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ADDITIONAL TECHNICAL PAPERS

On the Criterion for the Determination Transition Onset and Breakdown to Turbulence in Wall-Bounded Flows

[+] Author and Article Information
J. Jovanović, M. Pashtrapanska

Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg, Cauerstrasse 4, D-91058, Germany

J. Fluids Eng 126(4), 626-633 (Sep 10, 2004) (8 pages) doi:10.1115/1.1779663 History: Received March 12, 2003; Revised March 02, 2004; Online September 10, 2004
Copyright © 2004 by ASME
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References

Hinze, J. O., 1975, “Turbulence,” 2nd ed., McGraw-Hill, New York.
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.
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.
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.
Laufer,  J., 1975, “New Trends in Experimental Turbulence Research,” Annu. Rev. Fluid Mech., 7, pp. 307–326.
Laufer, J., 1982, “Flow Instability and Turbulence,” In Structure of Turbulence in Heat and Mass Transfer, Ed. by Z. Zarić, Hemisphere.
Fischer,  M., Jovanović,  J., and Durst,  F., 2000, “Near-Wall Behavior of Statistical Properties in Turbulent Flows,” Int. J. Heat Fluid Flow, 21, pp. 471–479.
Fischer, M., 1999, “Turbulente wandbebundene Strömungen bei kleinen Reynoldszhalen,” Ph.D. Thesis, Universität Erlangen-Nürnberg, pp. 63–65.
Chou,  P. Y., 1945, “On the Velocity Correlation and the Solution of the Equation of Turbulent Fluctuation,” Q. Appl. Math., 3, pp. 38–54.
Lumley,  J. L., and Newman,  G., 1977, “The Return to Isotropy of Homogeneous Turbulence,” J. Fluid Mech., 82, pp. 161–178.
Kolovandin,  B. A., and Vatutin,  I. A., 1972, “Statistical Transfer Theory in Nonhomogeneous Turbulence,” Int. J. Heat Mass Transfer, 15, pp. 2371–2383.
Jovanović,  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.
Jovanović, J., Ye, Q.-Y., and Durst, F., 1992, “Refinement of the Equation for the Determination of Turbulent Micro-Scale,” Universität Erlangen-Nürnberg Rep., LSTM 349/T/92.
Jovanović,  J., Otić,  I., and Bradshaw,  P., 2003, “On the Anisotropy of Axisymmetric Strained Turbulence in the Dissipation Range,” J. Fluids Eng., 125, pp. 401–413.
Tennekes, H., and Lumley, J. L., 1972, “A First Course in Turbulence,” MIT Press, Cambridge, MA.
Fischer,  M., Jovanović,  J., and Durst,  F., 2001, “Reynolds Number Effects in the Near-Wall Region of Turbulent Channel Flows,” Phys. Fluids, 13, pp. 1755–1767.
Jovanović, J., 2004, “The Statistical Dynamics of Turbulence,” Springer-Verlag, Berlin.
Lumley,  J. L., 1978, “Computational Modeling of Turbulent Flows,” Adv. Appl. Mech., 18, pp. 123–176.
Jovanović,  J., and Otić,  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.
Schumann,  U., 1977, “Realizability of Reynolds Stress Turbulence Models,” Phys. Fluids, 20, pp. 721–725.
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.
Schlichting, H., 1968, Boundary-Layer Theory, 6th edn., McGraw-Hill, New York.
Becker, S., 1999, personal communication.
Kolmogorov,  A. N., 1941, “On Degeneration of Isotropic Turbulence in an Incompressible Viscous Liquid,” Dokl. Akad. Nauk SSSR, 6, pp. 538–540.
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.
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.
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.
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.
Jovanović,  J., Hillerbrand,  R., and Pashtrapanska,  M., 2001, “Mit statistischer DNS-Datenanalyse der Enstehung von Turbulenz auf der Spur,” KONWIHR Quartl,31, pp. 6–8.
Jovanović,  J., and Hillerbrand,  R., 2003, “On the Chief Peculiarity of the Velocity Fluctuations in Wall-Bounded Flows,” J. Fluid Mech., submitted.
Jovičić, N., 2003, personal communication.
Seidl, V., 1997, “Entwicklung and Anwendung eines Parallelen Finite-Volume-Verfahrens zur Strömungssimulation auf unstrukturierten Gittern mit lokaler Verfeinerung,” Institut für Schiffbau, Universität Hamburg, Bericht Nr. 585.
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.
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.
Durst,  F., Fischer,  M., Jovanović,  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.
Orszag,  S. A., and Kells,  C., 1980, “Transition to Turbulence in Plane Poiseuille and Plane Couette Flow,” J. Fluid Mech., 96, pp. 159–205.
Alavyoon,  F., Henningson,  D. S., and Alfredsson,  P. H., 1986, “Turbulence Spots in Plane Poiseuille Flow-Flow Visualization,” Phys. Fluids, 29, pp. 1328–1331.
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.
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.
Laufer, J., 1953, “The Structure of Turbulence in Fully Developed Pipe Flow,” NACA TN, 2954.
Durst,  F., Jovanović,  J., and Sender,  J., 1995, “LDA Measurements in the Near-Wall Region of a Turbulent Pipe Flow,” J. Fluid Mech., 295, pp. 305–355.
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.
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.
Spalart,  P. R., 1986, “Numerical Study of Sink-Flow Boundary Layers,” J. Fluid Mech., 172, pp. 307–328.
Spalart,  P. R., 1988, “Direct Simulation of a Turbulent Boundary Layer up to Rϴ=1410,” J. Fluid Mech., 187, pp. 61–98.

Figures

Grahic Jump Location
Anisotropy-invariant mapping of the disturbances generated by small, two-dimensional roughness element in a initially laminar flat plate boundary layer from Fischer, Jovanović and Durst 7: (a) specially designed two-component laser-Doppler system for near-wall measurements; (b) schematic of flat plate arrangement in the wind tunnel with layout of two different beam configurations which allowed measurements of all components of the “apparent” stresses of the disturbances; (c) traces of the joint variations of invariants IIa and IIIa across the anisotropy invariant map confirm the two-component nature of the disturbances
Grahic Jump Location
Intermittency (Υ) measurements of the transition process from laminar to turbulent states at the channel centerline from Fischer 8: (a) channel flow test section; (b) transition due to the natural disturbances is accompanied by large hysteresis in the experimental data; (c) transition due to the two-component disturbances implies that for such disturbances the critical Reynolds number may be found by extrapolation data of a fully developed turbulent flow if the transition criterion is known
Grahic Jump Location
Anisotropy invariant map and the asymptotic forms for the unknown correlations involved in the equations for the “apparent” stresses
Grahic Jump Location
Anisotropy invariant mapping of turbulence in a channel flow. Data, which correspond to low Reynolds numbers, show the trend as Re→(Re)crit towards the theoretical solution valid for small, neutrally stable, statistically stationary, axisymmetric disturbances (Jovanović, Hillerbrand and Pashtrapanska 29). The shading indicates the area occupied by the stable disturbances: for such disturbances a laminar regime in the boundary layer will persist up to very high Reynolds numbers.
Grahic Jump Location
Turbulent dissipation rate at the wall normalized with the wall shear velocity and the kinematic viscosity of the flow medium versus the anisotropy of turbulence IIa at the wall. A best-line fit through the numerical data extrapolates fairly well the expected trend ε→0 as the one-component limit (IIa=2/3) is approached.
Grahic Jump Location
Cross plot of Rλ versus Reτ1/2 for fully developed turbulent pipe and channel flows at low Reynolds numbers
Grahic Jump Location
Cross plot of Rλ versus Reτ1/2 for turbulent boundary layer at low Reynolds numbers

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