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Accounting for Scale-Dependence in the Dynamic Smagorinsky Model

  • Charles Meneveau
  • Fernando Porté-Agel
  • Marc B. Parlange
Conference paper
Part of the Fluid Mechanics and its Applications book series (FMIA, volume 54)

Abstract

The dynamic model has been very successful in Large-Eddy Simulation of a variety of turbulent flows. The model makes the crucial assumption that the coefficient is scale-invariant, which is reasonable in the inertial range of turbulence. Surprisingly, the dynamic model’s success has occurred even in flows where the grid-scale is not in an ideal inertial range. It turns out that the most well-known successful applications (such as transitional flows, the viscous sublayer, etc..) are those where the true SGS stress is only a small contribution to the dynamics, and where the errors induced by the deviations from scale-invariance are of minor consequence. However, there are important flows in which the errors can have large effects, such as in LES of wall-bounded flows that do not resolve the viscous sublayer. Near the wall, the grid-scale is on the order of the local integral scale (the distance to the wall) and the SGS shear stress contributes significantly to the mean momentum balance. In this paper we show that the traditional dynamic model yields coefficients that are too small, which translates into high wavenumber pile-up of the longitudinal energy spectra near the wall. In order to correct for this problem in a dynamic fashion, a new scale-dependent dynamic model is proposed. It involves a secondary test-filter operation that allows one to probe from the simulated resolved field how the coefficient depends on scale. Applications to LES of a wall-bounded flow that does not resolve the viscous sublayer are presented, showing much improved longitudinal energy spectra and better mean velocity profiles.

Keywords

Inertial Range Viscous Sublayer Subgrid Scale Transitional Flow Smagorinsky Model 
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.

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References

  1. J.D. Albertson and M.B. Parlange. Surface length-scales and shear stress: implications for land-atmosphere interaction over complex terrain. Water Resour. Res., in press, (1999a).Google Scholar
  2. E. Balaras, C. Benocci, and U. Piomelli. Finite-difference computations of high Reynolds-number flows using the dynamic subgrid-scale model. Theor. Comp. Fluid Dyn., 7:207–216, (1995).zbMATHCrossRefGoogle Scholar
  3. J. W. Deardorff. Three-dimensional numerical study of the height and mean structure of a heated planetary boundary layer. Bound. Layer Meteor., 7:81, (1974).ADSGoogle Scholar
  4. M. Germano, U. Piomelli, P. Moin, and W.H. Cabot. A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A, A 3:1760, (1991).ADSCrossRefGoogle Scholar
  5. S. Ghosal, T.S. Lund, P. Moin, and K. Akselvoll. A dynamic localization model for large eddy simulation of turbulent flow. J. Fluid Mech., 286:229–255, (1995).MathSciNetADSzbMATHCrossRefGoogle Scholar
  6. B. Kader and A.M. Yaglom. Spectra and correlation functions of surface layer atmospheric turbulence in unstable thermal stratification. Turbulence and coherent structures (O. Métais and M. Lesieur, editors), Kluwer Academic, Norwell Mass. 450pp, (1991).Google Scholar
  7. D.K. Lilly. The representation of small-scale turbulence in numerical simulation experiments. In Proc. IBM Scientific Computing Symposium on Environmental Sciences, page 195, (1967).Google Scholar
  8. D.K. Lilly. A proposed modification of the Germano subgrid scale closure method. Phys. Fluids A, 4:633, (1992).ADSCrossRefGoogle Scholar
  9. S. Liu, J. Katz, and C. Meneveau. Evolution and modeling of subgrid scales during rapid straining of turbulence. J. Fluid Mech., 387:281–320, (1999).MathSciNetADSzbMATHCrossRefGoogle Scholar
  10. P.J. Mason and D.J. Thomson. Stochastic backscatter in large-eddy simulations of boundary layers. J. Fluid Mech., 242:51–78, (1992).ADSzbMATHCrossRefGoogle Scholar
  11. C. Meneveau and J. Katz. Scale-invariance and turbulence models for large-eddy-simulation. Annu. Rev. Fluid Mech., in press, (2000).Google Scholar
  12. C. Meneveau, T. Lund, and W. Cabot. A Lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech., 319:353–385, (1996).ADSzbMATHCrossRefGoogle Scholar
  13. C. Meneveau and T.S. Lund. The dynamic Smagorinsky model and scale-dependent coefficients in the viscous range of turbulence. Phys. Fluids, 9:3932–3934, (1997).MathSciNetADSzbMATHCrossRefGoogle Scholar
  14. P. Moin and J. Kim. Numerical investigation of channel flow. J. Fluid Mech., 118:341–377, (1982).ADSzbMATHCrossRefGoogle Scholar
  15. A.E. Perry, S. Henbest, and M.S. Chong. A theoretical and experimental study of wall turbulence. J. Fluid Mech., 165:163–199, (1986).MathSciNetADSzbMATHCrossRefGoogle Scholar
  16. U. Piomelli and T. A. Zang. Large-eddy-simulation of transitional channel flow. Comp. Phys. Comm., 65:224, (1991).ADSzbMATHCrossRefGoogle Scholar
  17. F. Porté-Agel, C. Meneveau, and M.B. Parlange. Dynamic model for large-eddy-simulations near the limits of the inertial range of turbulence. ASME FED 1999, FEDSM99-7835, (1999).Google Scholar
  18. F. Porté-Agel, C. Meneveau, and M.B. Parlange. A scale-dependent dynamic model for large-eddy simulation: application to the atmospheric boundary layer. J. Fluid Mech., submitted, (1999).Google Scholar
  19. U. Schumann. Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comp. Phys., 18:376, (1975).MathSciNetADSzbMATHCrossRefGoogle Scholar
  20. A. Scotti, C. Meneveau, and D.K. Lilly. Generalized Smagorinsky model for anisotropic grids. Phys. Fluids A, 5:2306, (1993).ADSzbMATHCrossRefGoogle Scholar
  21. J. Smagorinsky. General circulation experiments with the primitive equations. i. the basic experiment. Mon. Weather Rev., 91:99, (1963).ADSCrossRefGoogle Scholar
  22. L. M. Smith and V. Yakhot. Short-and long-time behavior of eddy-viscosity models. Theoret. Comput. Fluid Dynamics, 4:197, (1993).ADSzbMATHCrossRefGoogle Scholar
  23. P.R. Voke. Subgrid-scale modeling at low mesh Reynolds number. Theor. Comp. Fluid Dyn., 8:131–143, (1996).zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Charles Meneveau
    • 1
  • Fernando Porté-Agel
    • 2
  • Marc B. Parlange
    • 2
  1. 1.Department of Mechanical EngineeringJohns Hopkins UniversityBaltimoreUSA
  2. 2.Department of Geography and Environmental EngineeringJohns Hopkins UniversityBaltimoreUSA

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