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Structural ensemble dynamics based closure model for wall-bounded turbulent flow

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Abstract

Wall-bounded turbulent flow involves the development of multi-scale turbulent eddies, as well as a sharply varying boundary layer. Its theoretical descriptions are yet phenomenological. We present here a new framework called structural ensemble dynamics (SED), which aims at using systematically all relevant statistical properties of turbulent structures for a quantitative description of ensemble means. A new set of closure equations based on the SED approach for a turbulent channel flow is presented. SED order functions are defined, and numerically determined from data of direct numerical simulations (DNS). Computational results show that the new closure model reproduces accurately the solution of the original Navier–Stokes simulation, including the mean velocity profile, the kinetic energy of the streamwise velocity component, and every term in the energy budget equation. It is suggested that the SED-based studies of turbulent structure builds a bridge between the studies of physical mechanisms of turbulence and the development of accurate model equations for engineering predictions.

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References

  1. Sreenivasan K.R., Antonia R.A.: The phenomenology of small-scale turbulence. Annu. Rev. Fluid. Mech. 29, 435–472 (1997)

    Article  MathSciNet  Google Scholar 

  2. She Z.S., Leveque E.: Universal scaling laws in fully-developed turbulence. Phys. Rev. Lett. 72(3), 336–339 (1994)

    Article  Google Scholar 

  3. She Z.S., Ren K., Lewis G.S., Swinney H.L.: Scalings and structures in turbulent Couette-Taylor flow. Phys. Rev. E 64, 016308 (2001)

    Article  Google Scholar 

  4. Baroud C.N., Plapp B.B., Swinney H.L., She Z.S.: Scaling in three-dimensional and quasi-two-dimensional rotating turbulent flows. Phys. Fluids 15(8), 2091–2104 (2003)

    Article  MathSciNet  Google Scholar 

  5. Ching E.S.C., Kwok C.Y.: Statistics of local tperature dissipation in high Rayleigh number convection. Phys. Rev. E 62(6), R7587–R7590 (2000)

    Article  Google Scholar 

  6. Sun C., Zhou Q., Xia K.Q.: Cascades of velocity and temperature fluctuations in buoyancy-driven thermal turbulence. Phys. Rev. Lett. 97(14), 144504 (2006)

    Article  Google Scholar 

  7. Zou Z.P., Zhu Y.J., Zhou M.D., She Z.S.: Hierarchical structures in a turbulent pipe flow. Fluid. Dyn. Res. 33(5–6), 493–508 (2003)

    Article  MATH  Google Scholar 

  8. Jiang X.Q., Gong H., Liu J.K., Zhou M.D., She Z.S.: Hierarchical structures in a turbulent free shear flow. J. Fluid Mech. 569, 259–286 (2006)

    Article  MATH  Google Scholar 

  9. She Z.S., Zhang Z.X.: Universal hierarchical symmetry for turbulence and general multi-scale fluctuation systems. Acta Mech. Sin. 25, 279–294 (2009)

    Article  Google Scholar 

  10. Pope S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  11. Robinson S.K.: Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639 (1991)

    Article  Google Scholar 

  12. Adrian R.J., Meinhart C.D., Tomkins C.D.: Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  13. Barenblatt G.I.: Scaling laws for fully developed turbulent shear flows. Part I. Basic hypotheses and analysis. J. Fluid Mech. 248, 513–520 (1993). doi:10.1017/S0022112093000874

    Article  MATH  MathSciNet  Google Scholar 

  14. Buschmann M.H., Gad-el-Hak M.: New mixing-length approach for the mean velocity profile of turbulent boundary layers. J. Fluids Eng. 127, 393–396 (2005)

    Article  Google Scholar 

  15. Wilcox D.C.: Turbulence Modeling for CFD, 3rd edn. DCW Industries, La Canada (2006)

    Google Scholar 

  16. Kim J., Moin P., Moser R.D.: Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166 (1987). doi:10.1017/S0022112087000892

    Article  MATH  Google Scholar 

  17. Moser R.D., Kim J., Mansour N.N.: Direct numerical simulation of turbulent channel flow up to Re τ = 590. Phys. Fluids 11, 943–945 (1999)

    Article  MATH  Google Scholar 

  18. Iwamoto, K., Suzuki, Y., Kasagi, N.: Database of fully developed channel flow, THTLAB Internal Report, No. ILR-0201 (2002) see http://www.thtlab.t.u-tokyo.ac.jp

  19. Bradshaw P., Ferriss D.H., Atwell N.P.: Calculation of boundary layer development using the turbulent energy equation. J. Fluid Mech. 28, 593–616 (1967). doi:10.1017/S0022112067002319

    Article  Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory for Turbulence and Complex Systems and Dept Mechanical and Aerospace Engineering, College of Engineering, Peking University, 100871, Beijing, China

    Zhen-Su She, Ning Hu & You Wu

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  1. Zhen-Su She
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  2. Ning Hu
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  3. You Wu
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Correspondence to Zhen-Su She.

Additional information

The project was supported by the National Natural Science Foundation of China (90716008) and the MOST under 973 project (2009CB724100).

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She, ZS., Hu, N. & Wu, Y. Structural ensemble dynamics based closure model for wall-bounded turbulent flow. Acta Mech Sin 25, 731–736 (2009). https://doi.org/10.1007/s10409-009-0282-2

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  • DOI: https://doi.org/10.1007/s10409-009-0282-2

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