Abstract
A new and general approach is presented to allow standard subgrid schemes to besuitable both for surface layer and free-stream turbulence. Simple modificationsto subgrid schemes are proposed and derived for any vertical stabilityconditions. They are simple to implement in models and are suitable for morecomplicated simulations such as large-eddy simulation with inhomogeneoussurface conditions or complex topography. They are also applicable to mesoscaleand large-scale models. These modifications are physically justified by recentmeasurements of spectra close to the ground. The spectral analysis presentedshows how the energy deficit of blocked turbulence for a given dissipation(`anomalous dissipation') dramatically affects the coefficients to be used insubgrid schemes. As shown for neutral and convective cases with wind shear,these changes allow us to substantially improve the prediction of profiles for themean quantities in the surface layer. Agreement with similarity laws in the unstablecase is found up to about 0.2zi, for simulated shear, stabilityprofiles and dissipation rates of turbulent kinetic energy.
Similar content being viewed by others
References
Andreas, E. L.: 1987, ‘On the Kolmogorov Constants for the Temperature-Humidity Cospectrum and the Refractive Index Spectrum’ J. Atmos. Sci. 44, 2399-2406.
Andrén, Brown, A. R., Graf, J., Mason, P. J., Moeng, C., Nieuwstadt, F. T. M., and Schumann U.: 1994, ‘Large-Eddy Simulation of a Neutrally Stratified Boundary Layer: A Comparison of Four Computer Codes’ Quart. J. Roy. Meteorol. Soc. 120, 1457-1484.
Businger, J. A., Wyngaard, J. C., Izumi, Y., and Bradley, E. F.: 1971, ‘Flux-Profile Relationships in the Atmospheric Surface Layer’ J. Atmos. Sci. Sci. 28, 181-189.
Caughey, S. J. and Palmer, S. G.: 1979, ‘Some Aspects of Turbulence Structure through the Depth of the Convective Boundary Layer’ Quart. J. Roy. Meteorol. Soc. 105, 811-827.
Counihan, J.: 1975, ‘Adiabatic Atmospheric Boundary Layers: A Review and Analysis of Data from the Period 1880-1972’ Atmos. Environ. 9, 871-905.
Cuxart, J., Bougeault, Ph., and Redelsperger, J. L.: 2000, ‘A Multiscale Turbulence Scheme Apt for LES and Mesoscale Modelling’ Quart. J. Roy. Meteorol. Soc. 126, 1-30.
Deardorff, J. W.: 1970, ‘Convective Velocity and Temperature Scales for the Unstable Planetary Boundary Layer and for Rayleigh Convection’ J. Atmos. Sci. 27, 1211-1213.
Frenzen, P. and Vogel, C. A.: 1992, ‘The Turbulent Kinetic Energy Budget in the Atmospheric Surface Layer: A Review and an Experimental Reexamination in the Field’ Boundary-Layer Meteorol. 60, 49-76.
Fuerher, P. L. and Friehe, C. A.: 1999, ‘A Physically Based Turbulent Velocity Time Series Decomposition’ Boundary-Layer Meteorol. 90, 241-295.
Garratt, J. R.: 1992, The Atmospheric Boundary Layer, Cambridge University Press, Cambridge, 316 pp.
Hoxey, R. P. and Richards, P. J.: 1992, ‘Spectral Characteristics of the Atmospheric Boundary Layer near the Ground’ in 1st UK Wind Engineering Conference, Cambridge.
Hunt, J. C. R. and Carlotti, P.: 2001, ‘Statistical Structure of the High Reynolds Number Boundary Layer’ Flow Turbul. Combust., in press.
Hunt, J. C. R. and Morrison, J. F.: 2000, ‘Eddy Structure in Turbulent Boundary Layers’ Eur. J. Mech., B Fluids 19, 673-694.
Juneja, A. and Brasseur, J. G.: 1999, ‘Characteristics of Subgrid-Resolved-Scale Dynamics in Anisotropic Turbulence, with Application to Rough-Wall Boundary Layers’ Phys. Fluids 11, 3054-3067.
Khanna, S. and Brasseur, J. G.: 1997, ‘Analysis of Monin-Obukhov Similarity from Large-Eddy Simulation, J. Atmos. Sci. 345, 251-286.
Khanna, S. and Brasseur, J. G.: 1998, ‘Three-Dimensional Buoyancy-and Shear-Induced Local Structure of the Atmospheric Boundary Layer’ J. Atmos. Sci. 55, 710-743.
Kim, K. C. and Adrian, R. J.: 1999, ‘Very Large Scale Motion in the Outer Layer’ Phys. Fluids 11, 417-422.
Lafore, J. P., Stein, J., Asencio, N., Bougeault, P., Ducrocq, V., Duron, J., Fisher, C., Hereil, P., Mascart, P., Pinty, J. P., Redelsperger, J. L., Richard, E., and Vila-Guerau de Arellano, J.: 1998, ‘The Meso-NH Atmospheric Simulation System. Part I: Adiabatic Formulation and Control Simulations’ Ann. Geophys. 16, 90-109.
Louis, J. F.: 1979, ‘A ParametricModel of Vertical Eddy Fluxes in the Atmosphere’ Boundary-Layer Meteorol. 17, 187-202.
Mason, P. J.: 1989, ‘Large-Eddy Simulation of the Convective Atmospheric Boundary Layer’ J. Atmos. Sci. 46, 1492-1516.
Mason, P. J. and Thomson, D. J.: 1992, ‘Stochastic Backscatter in Large-Eddy Simulations of Boundary Layers’ J. Fluid Mech. 242, 51-78.
Moeng, C. H. and Sullivan, P. P.: 1994, ‘A Comparison of Shear-and Buoyancy-Driven Planetary Boundary Layer Flows’ J. Atmos. Sci. 51, 999-1022.
Moin, P. and Kim, J.: 1982, ‘Numerical Investigation of Turbulent Channel Flow’ J. Fluid Mech. 118, 341-377.
Panofsky, H. A., Tennekes, H., Lenschow, D. H., and Wyngaard, J. C.: 1977, ‘The Characteristics of Turbulent Velocity Components in the Surface Layer under Convective Conditions’ Boundary-Layer Meteorol. 11, 355-361.
Porté-Agel, F., Meneveau C., and Parlange, M. C.: 2000, ‘A Scale-Dependent Dynamic Model for Large-Eddy Simulation: Application to a Neutral Atmospheric Boundary Layer’ J. Fluid. Mech. 415, 261-284.
Redelsperger, J. L. and Sommeria, G.: 1981, ‘Méthode de représentation de la turbulence d'échelle inférieure à la maille pour un modèle tridimensionnel de convection nuageuse’ Boundary-Layer Meteorol. 21, 509-530.
Redelsperger, J. L. and Sommeria, G.: 1986, ‘Three-Dimensional Simulation of a Convective Storm: Sensitivity Studies on Subgrid Parameterization and Spatial Resolution’ J. Atmos. Sci. 43, 2619-2635.
Schmidt, H. and Schumman, U.: 1989, ‘Coherent Structure of the Convective Boundary Layer Derived from Large Eddy Simulations’ J. Fluid Mech. 200, 511-562.
Schumann U.: 1975, ‘Subgrid Scale Model for Finite Difference Simulations of Turbulent Flows in Plane Channels and Annuli’ J. Comp. Phys. 18, 376-404.
Sommeria, G.: 1976, ‘Three-Dimensional Simulation of Turbulent Processes in an Undisturbed Trade Wind Boundary Layer’ J. Atmos. Sci. 33, 216-241.
Stull, R.: 1988, An Introduction to Boundary Layer Meteorology, Kluwer Academic Publishers, Dordrecht, 666 pp.
Sullivan, P. P., McWilliams, J. C., and Moeng, C. H.: 1994, ‘A Subgrid-Scale Model for Large-Eddy Simulation of Planetary Boundary-Layer Flows’ Boundary-Layer Meteorol. 71, 247-276.
Thérry, G. and Lacarrère, P.: 1983, ‘Improving the Eddy Kinetic Energy Model for Planetary Boundary Layer Description’ Boundary-Layer Meteorol. 25, 63-68.
Townsend, A. A.: 1976, The Structure of Turbulent Shear Flow, Cambridge University Press, Cambridge, 429 pp.
Troen, I. and Mahrt, L.: 1986, ‘A Simple Model of the Atmospheric Boundary-Layer: Sensitivity to Surface Evaporation’ Boundary-Layer Meteorol. 37, 129-148.
Wyngaard, J. C. and Coté, O. R.: 1974, ‘The Evolution of a Convective Planetary Boundary Layer: A Higher Order Closure Model Study’ Boundary-Layer Meteorol. 7, 289-308.
Wyngaard, J. C., Coté, O. R., and Isumi, Y.: 1971, ‘Local Free Convection, Similarity and the Budgets of Shear Stress and Heat Flux’ J. Atmos. Sci. 28, 1171-1182.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Redelsperger, J.L., Mahé, F. & Carlotti, P. A Simple And General Subgrid Model Suitable Both For Surface Layer And Free-Stream Turbulence. Boundary-Layer Meteorology 101, 375–408 (2001). https://doi.org/10.1023/A:1019206001292
Issue Date:
DOI: https://doi.org/10.1023/A:1019206001292