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High Reynolds Number Wall-Bounded Turbulence and a Proposal for a New Eddy-Based Model

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Turbulence and Interactions

Part of the book series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design ((NNFM,volume 110))

Abstract

We propose a model for turbulent wall-bounded flows based on new understanding of the turbulent structure. Specifically, we identify three basic eddy motions: (1) the Large-Scale Motions (LSMs) which are related to the vortex packets defined by Head and Bandyopadhyay (1981) and Adrian et al. (2000); (2) the Very Large-Scale Motions (VLSMs) interpreted by Liu et al. (2001) and Balakumar and Adrian (2007) in terms of a concatenation of the outer layer bulges and by Monty et al. (2007) in terms of the meandering “superstructures” observed in pipe, channel and boundary layers; and (3) the streaks associated with longitudinal vortex-like structures in the near-wall region, as identified by Kline et al. (1967). The new model maps the attributes of each eddy type in physical space to wavenumber space. Experimental data are then used to determine the scaling behavior of the three basic eddy motions in wavenumber space, and the scaling behavior of the Reynolds stress behavior is recovered b! y integrating over all wavenumbers.

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References

  1. Adrian, R.C., 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 

  2. Balakumar, B.J., Adrian, R.J.: Large- and very-large-scale motions in channel and boundary-layer flows. Phil. Trans. R. Soc. A 365, 665–681 (2007)

    Article  MATH  Google Scholar 

  3. Bailey, S.C.C., Hultmark, M., Smits, A.J., Schultz, M.P.: Azimuthal structure of turbulence in high Reynolds number pipe flow. J. Fluid Mech. 615, 121–138 (2008)

    Article  MATH  Google Scholar 

  4. Del Álamo, J.C., Jiménez, J., Zandonade, P., Moser, R.D.: Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144 (2004)

    Article  MATH  Google Scholar 

  5. Dussauge, J.P., Smits, A.J.: Characteristic scales for energetic eddies in turbulent supersonic boundary layers. Experimental Thermal and Fluid Science 14(1) (1997)

    Google Scholar 

  6. Fernando, E.M., Smits, A.J.: The kinematics of simple vortex loop arrays, AIAA Paper 88-3657. In: First National Fluid Dynamics Conference, Cincinnati, Ohio, July 24-28 (1988)

    Google Scholar 

  7. Ganapathisubramani, B., Longmire, E.K., Marusic, I.: Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478, 35–46 (2003)

    Article  MATH  Google Scholar 

  8. Guala, M., Hommema, S.E., Adrian, R.J.: Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521–542 (2006)

    Article  MATH  Google Scholar 

  9. Head, M.R., Bandyopadhyay, P.R.: New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 297–338 (1981)

    Article  Google Scholar 

  10. Hutchins, N., Ganapathisubramani, B., Marusic, I.: Dominant spanwise Fourier modes and the existence of very large scale coherence in turbulent boundary layers. In: Proc. 15th Australasian Fluid Mechanics Conference, Sydney, Australia (2004)

    Google Scholar 

  11. Hutchins, N., Marusic, I.: Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28 (2007a)

    Article  MATH  Google Scholar 

  12. Hutchins, N., Marusic, I.: Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. A 365, 647–664 (2007b)

    Article  MATH  Google Scholar 

  13. Kim, K.C., Adrian, R.J.: Very large-scale motion in the outer layer. Phys. Fluids 11(2), 417–422 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  14. Kline, S.J., Reynolds, W.C., Schraub, F.A., Runstadler, P.W.: The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773 (1967)

    Article  Google Scholar 

  15. Liu, Z., Adrian, R.J., Hanratty, T.J.: Large-scale modes of turbulent channel flow: transport and structure. J. Fluid Mech. 448, 53–80 (2001)

    Article  MATH  Google Scholar 

  16. Lundgren, T.S.: Strained spiral vortex model for turbulent ne structure. Phys. Fluids 25, 2193–2203 (1982)

    Article  MATH  Google Scholar 

  17. Marusic, I., Uddin, M., Perry, A.E.: Similarity law for the streamwise turbulence intensity in zero-pressure-gradient turbulent boundary layers. Phys. Fluids 9(12), 3718–3726 (1997)

    Article  Google Scholar 

  18. Marusic, I., Kunkel, G.J.: Streamwise turbulence intensity formulation for flat-plate boundary layers. Phys. Fluids 15(8), 2461–2464 (2003)

    Article  Google Scholar 

  19. Meinhart, C.D., Adrian, R.J.: On the existence of uniform momentum zones in a turbulent boundary layer. Phys. Fluids 7(4), 694–696 (1995)

    Article  Google Scholar 

  20. Misra, A., Pullin, D.I.: A vortex-based subgrid stress model for large-eddy simulation. Phys. Fluids 9, 2443–2454 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  21. Monty, J.P., Stewart, J.A., Williams, R.C., Chong, M.S.: Large-scale features in turbulent pipe and channel flows. J. Fluid Mech. 589, 147–156 (2007)

    Article  MATH  Google Scholar 

  22. Morrison, J.F., McKeon, B.J., Jiang, W., Smits, A.J.: Scaling of the streamwise velocity component in turbulent pipe flow. J. Fluid Mech. 508, 99–131 (2004)

    Article  MATH  Google Scholar 

  23. Nickels, T.B., Marusic, I., Hafez, S.M., Hutchins, N., Chong, M.S.: Some predictions of the attached eddy model for a high Reynolds number boundary layer Phil. Trans. R. Soc. Lond. A 365, 807–822 (2007)

    Article  MATH  Google Scholar 

  24. Perry, A.E., Henbest, S.M., Chong, M.S.: An experimental study of the turbulence structure in smooth- and rough- wall boundary layers. J. Fluid Mech. 177, 437–466 (1986)

    Article  MathSciNet  Google Scholar 

  25. Perry, A.E., Li, J.D.: Experimental support for the attached-eddy hypothesis in zero-pressure- gradient turbulent boundary layers. J. Fluid Mech. 218, 405–438 (1990)

    Article  Google Scholar 

  26. Perry, A.E., Marusic, I., Jones, M.B.: On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients. J. Fluid Mech. 461, 61–91 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  27. Tennekes, H., Lumley, J.L.: A First Course in Turbulence. The MIT Press, Cambridge (1972)

    Google Scholar 

  28. Tomkins, C.D., Adrian, R.J.: Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 37–74 (2003)

    Article  MATH  Google Scholar 

  29. Tomkins, C.D., Adrian, R.J.: Energetic spanwise modes in the logarithmic layer of a turbulent boundary layer. J. Fluid Mech. 545, 141–162 (2005)

    Article  MATH  Google Scholar 

  30. Townsend, A.A.: The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press, Cambridge (1976)

    MATH  Google Scholar 

  31. Zhou, J., Adrian, R.J., Balachandar, S., Kendall, T.M.: Mechanisms for generating coherent packets of hairpin vortices in channel flows. J. Fluid Mech. 387, 353–396 (1999)

    Article  MATH  MathSciNet  Google Scholar 

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Smits, A.J. (2010). High Reynolds Number Wall-Bounded Turbulence and a Proposal for a New Eddy-Based Model. In: Deville, M., Lê, TH., Sagaut, P. (eds) Turbulence and Interactions. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14139-3_6

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  • DOI: https://doi.org/10.1007/978-3-642-14139-3_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14138-6

  • Online ISBN: 978-3-642-14139-3

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