Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

A subgrid-scale model for large-eddy simulation of planetary boundary-layer flows

Abstract

A long-standing problem in large-eddy simulations (LES) of the planetary boundary layer (PBL) is that the mean wind and temperature profiles differ from the Monin-Obukhov similarity forms in the surface layer. This shortcoming of LES has been attributed to poor grid resolution and inadequate sub-grid-scale (SGS) modeling. We study this deficiency in PBL LES solutions calculated over a range of shear and buoyancy forcing conditions. The discrepancy from similarity forms becomes larger with increasing shear and smaller buoyancy forcing, and persists even with substantial horizontal grid refinement. With strong buoyancy forcing, however, the error is negligible.

In order to achieve better agreement between LES and similarity forms in the surface layer, a two-part SGS eddy-viscosity model is proposed. The model preserves the usual SGS turbulent kinetic energy formulation for the SGS eddy viscosity, but it explicitly includes a contribution from the mean flow and a reduction of the contributions from the turbulent fluctuations near the surface. Solutions with the new model yield increased fluctuation amplitudes near the surface and better correspondence with similarity forms out to a distance of 0.1–0.2 times the PBL depth, i.e., a typical surface-layer depth. These results are also found to be independent of grid anisotropy. The new model is simple to implement and computationally inexpensive.

This is a preview of subscription content, log in to check access.

References

  1. Bardina, J., Ferziger, J. H., and Reynolds, W. C.: 1983,Improved Turbulence Models Based on Large Eddy Simulation of Homogeneous, Incompressible, Turbulent Flows. Thermosciences Report TF-19. Stanford University.

  2. Businger, J. A., Wyngaard, J. C., Izumi, Y. and Bradley, E. F.: 1971, ‘Flux-Profile Relationships in the Atmospheric Surface Layer’,J. Atmos. Sci. 28, 181–189.

  3. Cebecci, T. and Bradshaw, P.: 1988,Physical and Computational Aspects of Convective Heat Transfer. Springer-Verlag, 187 pp.

  4. Canuto, V. M. and Minotti, F.: 1993, ‘Stratified Turbulence in the Atmosphere and Oceans: A New Subgrid Model’,J. Atmos. Sci. 50, 1925–1935.

  5. Clark, R. A., Ferziger, J. H., and Reynolds, W. C.: 1979, ‘Evaluation of Subgrid-Scale Models Using an Accurately Simulated Turbulent Flow’,J. Fluid Mech 91, 1–16.

  6. Coleman, G. N., Ferziger, J. H., and Spalart, P. R.: 1990, ‘A Numerical Study of the Turbulent Ekman Layer’,J. Fluid Mech. 213, 313–348.

  7. Deardorff, J. W.: 1970, ‘Numerical Simulation of Turbulent Channel Flow at Large Reynolds Number’,J. Fluid Mech. 41, 452–480.

  8. Deardorff, J. W.: 1980, ‘Stratocumulus-Capped Mixed Layers Derived from a Three-Dimensional Model’,Boundary-Layer Meteorol. 18, 495–527.

  9. Germano, M., Piomelli, U., Moin, P. and Cabot, W. H.: 1991: ‘A Dynamic Subgrid-Scale Eddy Viscosity Model’,Phys. Fluids A 7, 1760–1771.

  10. Gerz, T. and Schumann, U.: 1989, ‘Direct Simulation of Homogeneous Turbulence and Gravity Waves in Sheared and Unsheared Stratified Flows’, in Durst et al. (eds.),Turbulent Shear Flows, Vol. 7, Springer-Verlag, Berlin, 27 pp.

  11. Grotzbach, G. and Schumann, U.: 1977,Direct Numerical Simulation of Turbulent Velocity-Pressure-, and Temperature-Fields in Channel Flows. Symposium on Turbulent Shear Flows, The Pennsylvania State University, April 18–20.

  12. Horiuti, K.: 1993, ‘A Proper Velocity Scale for Modeling Subgrid-Scale Eddy Viscosities in Large Eddy Simulation’,Phys. Fluids,5, 146–157.

  13. Mahrt, L. and Gibson, W.: 1992, ‘Flux Decomposition into Coherent Structures’,Boundary-Layer Meteorol. 60, 143–168.

  14. Mason, P. J. and Callen, N. S.: 1986, ‘On the Magnitude of the Subgrid-Scale Eddy Coefficient in Large-Eddy Simulations of Turbulent Channel Flow’,J. Fluid Mech. 162, 439–462.

  15. Mason, P. J. and Thomson, D. J.: 1992, ‘Stochastic Backscatter in Large-Eddy Simulations of Boundary Layers’,J. Fluid Mech. 242, 51–78.

  16. Moeng, C.-H.: 1984, ‘A Large-Eddy-Simulation Model for the Study of Planetary Boundary-Layer Turbulence’,J. Atmos. Sci. 41, 2052–2062.

  17. Moeng, C.-H. and Wyngaard, J. C.: 1988, ‘Spectral Analysis of Large-Eddy Simulations of the Convective Boundary Layer’,J. Atmos. Sci. 45, 3575–3587.

  18. Moeng, C.-H. and Sullivan, P. P.: 1994, ‘A Comparison of Shear and Buoyancy Driven Planetary-Boundary Flows’,J. Atmos. Sci. 51, 999–1022.

  19. Moin, P. and Kim, J.: 1982, ‘Numerical Investigation of Turbulent Channel Flow’,J. Fluid Mech. 118, 341–377.

  20. Nieuwstadt, F. T. M. and Brost, R. A.: 1986, ‘The Decay of Convective Turbulence’,J. Atmos. Sci. 43, 532–546.

  21. Nieuwstadt, F. T. M., Mason, P. J., Moeng, C.-H., and Schumann, U.: 1993, ‘Large-Eddy Simulation of the Convective Boundary Layer: A Comparison of Four Computer Codes’, in Durst et al. (eds.),Turbulent Shear Flows, Vol. 8, Springer-Verlag, Berlin, 431 pp.

  22. Piomelli, U., Moin, P., and Ferziger, J. E.: 1988, ‘Model Consistency in Large Eddy Simulation of Turbulent Channel Flows’,Phys. Fluids 31, 1884–1891.

  23. Piomelli, U., Ferziger, J. H., and Moin, P.: 1989, ‘New Approximate Boundary Conditions for Large Eddy Simulations of Wall Bounded Flows’,Phys. Fluids A 6, 1061–1068.

  24. Reynolds, W. C.: 1989, ‘The Potential and Limitations of Direct and Large Eddy Simulation’,Whither Turbulence? or Turbulence at the Crossrods, Cornell University.

  25. Rogallo, R. S. and Moin, P.: 1984, ‘Numerical Simulation of Turbulent Flows’,Ann. Rev. Fluid Mech. 16, 99–137.

  26. Schmidt, H. and Schumann, U.: 1989, ‘Coherent Struture of the Convective Boundary Layer Derived from Large-Eddy Simulations’,J. Fluid Mech. 200, 511–562.

  27. Schumann, U.: 1975, ‘Subgrid Scale Model for Finite Difference Simulations of Turbulent Flows in Plane Channels and Annuli’,J. Comp. Phys. 18, 376–404.

  28. Schumann, U., Grotzbach, G., and Kleiser, L.: 1980, ‘Direct Numerical Simulation of Turbulence’,Prediction Methods for Turbulent flows, Editor Wolfgang Kollmann.

  29. Schumann, U.: 1991, ‘Subgrid Length-Scales for Large-Eddy Simulation of Stratified Turbulence’,Theoretical and Computational Fluid Dynamic 2, 279–290.

  30. Schumann, U.: 1993, ‘Stochastic Backscatter of Turbulence Energy and Scalar Variance from Random Subgrid-Scale Fluxes’,Phys. Fluids, Preprint.

  31. Scotti, A., Meneveau, C., and Lilly, D. K.: 1993, ‘Generalized Smagorinsky Model for Anisotropic Grids’,Phys. Fluids 5, 2306–2308.

  32. Smagorinsky, J.: 1963, ‘General Circulation Experiments with the Primitive Equations. I. The Basic Experiment’,Mon. Weather Rev. 91, 99–164.

  33. Spalart, P. R.: 1988, ‘Direct Simulation of a Turbulent Boundary Layer up toR θ=1410’,J. Fluid Mech. 187, 61–98.

  34. Tennekes, H. and Lumley, J. L.: 1972,A First Course in Turbulence, The MIT Press, 266 pp.

  35. Van Driest, E. R.: 1956, ‘On the Turbulent Flow near a Wall’,J. Aero. Sci. 23, 1007–1011.

  36. Wyngaard, J. C.: 1984,Large-Eddy Simulation: Guidelines for its Application to Planetary Boundary Layer Research, US Army Research Office Contract No. 0804.

  37. Wyngaard, J. C.: 1988, ‘Structure of the PBL’, in A. Venkatram and J. C. Wyngaard (ed.),Lectures on Air Pollution Modeling, AMS, Boston, pp. 9–61.

  38. Yakhot, A., Orszag, S., Yakhot, V., and Israeli, M.: 1989, ‘Renormalization Group Formulation of Large-Eddy Simulations’,J. Sci. Comp. 4, 139–158.

  39. Yoshizawa, A.: 1989, ‘Subgrid-Scale Modeling with a Variable Length Scale’,Phys. Fluids A 1, 1293–1295.

Download references

Author information

Additional information

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Sullivan, P.P., McWilliams, J.C. & Moeng, C. A subgrid-scale model for large-eddy simulation of planetary boundary-layer flows. Boundary-Layer Meteorol 71, 247–276 (1994). https://doi.org/10.1007/BF00713741

Download citation

Keywords

  • Turbulent Kinetic Energy
  • Planetary Boundary Layer
  • Eddy Viscosity
  • Grid Refinement
  • Planetary Boundary Layer Depth