Abstract
Turbulence in a non-strongly stably stratified large-eddy simulation (LES) case is studied through probability density functions (PDFs) to obtain additional information than that provided by classical LES averages. The PDFs are computed for one hour within the steady-state regime at three different levels: near the surface, in the middle and at the top of the boundary layer, for the wind components and the temperature. The physical significance of these PDFs from LES is discussed and they are compared to those obtained from observations. The analysis of the eddy structures within the stably stratified boundary layer is made through the combined study of the fields, the spectra and the statistical moments obtained from the PDFs and joint PDFs. The homogeneity of the fields is inspected through a comparison of the ensemble to the temporal and the spatial PDFs, showing that the ergodic theorem is not fulfilled. To this end, the sensitivity of the PDF moments to the LES resolution is explored.
Similar content being viewed by others
References
Adams N.A., and Stolz S., (2002), ‘A Subgrid-Scale Deconvolution Approach for Shock Capturing’. J. Comput. Phys. 178, 391–426
Beare R.J., MacVean M.K., Holtslag A.A.M., Cuxart J., Esau I., Golaz J.-C., Jiménez M.A., Khairoutdinov M., Kosovic B., Lewellen D., Lund T.S., Lundquist J.K., McCabe A., Moene A.F., Noh Y., Raasch S., and Sullivan P., (2006), ‘An Inter-Comparison of Large-eddy Simulations of the Stable Boundary Layer’. Boundary-Layer Meteorol. In press.
Chu C.R., Parlange M.B., Katul G.G., and Albertson J.D., (1996), ‘Probability Density Functions of Turbulent Velocity and Temperature in the Atmospheric Surface Layer’. Water Resources Res. 32, 1681–1688
Cuxart J., Bougeault P., and Redelsperger J.-L., (2000), ‘A Turbulence Scheme Allowing for Mesoscale and Large-eddy Simulations’. Quart. J. Roy. Meteorol. Soc. 126, 1–30
Cuxart J., Holtslag A.A.M., Beare R.J., Bazile E., Beljaars A., Conangla L., Ek M., Freedman F., Hamdi R., Kerstein A., Kitagawa A., Lenderink G., Lewellen D., Mailhot J., Mauritsen T., Perov V., Schayes G., Steeneveld G.-J., Svensson G., Taylor P., Weng W., Wunsch S., and Xu K.-M., (2006), ‘Single-column Model Inter-Comparison for a Stably Stratified Atmospheric Boundary Layer’. Boundary-Layer Meteorol. In press.
Deardorff J.W., Willis G.E., (1985), ‘Further Results from a Laboratory Model of the Convective Planetary Boundary Layer’. Boundary-Layer Meteorol. 32, 205–236
Jiménez M.A., and Cuxart J., (2005), ‘Large-eddy Simulations of the Stable Boundary Layer using the Standard Kolmogorov Theory: Range of Applicability’. Boundary-Layer Meteorol. 115, 241–261
Kampé de Fériet J., (1939), ‘Les Fonctions Aléatoires Stationnaires et la Théorie Statistique de la Turbulence Homogéne’. Ann. Soc. Sci. Bruxelles 59, 145–194
Kosovic B., Curry J.A., (2000), ‘A Large Eddy Simulation Study of a Quasi-steady, Stably Stratified Atmospheric Boundary Layer’. J. Atmos. Sci. 57, 1052–1068
Lafore J.P., Stein J., Asencio N., Bougeault P., Ducrocq V., Duron J., Fisher C., Héreil P., Mascart P., Masson V., Pinty J.P., Redelsperger J.-L., Richard E., Vilá-Guerau de Arellano J., (1998), ‘The Meso-NH Atmospheric Simulation System. Part I: Adiabatic Formulation and Control Simulation’. Ann. Geophys. 16, 90–109
Larson V.E., Wood R., Field P.R., Golaz J.-C., Vonder, T. H and Cotton W.R., (2001), ‘Small-scale and Mesoscale Variability of Scalars in Cloudy Boundary Layers: One-dimensional Probability Density Functions’. J. Atmos. Sci. 58, 1978–1994
Mahrt L., Paumier J., (1984), ‘Heat Transport in the Atmospheric Boundary Layer’. J. Atmos. Sci. 41, 3061–3075
Millionshchikov M.D., (1939), ‘Decay of Homogeneous Isotropic Turbulence in Viscous Incompressible Fluids’. Doklady AN SSSR 22, 236–240
Monin A.S., Yaglom A.M., (1971), ‘Statistical Fluid Mechanics. Vol. I’ The Massachusetts Institute of Technology, 769 pp.
Nieuwstadt F.T.M., Mason P.J., Moeng C.-H., 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 8 Springer-Verlag, 343–367.
Tennekes H., Lumley J.L., (1982), A First Course in Turbulence, The Massachusetts Institute of Technology, 300 pp.
Thoroddsen S.T., Van Atta C.W., (1992), ‘Exponential Tails and Skewness of Density-Gradient Probability Density Functions in Stably Stratified Turbulence’. J. Fluid Mech. 244, 547–566
Wang S., Stevens B., (2000), ‘Top-Hat Representation of Turbulence Statistics in Cloud-topped Boundary Layers: A Large Eddy Simulation Study’. J. Atmos. Sci. 57, 432–441
Wilks D.S., (1995), Statistical Methods in the Atmospheric Sciences. Academic Press, New York, pp. 467
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jiménez, M.A., CUXART, J. Study of the Probability Density Functions From a Large-Eddy Simulation for a Stably Stratified Boundary Layer. Boundary-Layer Meteorol 118, 401–420 (2006). https://doi.org/10.1007/s10546-005-9009-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10546-005-9009-5