Modeling Multi-point Correlations in Wall-Bounded Turbulence

  • Robert D. Moser
  • Amitabh Bhattacharya
  • Nicholas Malaya
Part of the ERCOFTAC Series book series (ERCO, volume 14)

Abstract

In large eddy simulation (LES), one is generally not interested in the large-scale or filtered quantities computed in the simulation, but rather the corresponding characteristics of the underlying real turbulence. One approach to reconstructing the statistics of turbulence from the filtered statistics of an LES is to employ models for the small separation multi-point velocity correlations, which can be parameterized using the statistics of the LES. This has been employed to good effect in isotropic turbulence, but to employ this technique for near-wall turbulent shear flows requires a model for the anisotropy and inhomogeneity in the correlations. Here we explore the use of multi-point correlation models in LES modeling and reconstruction, and propose a anisotropy/inhomogeneity model for the two-point second-order correlation.

Keywords

Large Eddy Simulation Isotropic Turbulence Inertial Range Velocity Correlation Turbulent Shear Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The financial support of the National Science Foundation, the Air Force Office of Scientific Research and the National Aeronautics and Space Administration are gratefully acknowledged. In addition, we would like to thank Profs. Javier Jimenez and Ron Adrian for many helpful discussions of near-wall turbulence.

References

  1. 1.
    Adrian, R.: On the role of conditional averages in turbulence theory. In: Zakin, J., Patterson, G. (eds.) Turbulence in Liquids, pp. 323–332. Science Press, Princeton (1977) Google Scholar
  2. 2.
    Adrian, R.: Stochastic estimation of sub-grid scale motions. Appl. Mech. Rev. 43(5), 214–218 (1990) CrossRefGoogle Scholar
  3. 3.
    Adrian, R., Jones, B., Chung, M., Hassan, Y., Nithianandan, C., Tung, A.: Approximation of turbulent conditional averages by stochastic estimation. Phys. Fluids 1(6), 992–998 (1989) CrossRefGoogle Scholar
  4. 4.
    Arad, I., L’vov, V.S., Procaccia, I.: Correlation functions in isotropic and anisotropic turbulence: the role of the symmetry group. Phys. Rev. E 59(6), 6753–6765 (1999). doi: 10.1103/PhysRevE.59.6753 MathSciNetCrossRefGoogle Scholar
  5. 5.
    Bhattacharya, A., Kassinos, S.C., Moser, R.D.: Representing anisotropy of two-point second-order turbulence velocity correlations using structure tensors. Phys. Fluids 20(10) (2008). doi: 10.1063/1.3005818
  6. 6.
    Biferale, L., Lohse, D., Mazzitelli, I., Toschi, F.: Probing structures in channel flow through SO(3) and SO(2) decomposition. J. Fluid Mech. 452, 39–59 (2002) MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Cambon, C., Rubinstein, R.: Anisotropic developments for homogeneous shear flows. Phys. Fluids 18(8) (2006) Google Scholar
  8. 8.
    Chang, H., Moser, R.D.: An inertial range model for the three-point third-order velocity correlation. Phys. Fluids 19, 105,111 (2007) Google Scholar
  9. 9.
    Del Álamo, J., Jiménez, J., Zandonade, P., Moser, R.: Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144 (2004) MATHCrossRefGoogle Scholar
  10. 10.
    Frisch, U.: Turbulence: The Legacy of A.N. Kolmogorov. Cambridge University Press, Cambridge (1995) MATHGoogle Scholar
  11. 11.
    Kassinos, S., Reynolds, W., Rogers, M.: One-point turbulence structure tensors. J. Fluid Mech. 428, 213–248 (2001) MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Kolmogorov, A.N.: The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. C. R. Acad. Sci. USSR 30, 301 (1941) Google Scholar
  13. 13.
    Langford, J.A., Moser, R.D.: Optimal LES formulations for isotropic turbulence. J. Fluid Mech. 398, 321–346 (1999) MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Langford, J.A., Moser, R.D.: Breakdown of continuity in large-eddy simulation. Phys. Fluids 11, 943–945 (2001) Google Scholar
  15. 15.
    Misra, A., Pullin, D.I.: A vortex-based subgrid model for large-eddy simulation. Phys. Fluids 9, 2443–2454 (1997) MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Moser, R.D., Zandonade, P.S., Vedula, P., Malaya, N., Chang, H., Bhattacharya, A., Haselbacher, A.: Theoretically based optimal large-eddy simulation. Phys. Fluids 21(10) (2009) Google Scholar
  17. 17.
    Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000) MATHCrossRefGoogle Scholar
  18. 18.
    Sirovich, L., Smith, L., Yakhot, V.: Energy spectrum of homogeneous and isotropic turbulence in the far dissipation range. Phys. Rev. Lett. 72, 344–347 (1994) CrossRefGoogle Scholar
  19. 19.
    Vedula, P., Moser, R.D., Zandonade, P.S.: On the validity of quasi-normal approximation in turbulent channel flow. Phys. Fluids 17, 055,106 (2005) CrossRefGoogle Scholar
  20. 20.
    Voelkl, T., Pullin, D.I., Chan, D.C.: A physical-space version of the stretched-vortex subgrid-stress model for large-eddy simulation. Phys. Fluids 13, 1810–1825 (2000) MathSciNetCrossRefGoogle Scholar
  21. 21.
    Volker, S., Venugopal, P., Moser, R.D.: Optimal large eddy simulation of turbulent channel flow based on direct numerical simulation statistical data. Phys. Fluids 14, 3675 (2002) CrossRefGoogle Scholar
  22. 22.
    Zandonade, P.S., Langford, J.A., Moser, R.D.: Finite volume optimal large-eddy simulation of isotropic turbulence. Phys. Fluids 16, 2255–2271 (2004) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Robert D. Moser
    • 1
  • Amitabh Bhattacharya
    • 2
  • Nicholas Malaya
    • 1
  1. 1.University of Texas at AustinAustinUSA
  2. 2.University of PittsburghPittsburghUSA

Personalised recommendations