Editorial Type:
Article
Article Type:
Research Article

Second-Moment Budgets and Mixing Intensity in the Stably Stratified Atmospheric Boundary Layer over Thermally Heterogeneous Surfaces

Dmitrii V. Mironov German Weather Service, Offenbach am Main, Germany

Search for other papers by Dmitrii V. Mironov in
Current site
Google Scholar
PubMed Close
and
Peter P. Sullivan National Center for Atmospheric Research,* Boulder, Colorado

Search for other papers by Peter P. Sullivan in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Jan 2016
DOI:
https://doi.org/10.1175/JAS-D-15-0075.1
Page(s):
449–464
Restricted access

We are aware of a technical issue preventing figures and tables from showing in some newly published articles in the full-text HTML view.
While we are resolving the problem, please use the online PDF version of these articles to view figures and tables.

Abstract

The effect of horizontal temperature heterogeneity of the underlying surface on the turbulence structure and mixing intensity in the stably stratified boundary layer (SBL) is analyzed using large-eddy simulation (LES). Idealized LESs of flows driven by fixed winds and homogeneous and heterogeneous surface temperatures are compared. The LES data are used to compute statistical moments, to estimate budgets of the turbulence kinetic energy (TKE), of the temperature variance and of the temperature flux, and to assess the relative importance of various terms in maintaining the budgets. Unlike most previous studies, the LES-based second-moment budgets are estimated with due regard for the subgrid-scale contributions.

The SBL over a heterogeneous surface is more turbulent with larger variances (and TKE), is better vertically mixed, and is deeper compared to its homogeneous counterpart. The most striking difference between the cases is exhibited in the temperature variance and its budget. Because of surface heterogeneity, the turbulent transport term (divergence of the third-order moment) not only redistributes the temperature variance vertically but is a net gain. The increase in the temperature variance near the heterogeneous surface explains the reduced magnitude of the downward buoyancy flux and the ensuing increase in TKE that leads to more vigorous mixing. Analysis of the temperature flux budget shows that the transport term contributes to net production/destruction. Importantly, the role of the third-order transport cannot be elucidated if the budgets are computed based solely on resolved-scale fields. Implications for modeling (parameterizing) the SBL over thermally heterogeneous surfaces are discussed.

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

Corresponding author address: Dmitrii V. Mironov, Deutscher Wetterdienst, FE14, Frankfurter Str. 135, D-63067 Offenbach am Main, Germany. E-mail: dmitrii.mironov@dwd.de

Abstract

The effect of horizontal temperature heterogeneity of the underlying surface on the turbulence structure and mixing intensity in the stably stratified boundary layer (SBL) is analyzed using large-eddy simulation (LES). Idealized LESs of flows driven by fixed winds and homogeneous and heterogeneous surface temperatures are compared. The LES data are used to compute statistical moments, to estimate budgets of the turbulence kinetic energy (TKE), of the temperature variance and of the temperature flux, and to assess the relative importance of various terms in maintaining the budgets. Unlike most previous studies, the LES-based second-moment budgets are estimated with due regard for the subgrid-scale contributions.

The SBL over a heterogeneous surface is more turbulent with larger variances (and TKE), is better vertically mixed, and is deeper compared to its homogeneous counterpart. The most striking difference between the cases is exhibited in the temperature variance and its budget. Because of surface heterogeneity, the turbulent transport term (divergence of the third-order moment) not only redistributes the temperature variance vertically but is a net gain. The increase in the temperature variance near the heterogeneous surface explains the reduced magnitude of the downward buoyancy flux and the ensuing increase in TKE that leads to more vigorous mixing. Analysis of the temperature flux budget shows that the transport term contributes to net production/destruction. Importantly, the role of the third-order transport cannot be elucidated if the budgets are computed based solely on resolved-scale fields. Implications for modeling (parameterizing) the SBL over thermally heterogeneous surfaces are discussed.

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

Corresponding author address: Dmitrii V. Mironov, Deutscher Wetterdienst, FE14, Frankfurter Str. 135, D-63067 Offenbach am Main, Germany. E-mail: dmitrii.mironov@dwd.de
Save
Cover Journal of the Atmospheric Sciences
Journal of the Atmospheric Sciences

  • Andrén, A., 1995: The structure of stably stratified atmospheric boundary layers: A large-eddy simulation study. Quart. J. Roy. Meteor. Soc., 121, 961–985, doi:10.1002/qj.49712152502.

    • Search Google Scholar
    • Export Citation

  • Ansorge, C., and J. P. Mellado, 2014: Global intermittency and collapsing turbulence in the stratified planetary boundary layer. Bound.-Layer Meteor., 153, 89–116, doi:10.1007/s10546-014-9941-3.

    • Search Google Scholar
    • Export Citation

  • Avissar, R., and R. A. Pielke, 1989: A parameterization of heterogeneous land surfaces for atmospheric numerical models and its impact on regional meteorology. Mon. Wea. Rev., 117, 2113–2136, doi:10.1175/1520-0493(1989)117<2113:APOHLS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Beare, R. J., and Coauthors, 2006: An intercomparison of large-eddy simulations of the stable boundary layer. Bound.-Layer Meteor., 118, 247–272, doi:10.1007/s10546-004-2820-6.

    • Search Google Scholar
    • Export Citation

  • Brown, A. R., S. H. Derbyshire, and P. J. Mason, 1994: Large-eddy simulation of stable atmospheric boundary layers with a revised stochastic subgrid model. Quart. J. Roy. Meteor. Soc., 120, 1485–1512, doi:10.1002/qj.49712052004.

    • Search Google Scholar
    • Export Citation

  • Coleman, G. N., J. H. Ferziger, and P. R. Spalart, 1992: Direct simulation of the stably stratified turbulent Ekman layer. J. Fluid Mech., 244, 677–712, doi:10.1017/S0022112092003264.

    • Search Google Scholar
    • Export Citation

  • Deardorff, J. W., 1973: The use of subgrid transport equations in a three-dimensional model of atmospheric turbulence. J. Fluids Eng., 95, 429–438, doi:10.1115/1.3447047.

    • Search Google Scholar
    • Export Citation

  • Deardorff, J. W., 1974a: Three-dimensional numerical study of the height and mean structure of a heated planetary boundary layer. Bound.-Layer Meteor., 7, 81–106, doi:10.1007/BF00224974.

    • Search Google Scholar
    • Export Citation

  • Deardorff, J. W., 1974b: Three-dimensional numerical study of turbulence in an entraining mixed layer. Bound.-Layer Meteor., 7, 199–226, doi:10.1007/BF00227913.

    • Search Google Scholar
    • Export Citation

  • Deardorff, J. W., 1980: Stratocumulus-capped mixed layers derived from a three-dimensional model. Bound.-Layer Meteor., 18, 495–527, doi:10.1007/BF00119502.

    • Search Google Scholar
    • Export Citation

  • Flores, O., and J. J. Riley, 2011: Analysis of turbulence collapse in the stably stratified surface layer using direct numerical simulation. Bound.-Layer Meteor., 139, 241–259, doi:10.1007/s10546-011-9588-2.

    • Search Google Scholar
    • Export Citation

  • Giorgi, F., and R. Avissar, 1997: Representation of heterogeneity effects in Earth system modeling: Experience from land surface modeling. Rev. Geophys., 35, 413–438, doi:10.1029/97RG01754.

    • Search Google Scholar
    • Export Citation

  • Heinze, R., D. Mironov, and S. Raasch, 2015: Second-moment budgets in cloud-topped boundary layers: A large-eddy simulation study. J. Adv. Model. Earth Syst., 7, 510–536, doi:10.1002/2014MS000376.

    • Search Google Scholar
    • Export Citation

  • Huang, J., and E. Bou-Zeid, 2013: Turbulence and vertical fluxes in the stable atmospheric boundary layer. Part I: A large-eddy simulation study. J. Atmos. Sci., 70, 1513–1527, doi:10.1175/JAS-D-12-0167.1.

    • Search Google Scholar
    • Export Citation

  • Jiménez, M. A., and J. Cuxart, 2005: Large-eddy simulations of the stable boundary layer using the standard Kolmogorov theory: Range of applicability. Bound.-Layer Meteor., 115, 241–261, doi:10.1007/s10546-004-3470-4.

    • Search Google Scholar
    • Export Citation

  • Khanna, S., 1998: Comparison of Kansas data with high-resolution large-eddy simulation fields. Bound.-Layer Meteor., 88, 121–144, doi:10.1023/A:1001068612129.

    • Search Google Scholar
    • Export Citation

  • Kosović, B., and J. A. Curry, 2000: A large-eddy simulation study of a quasi-steady, stably stratified atmospheric boundary layer. J. Atmos. Sci., 57, 1052–1068, doi:10.1175/1520-0469(2000)057<1052:ALESSO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Lilly, D. K., 1967: The representation of small-scale turbulence in numerical simulation experiments. Proc. IBM Scientific Computing Symp. on Environmental Sciences, IBM Form 320-1951, Yorktown Heights, NY, International Business Machines Corporation, 195–210.

  • Machulskaya, E., and D. Mironov, 2013: Implementation of TKE–scalar variance mixing scheme into COSMO. COSMO Newsletter, No. 13, Consortium for Small-Scale Modeling, 25–33.

  • Mahrt, L., 2014: Stably stratified atmospheric boundary layers. Annu. Rev. Fluid Mech., 46, 23–45, doi:10.1146/annurev-fluid-010313-141354.

    • Search Google Scholar
    • Export Citation

  • Mason, P. J., and S. H. Derbyshire, 1990: Large-eddy simulation of the stably-stratified atmospheric boundary layer. Bound.-Layer Meteor., 53, 117–162, doi:10.1007/BF00122467.

    • Search Google Scholar
    • Export Citation

  • Mironov, D. V., 2001: Pressure–potential-temperature covariance in convection with rotation. Quart. J. Roy. Meteor. Soc., 127, 89–110, doi:10.1002/qj.49712757106.

    • Search Google Scholar
    • Export Citation

  • Mironov, D. V., 2009: Turbulence in the lower troposphere: Second-order closure and mass–flux modelling frameworks. Interdisciplinary Aspects of Turbulence, W. Hillebrandt and F. Kupka, Eds., Lecture Notes in Physics, Vol. 756, Springer-Verlag, 161–221, doi:10.1007/978-3-540-78961-1_5.

  • Mironov, D. V., V. M. Gryanik, C.-H. Moeng, D. J. Olbers, and T. H. Warncke, 2000: Vertical turbulence structure and second-moment budgets in convection with rotation: A large-eddy simulation study. Quart. J. Roy. Meteor. Soc., 126, 477–515, doi:10.1002/qj.49712656306.

    • Search Google Scholar
    • Export Citation

  • Moene, A. F., and J. C. van Dam, 2014: Transport in the Atmosphere–Vegetation–Soil Continuum. Cambridge University Press, 436 pp.

  • Moeng, C.-H., 1984: A large-eddy-simulation model for the study of planetary boundary-layer turbulence. J. Atmos. Sci., 41, 2052–2062, doi:10.1175/1520-0469(1984)041<2052:ALESMF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Moeng, C.-H., and J. C. Wyngaard, 1988: Spectral analysis of large-eddy simulations of the convective boundary layer. J. Atmos. Sci., 45, 3573–3587, doi:10.1175/1520-0469(1988)045<3573:SAOLES>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Moeng, C. H., and J. C. Wyngaard, 1989: Evaluation of turbulent transport and dissipation closures in second-order modeling. J. Atmos. Sci., 46, 2311–2330, doi:10.1175/1520-0469(1989)046<2311:EOTTAD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Nieuwstadt, F. T. M., 2005: Direct numerical simulation of stable channel flow at large stability. Bound.-Layer Meteor., 116, 277–299, doi:10.1007/s10546-004-2818-0.

    • Search Google Scholar
    • Export Citation

  • Nieuwstadt, F. T. M., P. J. Mason, C. H. Moeng, and U. Schumann, 1993: Large-eddy simulation of the convective boundary layer: A comparison of four computer codes. Turbulent Shear Flows 8, F. Durst et al., Eds., Springer-Verlag, 343–367, doi:10.1007/978-3-642-77674-8_24.

  • Peltier, L. J., and J. C. Wyngaard, 1995: Structure–function parameters in the convective boundary layer from large-eddy simulation. J. Atmos. Sci., 52, 3641–3660, doi:10.1175/1520-0469(1995)052<3641:SPITCB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Pope, S. B., 2000: Turbulent Flows. Cambridge University Press, 771 pp.

  • Saiki, E. M., C.-H. Moeng, and P. P. Sullivan, 2000: Large-eddy simulation of the stably stratified planetary boundary layer. Bound.-Layer Meteor., 95, 1–30, doi:10.1023/A:1002428223156.

    • Search Google Scholar
    • Export Citation

  • Stoll, R., and F. Porté-Agel, 2006: Effect of roughness on surface boundary conditions for large-eddy simulation. Bound.-Layer Meteor., 118, 169–187, doi:10.1007/s10546-005-4735-2.

    • Search Google Scholar
    • Export Citation

  • Stoll, R., and F. Porté-Agel, 2009: Surface heterogeneity effects on regional-scale fluxes in stable boundary layers: Surface temperature transitions. J. Atmos. Sci., 66, 412–431, doi:10.1175/2008JAS2668.1.

    • Search Google Scholar
    • Export Citation

  • Sullivan, P. P., and E. G. Patton, 2008: A highly parallel algorithm for turbulence simulations in planetary boundary layers: Results with meshes up to . 18th Symp. on Boundary Layers and Turbulence, Stockholm, Sweden, Amer. Meteor. Soc., 11B.5. [Available online at https://ams.confex.com/ams/18BLT/techprogram/paper_139870.htm.]

  • Sullivan, P. P., and E. G. Patton, 2011: The effect of mesh resolution on convective boundary layer statistics and structures generated by large-eddy simulation. J. Atmos. Sci., 68, 2395–2415, doi:10.1175/JAS-D-10-05010.1.

    • Search Google Scholar
    • Export Citation

  • Sullivan, P. P., J. C. McWilliams, and C.-H. Moeng, 1994: A subgrid-scale model for large-eddy simulation of planetary boundary-layer flows. Bound.-Layer Meteor., 71, 247–276, doi:10.1007/BF00713741.

    • Search Google Scholar
    • Export Citation

  • Sullivan, P. P., J. C. McWilliams, and C.-H. Moeng, 1996: A grid nesting method for large-eddy simulation of planetary boundary-layer flows. Bound.-Layer Meteor., 80, 167–202, doi:10.1007/BF00119016.

    • Search Google Scholar
    • Export Citation

  • Taylor, J. R., and S. Sarkar, 2008: Stratification effects in a bottom Ekman layer. J. Phys. Oceanogr., 38, 2535–2555, doi:10.1175/2008JPO3942.1.

    • Search Google Scholar
    • Export Citation

  • van Dop, H., and S. Axelsen, 2007: Large eddy simulation of the stable boundary-layer: A retrospect to Nieuwstadt’s early work. Flow Turbul. Combust., 79, 235–249, doi:10.1007/s10494-007-9093-3.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 625 321 129
PDF Downloads 305 84 9