Large-Eddy Simulation of the Stable Boundary Layer with Explicit Filtering and Reconstruction Turbulence Modeling

Bowen Zhou Civil and Environmental Engineering, University of California, Berkeley, Berkeley, California

Search for other papers by Bowen Zhou in
Current site
Google Scholar
PubMed
Close
and
Fotini Katopodes Chow Civil and Environmental Engineering, University of California, Berkeley, Berkeley, California

Search for other papers by Fotini Katopodes Chow in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Large-eddy simulation (LES) of the stably stratified atmospheric boundary layer is performed using an explicit filtering and reconstruction approach with a finite difference method. Turbulent stresses are split into the resolvable subfilter-scale and subgrid-scale stresses. The former are recovered from a reconstruction approach, and the latter are represented by a dynamic eddy-viscosity model. The resulting dynamic reconstruction model (DRM) can sustain resolved turbulence with less stringent resolution requirements than conventional closure models, even under strong atmospheric stability. This is achieved by proper representation of subfilter-scale (SFS) backscatter of turbulent kinetic energy (TKE). The flow structure and turbulence statistics for the moderately stable boundary layer (SBL) are analyzed with high-resolution simulations. The DRM simulations show good agreement with established empirical formulations such as flux and gradient-based surface similarity, even at relatively coarse resolution. Similar results can be obtained with traditional closure models at the cost of higher resolution. SBL turbulence under strong stability is also explored. Simulations show an intermittent presence of elevated TKE below the low-level jet. Overall, the explicit filtering and reconstruction approach is advantageous for simulations of the SBL. At coarse resolution, it can extend the working range of LES to stronger stability, while maintaining agreement to similarity theory; at fine resolution, good agreement with theoretical formulations provides confidence in the results and allows for detailed investigation of the flow structure under moderate to strong stability conditions.

Corresponding author address: Fotini Chow, Dept. of Civil and Environmental Engineering, University of California, Berkeley, Berkeley, CA 94720-1710. E-mail: tinakc@berkeley.edu

Abstract

Large-eddy simulation (LES) of the stably stratified atmospheric boundary layer is performed using an explicit filtering and reconstruction approach with a finite difference method. Turbulent stresses are split into the resolvable subfilter-scale and subgrid-scale stresses. The former are recovered from a reconstruction approach, and the latter are represented by a dynamic eddy-viscosity model. The resulting dynamic reconstruction model (DRM) can sustain resolved turbulence with less stringent resolution requirements than conventional closure models, even under strong atmospheric stability. This is achieved by proper representation of subfilter-scale (SFS) backscatter of turbulent kinetic energy (TKE). The flow structure and turbulence statistics for the moderately stable boundary layer (SBL) are analyzed with high-resolution simulations. The DRM simulations show good agreement with established empirical formulations such as flux and gradient-based surface similarity, even at relatively coarse resolution. Similar results can be obtained with traditional closure models at the cost of higher resolution. SBL turbulence under strong stability is also explored. Simulations show an intermittent presence of elevated TKE below the low-level jet. Overall, the explicit filtering and reconstruction approach is advantageous for simulations of the SBL. At coarse resolution, it can extend the working range of LES to stronger stability, while maintaining agreement to similarity theory; at fine resolution, good agreement with theoretical formulations provides confidence in the results and allows for detailed investigation of the flow structure under moderate to strong stability conditions.

Corresponding author address: Fotini Chow, Dept. of Civil and Environmental Engineering, University of California, Berkeley, Berkeley, CA 94720-1710. E-mail: tinakc@berkeley.edu
Save
  • Bardina, J., J. Ferziger, and W. Reynolds, 1983: Improved turbulence models based on large eddy simulation of homogeneous, incompressible, turbulent flows. Dept. of Mechanical Engineering Tech. Rep. TF-19, Stanford University, 97 pp.

    • Search Google Scholar
    • Export Citation
  • Basu, S., and F. Porté-Agel, 2006: Large-eddy simulation of stably stratified atmospheric boundary layer turbulence: A scale-dependent dynamic modeling approach. J. Atmos. Sci., 63, 20742091.

    • Search Google Scholar
    • Export Citation
  • Beare, R., and Coauthors, 2006: An intercomparison of large-eddy simulations of the stable boundary layer. Bound.-Layer Meteor., 118, 247272.

    • Search Google Scholar
    • Export Citation
  • Brasseur, J. G., and T. Wei, 2010: Designing large-eddy simulation of the turbulent boundary layer to capture law-of-the-wall scaling. Phys. Fluids, 22, 021303, doi:10.1063/1.3319073.

    • Search Google Scholar
    • Export Citation
  • Brown, A., J. Hobson, and N. Wood, 2001: Large-eddy simulation of neutral turbulent flow over rough sinusoidal ridges. Bound.-Layer Meteor., 98, 411441.

    • Search Google Scholar
    • Export Citation
  • Businger, J., J. Wyngaard, Y. Izumi, and E. Bradley, 1971: Flux-profile relationships in atmospheric surface layer. J. Atmos. Sci., 28, 181189.

    • Search Google Scholar
    • Export Citation
  • Carati, D., G. Winckelmans, and H. Jeanmart, 2001: On the modelling of the subgrid-scale and filtered-scale stress tensors in large-eddy simulation. J. Fluid Mech., 441, 119138.

    • Search Google Scholar
    • Export Citation
  • Carper, M., and F. Porté-Agel, 2004: The role of coherent structures in subfilter-scale dissipation of turbulence measured in the atmospheric surface layer. J. Turbul., 5, 040, doi:10.1088/1468-5248/5/1/040.

    • Search Google Scholar
    • Export Citation
  • Cederwall, R. T., 2001: Large-eddy simulation of the evolving boundary layer over flat terrain. Ph.D. thesis, Stanford University, 231 pp.

  • Chow, F. K., 2004: Subfilter-scale turbulence modeling for large-eddy simulation of the atmospheric boundary layer over complex terrain. Ph.D. thesis, Stanford University, 339 pp.

  • Chow, F. K., and R. L. Street, 2002: Modeling unresolved motions in les of field-scale flows. Preprints, 15th Symp. on Boundary Layer and Turbulence, Wageningen, Netherlands, Amer. Meteor. Soc., 9.5. [Available online at http://ams.confex.com/ams/pdfpapers/44769.pdf.]

    • Search Google Scholar
    • Export Citation
  • Chow, F. K., and R. L. Street, 2009: Evaluation of turbulence closure models for large-eddy simulation over complex terrain: Flow over Askervein Hill. J. Appl. Meteor. Climatol., 48, 10501065.

    • Search Google Scholar
    • Export Citation
  • Chow, F. K., R. L. Street, M. Xue, and J. Ferziger, 2005: Explicit filtering and reconstruction turbulence modeling for large-eddy simulation of neutral boundary layer flow. J. Atmos. Sci., 62, 20582077.

    • Search Google Scholar
    • Export Citation
  • Conangla, L., and J. Cuxart, 2006: On the turbulence in the upper part of the low-level jet: An experimental and numerical study. Bound.-Layer Meteor., 118, 379400.

    • Search Google Scholar
    • Export Citation
  • Coulter, R., and J. Doran, 2002: Spatial and temporal occurrences of intermittent turbulence during CASES-99. Bound.-Layer Meteor., 105, 329349.

    • Search Google Scholar
    • Export Citation
  • Cuxart, J., and M. A. Jiménez, 2007: Mixing processes in a nocturnal low-level jet: An LES study. J. Atmos. Sci., 64, 16661679.

  • Derbyshire, S., 1990: Nieuwstadt stable boundary-layer revisited. Quart. J. Roy. Meteor. Soc., 116A, 127158.

  • Garratt, J. R., 1992: The Atmospheric Boundary Layer. Cambridge University Press, 316 pp.

  • Gerz, T., U. Schumann, and S. Elghobashi, 1989: Direct numerical simulation of the stratified homogeneous turbulent shear flows. J. Fluid Mech., 200, 563594.

    • Search Google Scholar
    • Export Citation
  • Grachev, A. A., E. L Andreas, C. W. Fairall, P. S. Guest, and P. O. G. Persson, 2007: On the turbulent Prandtl number in the stable atmospheric boundary layer. Bound.-Layer Meteor., 125, 329341.

    • Search Google Scholar
    • Export Citation
  • Gullbrand, J., 2001: Explicit filtering and subgrid-scale models in turbulent channel flow. Annual Research Briefs, Center for Turbulence Research, NASA Ames–Stanford University, 31–42.

    • Search Google Scholar
    • Export Citation
  • Gullbrand, J., and F. Chow, 2003: The effect of numerical errors and turbulence models in large-eddy simulations of channel flow, with and without explicit filtering. J. Fluid Mech., 495, 323341.

    • Search Google Scholar
    • Export Citation
  • Jiménez, M., and J. Cuxart, 2005: Large-eddy simulations of the stable boundary layer using the standard Kolmogorov theory: Range of applicability. Bound.-Layer Meteor., 115, 241261.

    • Search Google Scholar
    • Export Citation
  • Kirkpatrick, M., A. Ackerman, D. Stevens, and N. Mansour, 2006: On the application of the dynamic Smagorinsky model to large-eddy simulations of the cloud-topped atmospheric boundary layer. J. Atmos. Sci., 63, 526546.

    • Search Google Scholar
    • Export Citation
  • Kosovic, B., and J. Curry, 2000: A large eddy simulation study of a quasi-steady, stably stratified atmospheric boundary layer. J. Atmos. Sci., 57, 10521068.

    • Search Google Scholar
    • Export Citation
  • Lilly, D. K., 1992: A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids, 4A, 633635.

  • Ludwig, F. L., F. K. Chow, and R. L. Street, 2009: Effect of turbulence models and spatial resolution on resolved velocity structure and momentum fluxes in large-eddy simulations of neutral boundary layer flow. J. Appl. Meteor. Climatol., 48, 11611180.

    • Search Google Scholar
    • Export Citation
  • Lund, T. S., 1997: On the use of discrete filters for large eddy simulation. Annual Research Briefs, Center for Turbulence Research, NASA Ames–Stanford University, 83–95.

    • Search Google Scholar
    • Export Citation
  • Mason, P., and S. Derbyshire, 1990: Large-eddy simulation of the stably stratified atmospheric boundary-layer. Bound.-Layer Meteor., 53, 117162.

    • Search Google Scholar
    • Export Citation
  • Mason, P., and D. Thomson, 1992: Stochastic backscatter in large-eddy simulations of boundary-layers. J. Fluid Mech., 242, 5178.

  • Michioka, T., and F. K. Chow, 2008: High-resolution large-eddy simulations of scalar transport in atmospheric boundary layer flow over complex terrain. J. Appl. Meteor. Climatol., 47, 31503169.

    • Search Google Scholar
    • Export Citation
  • Mirocha, J. D., J. K. Lundquist, and B. Kosovic, 2010: Implementation of a nonlinear subfilter turbulence stress model for large-eddy simulation in the Advanced Research WRF model. Mon. Wea. Rev., 138, 42124228.

    • Search Google Scholar
    • Export Citation
  • Nakamura, R., and L. Mahrt, 2005: A study of intermittent turbulence with CASES-99 tower measurements. Bound.-Layer Meteor., 114, 367387.

    • Search Google Scholar
    • Export Citation
  • Nieuwstadt, F., 1984: The turbulent structure of the stable, nocturnal boundary-layer. J. Atmos. Sci., 41, 22022216.

  • Perry, A., S. Henbest, and M. Chong, 1986: A theoretical and experimental-study of wall turbulence. J. Fluid Mech., 165, 163199.

  • Porté-Agel, F., M. Parlange, C. Meneveau, W. Eichinger, and M. Pahlow, 2000: Subgrid-scale dissipation in the atmospheric surface layer: Effects of stability and filter dimension. J. Hydrometeor., 1, 7587.

    • Search Google Scholar
    • Export Citation
  • Saiki, E., C. Moeng, and P. Sullivan, 2000: Large-eddy simulation of the stably stratified planetary boundary layer. Bound.-Layer Meteor., 95, 130.

    • Search Google Scholar
    • Export Citation
  • Schumann, U., and T. Gerz, 1995: Turbulent mixing in stably stratified shear flows. J. Appl. Meteor., 34, 3348.

  • Sorbjan, Z., 2006: Local structure of turbulence in stably stratified boundary layers. J. Atmos. Sci., 63, 15261537.

  • Sorbjan, Z., 2010: Gradient-based scales and similarity laws in the stable boundary layer. Quart. J. Roy. Meteor. Soc., 136A, 12431254.

    • Search Google Scholar
    • Export Citation
  • Sorbjan, Z., and A. A. Grachev, 2010: An evaluation of the flux-gradient relationship in the stable boundary layer. Bound.-Layer Meteor., 135, 385405.

    • Search Google Scholar
    • Export Citation
  • Stolz, S., N. Adams, and L. Kleiser, 2001: The approximate deconvolution model for large-eddy simulations of compressible flows and its application to shock-turbulent-boundary-layer interaction. Phys. Fluids, 13, 29853001.

    • Search Google Scholar
    • Export Citation
  • van Cittert, P., 1931: Der spaltbreite auf die intensitasverteilung in spektrallinien ii. Z. Phys., 69, 298308.

  • Winckelmans, G., A. Wray, O. Vasilyev, and H. Jeanmart, 2001: Explicit-filtering large-eddy simulation using the tensor-diffusivity model supplemented by a dynamic Smagorinsky term. Phys. Fluids, 13, 13851403.

    • Search Google Scholar
    • Export Citation
  • Wong, V., and D. Lilly, 1994: A comparison of 2 dynamic subgrid closure methods for turbulent thermal-convection. Phys. Fluids, 6, 10161023.

    • Search Google Scholar
    • Export Citation
  • Xue, M., K. Droegemeier, and V. Wong, 2000: The Advanced Regional Prediction System (ARPS)—A multi-scale nonhydrostatic atmospheric simulation and prediction model. Part I: Model dynamics and verification. Meteor. Atmos. Phys., 75, 161193.

    • Search Google Scholar
    • Export Citation
  • Zang, Y., R. Street, and J. Koseff, 1993: A dynamic mixed subgrid-scale model and its application to turbulent recirculation-flows. Phys. Fluids, 5A, 31863196.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 753 271 37
PDF Downloads 397 92 14