• Bardina, J., , J. H. Ferziger, , and W. C. Reynolds, 1983: Improved turbulence models based on large eddy simulation of homogeneous, incompressible, turbulent flows. NASA Tech. Rep. TF–19, Department of Mechanical Engineering, Stanford University, Stanford, California, 175 pp. [Available online at http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19840009460.pdf.]

  • Boer, G. J., , and T. G. Shepherd, 1983: Large-scale two-dimensional turbulence in the atmosphere. J. Atmos. Sci., 40, 164184, doi:10.1175/1520-0469(1983)040<0164:LSTDTI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bose, S. T., 2012: Explicitly filtered large-eddy simulations with application to grid adaptation and wall modeling. Ph.D. dissertation, Stanford University, Stanford, California, 194 pp. [Available online at http://purl.stanford.edu/dk035ff8905.]

  • Canuto, C., , M. Y. Hussaini, , A. Quarteroni, , and T. A. Zang, 2006: Spectral Methods: Fundamentals in Single Domains. Springer, 603 pp.

  • Charney, J. G., , R. Fjørtoft, , and J. Von Neumann, 1950: Numerical integration of the barotropic vorticity equation. Tellus, 2A, 237254, doi:10.1111/j.2153-3490.1950.tb00336.x.

    • Search Google Scholar
    • Export Citation
  • Cho, J. Y.-K., , and L. M. Polvani, 1996: The emergence of jets and vortices in freely evolving, shallow-water turbulence on a sphere. Phys. Fluids, 8, 15311552, doi:10.1063/1.868929.

    • Search Google Scholar
    • Export Citation
  • Chow, F., , R. L. Street, , M. Xue, , and J. H. Ferziger, 2005: Explicit filtering and reconstruction turbulence modeling for large-eddy simulation of neutral boundary layer flow. J. Atmos. Sci., 62, 20582077, doi:10.1175/JAS3456.1.

    • Search Google Scholar
    • Export Citation
  • Clark, R. A., , J. H. Ferziger, , and W. C. Reynolds, 1979: Evaluation of subgrid-scale models using an accurately simulated turbulent flow. J. Fluid Mech., 91, 116, doi:10.1017/S002211207900001X.

    • Search Google Scholar
    • Export Citation
  • Domaradzki, J. A., , and E. M. Saiki, 1997: A subgrid-scale model based on the estimation of unresolved scales of turbulence. Phys. Fluids, 9, 21482164, doi:10.1063/1.869334.

    • Search Google Scholar
    • Export Citation
  • Frederiksen, J. S., , and A. G. Davies, 1997: Eddy viscosity and stochastic backscatter parameterizations on the sphere for atmospheric circulation models. J. Atmos. Sci., 54, 24752492, doi:10.1175/1520-0469(1997)054<2475:EVASBP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Frederiksen, J. S., , and S. M. Kepert, 2006: Dynamical subgrid-scale parameterizations from direct numerical simulations. J. Atmos. Sci., 63, 30063019, doi:10.1175/JAS3795.1.

    • Search Google Scholar
    • Export Citation
  • Gelb, A., , and J. P. Gleeson, 2001: Spectral viscosity for shallow-water equations in spherical geometry. Mon. Wea. Rev., 129, 23462360, doi:10.1175/1520-0493(2001)129<2346:SVFSWE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Germano, M., 1986a: Differential filters for the large eddy numerical simulation of turbulent flows. Phys. Fluids, 29, 17551756, doi:10.1063/1.865649.

    • Search Google Scholar
    • Export Citation
  • Germano, M., 1986b: Differential filters of elliptic type. Phys. Fluids, 29, 17571758, doi:10.1063/1.865650.

  • Germano, M., , U. Piomelli, , P. Moin, , and W. H. Cabot, 1991: A dynamic subgrid-scale eddy viscosity model. Phys. Fluids, 3A, 17601765, doi:10.1063/1.857955.

    • Search Google Scholar
    • Export Citation
  • Koshyk, J. N., , and G. J. Boer, 1995: Parameterization of dynamical subgrid-scale processes in a spectral GCM. J. Atmos. Sci., 52, 965976, doi:10.1175/1520-0469(1995)052<0965:PODSSP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kraichnan, R. H., 1976: Eddy viscosity in two and three dimensions. J. Atmos. Sci., 33, 15211536, doi:10.1175/1520-0469(1976)033<1521:EVITAT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Leith, C. E., 1971: Atmospheric predictability and two-dimensional turbulence. J. Atmos. Sci., 28, 145161, doi:10.1175/1520-0469(1971)028<0145:APATDT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Leonard, A., 1974: Energy cascade in large-eddy simulations of turbulent fluid flows. Advances in Geophysics, Vol. 18, Academic Press, 237–248, doi:10.1016/S0065-2687(08)60464-1.

    • Search Google Scholar
    • Export Citation
  • Lund, T. S., 2003: The use of explicit filters in large eddy simulation. Comput. Math. Appl., 46, 603616, doi:10.1016/S0898-1221(03)90019-8.

    • Search Google Scholar
    • Export Citation
  • Maday, Y., , S. M. O. Kaber, , and E. Tadmor, 1993: Legendre pseudospectral viscosity method for nonlinear conservation laws. SIAM J. Numer. Anal., 30, 321342, doi:10.1137/0730016.

    • Search Google Scholar
    • Export Citation
  • Rhines, P. B., 1975: Waves and turbulence on a beta-plane. J. Fluid Mech., 69, 417443, doi:10.1017/S0022112075001504.

  • San, O., , A. E. Staples, , Z. Wang, , and T. Iliescu, 2011: Approximate deconvolution large eddy simulation of a barotropic ocean circulation model. Ocean Modell., 40, 120132, doi:10.1016/j.ocemod.2011.08.003.

    • Search Google Scholar
    • Export Citation
  • San, O., , A. E. Staples, , and T. Iliescu, 2013: Approximate deconvolution large eddy simulation of a stratified two-layer quasigeostrophic ocean model. Ocean Modell., 63, 120, doi:10.1016/j.ocemod.2012.12.007.

    • Search Google Scholar
    • Export Citation
  • Stolz, S., , and N. A. Adams, 1999: An approximate deconvolution procedure for large-eddy simulation. Phys. Fluids, 11, 16991701, doi:10.1063/1.869867.

    • Search Google Scholar
    • Export Citation
  • van Citteret, P. H., 1931: On the influence of the slit width on the intensity distribution in spectral lines. Z. Phys., 69, 298308.

  • Vasilyev, O. V., , T. S. Lund, , and P. Moin, 1998: A general class of commutative filters for LES in complex geometries. J. Comput. Phys., 146, 82104, doi:10.1006/jcph.1998.6060.

    • Search Google Scholar
    • Export Citation
  • Zhou, Y., , J. G. Brasseur, , and A. Juneja, 2001: A resolvable subfilter-scale model specific to large-eddy simulation of under-resolved turbulence. Phys. Fluids, 13, 26022610, doi:10.1063/1.1388053.

    • Search Google Scholar
    • Export Citation
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Large-Eddy Simulation of Turbulent Barotropic Flows in Spectral Space on a Sphere

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  • 1 Department of Engineering Science and Mechanics, Virginia Tech, Blacksburg, Virginia
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Abstract

Numerical simulations of atmospheric circulation models are limited by their finite spatial resolution, so large-eddy simulation (LES) is a preferred approach to study these models. In LES, a low-pass filter is applied to the flow field to separate the large- and small-scale motions. In implicitly filtered LES, the computational mesh and discretization schemes are considered to be the low-pass filter, while in the explicitly filtered LES approach, the filtering procedure is separated from the grid and discretization operators and allows for better control of the numerical errors. The aim of this paper is to study and compare implicitly filtered and explicitly filtered LES of atmospheric circulation models in spectral space. To achieve this goal, the results of implicitly filtered and explicitly filtered LES of a barotropic atmosphere circulation model on a sphere in spectral space are presented and compared with the results obtained from direct numerical simulation (DNS). Different numerical experiments are performed to investigate the efficiency of explicit filtering over implicit filtering under different dissipation terms and rotation rates. The study shows that explicit filtering increases the accuracy of the computations and improves the results, particularly where the location of coherent structures is concerned, a topic of particular importance in LES of atmospheric flows for climate and weather applications.

Corresponding author address: L. N. Azadani, Department of Engineering Science and Mechanics, Virginia Tech, 495 Old Turner Street, Blacksburg, VA 24061. E-mail: leila@vt.edu

Abstract

Numerical simulations of atmospheric circulation models are limited by their finite spatial resolution, so large-eddy simulation (LES) is a preferred approach to study these models. In LES, a low-pass filter is applied to the flow field to separate the large- and small-scale motions. In implicitly filtered LES, the computational mesh and discretization schemes are considered to be the low-pass filter, while in the explicitly filtered LES approach, the filtering procedure is separated from the grid and discretization operators and allows for better control of the numerical errors. The aim of this paper is to study and compare implicitly filtered and explicitly filtered LES of atmospheric circulation models in spectral space. To achieve this goal, the results of implicitly filtered and explicitly filtered LES of a barotropic atmosphere circulation model on a sphere in spectral space are presented and compared with the results obtained from direct numerical simulation (DNS). Different numerical experiments are performed to investigate the efficiency of explicit filtering over implicit filtering under different dissipation terms and rotation rates. The study shows that explicit filtering increases the accuracy of the computations and improves the results, particularly where the location of coherent structures is concerned, a topic of particular importance in LES of atmospheric flows for climate and weather applications.

Corresponding author address: L. N. Azadani, Department of Engineering Science and Mechanics, Virginia Tech, 495 Old Turner Street, Blacksburg, VA 24061. E-mail: leila@vt.edu
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