Simulation of the Turbulent Plane Couette-Poiseulle Flows: Effect of Mean Shear on the Near Wall Turbulence Structures,” Proc. 9th Symp. on Turbulent Shear Flows, Kyoto, pp. 8.4.1–8.4.6.
29.
Jovanovic´
, J.
, Hillerbrand
, R.
, and Pashtrapanska
, M.
, 2001
, “Mit statistischer DNS-Datenanalyse der Enstehung von Turbulenz auf der Spur,”
KONWIHR Quartl
, 31
, pp. 6
–8
.30.
Jovanovic´
, J.
, and Hillerbrand
, R.
, 2003
, “On the Chief Peculiarity of the Velocity Fluctuations in Wall-Bounded Flows
,” J. Fluid Mech., submitted.31.
Jovicˇic´, N., 2003, personal communication.
32.
Seidl, V., 1997, “Entwicklung and Anwendung eines Parallelen Finite-Volume-Verfahrens zur Stro¨mungssimulation auf unstrukturierten Gittern mit lokaler Verfeinerung,” Institut fu¨r Schiffbau, Universita¨t Hamburg, Bericht Nr. 585.
33.
Gilbert, N., and Kleiser, L., 1991, “Turbulence Model Testing With the Aid of Direct Numerical Simulation Results,” Proc. Eighth Symp. on Turbulent Shear Flows, Munich, pp. 26.1.1–26.1.6.
34.
Horiuti, K., Miyake, Y., Miyauchi, T., Nagano, Y., and Kasagi, N., 1992, “Establishment of the DNS Database of Turbulent Transport Phenomena,” Rep. Grants-in-aid for Scientific Research, No. 02302043.
35.
Durst
, F.
, Fischer
, M.
, Jovanovic´
, J.
, and Kikura
, H.
, 1998
, “Methods to Set-up and Investigate Low Reynolds Number, Fully Developed Turbulent Plane Channel Flows
,” J. Fluids Eng.
, 120
, pp. 496
–503
.36.
Orszag
, S. A.
, and Kells
, C.
, 1980
, “Transition to Turbulence in Plane Poiseuille and Plane Couette Flow
,” J. Fluid Mech.
, 96
, pp. 159
–205
.37.
Alavyoon
, F.
, Henningson
, D. S.
, and Alfredsson
, P. H.
, 1986
, “Turbulence Spots in Plane Poiseuille Flow-Flow Visualization
,” Phys. Fluids
, 29
, pp. 1328
–1331
.38.
Carlson
, D. R.
, Widnall
, S. E.
, and Paeters
, M. F.
, 1982
, “A Flow-Visualization Study of Transition in Plane Poiseuille Flow
,” J. Fluid Mech.
, 121
, pp. 487
–505
.39.
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
.40.
Laufer, J., 1953, “The Structure of Turbulence in Fully Developed Pipe Flow,” NACA TN, 2954.
41.
Durst
, F.
, Jovanovic´
, J.
, and Sender
, J.
, 1995
, “LDA Measurements in the Near-Wall Region of a Turbulent Pipe Flow
,” J. Fluid Mech.
, 295
, pp. 305
–355
.42.
Reynolds
, O.
, 1883
, “An Experimental Investigation of the Circumstances Which Determine Whether the Motion of Water Shall be Direct or Sinuous, and the Law of Resistance in Parallel Channels
,” Philos. Trans. R. Soc. London
, 174
, pp. 935
–982
.43.
Monin, A. S., and Yaglom, A. M., 1997, Statistical Fluid Mechanics—Mechanics of Turbulence, Vol. I, Chapter 2, CTR Monograph, Stanford University, Stanford, CA, pp. 7–25.
44.
Spalart
, P. R.
, 1986
, “Numerical Study of Sink-Flow Boundary Layers
,” J. Fluid Mech.
, 172
, pp. 307
–328
.45.
Spalart
, P. R.
, 1988
, “Direct Simulation of a Turbulent Boundary Layer up to Rϴ=1410,
” J. Fluid Mech.
, 187
, pp. 61
–98
.Copyright © 2004
by ASME
You do not currently have access to this content.
