Skip to main content
Log in

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

  • Published:
Boundary-Layer Meteorology Aims and scope Submit manuscript

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 via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • 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.

  • 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.

    Google Scholar 

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

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

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

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

    Google Scholar 

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

    Google Scholar 

  • 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.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • 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.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • 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.

    Google Scholar 

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

    Google Scholar 

  • 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.

    Google Scholar 

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

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

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

    Google Scholar 

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

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

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

    Google Scholar 

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

  • 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.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

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, CH. 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

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00713741

Keywords

Navigation