Editorial Type:
Article
Article Type:
Research Article

Direct Numerical Simulation of the Turbulent Ekman Layer: Evaluation of Closure Models

Stuart Marlatt Department of Aerospace Engineering Sciences, University of Colorado, Boulder, Colorado

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Scott Waggy Department of Aerospace Engineering Sciences, University of Colorado, Boulder, Colorado

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Sedat Biringen Department of Aerospace Engineering Sciences, University of Colorado, Boulder, Colorado

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Print Publication:
01 Mar 2012
DOI:
https://doi.org/10.1175/JAS-D-11-0107.1
Page(s):
1106–1117
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Abstract

A direct numerical simulation (DNS) at a Reynolds number of 1000 was performed for the neutral atmospheric boundary layer (ABL) using the Ekman layer approximation. The DNS results were used to evaluate several closure approximations that model the turbulent stresses in the Reynolds averaged momentum equations. Two first-order closure equations proposed by O’Brien and by Large, McWilliams, and Doney were tested; both models approximate the eddy diffusivity as a function of height using cubic polynomials. Of these two models, the O’Brien model, which requires data both at the surface layer and at the top of the boundary layer, proved superior. The higher-order k–ε model also agreed well with DNS results and more accurately represented the eddy diffusivity in this rotational flow.

Current affiliation: United Launch Alliance, Littleton, Colorado.

Corresponding author address: Sedat Biringen, Aerospace Engineering Sciences, CB 429, University of Colorado, Boulder, CO 80309. E-mail: biringen@colorado.edu

Abstract

A direct numerical simulation (DNS) at a Reynolds number of 1000 was performed for the neutral atmospheric boundary layer (ABL) using the Ekman layer approximation. The DNS results were used to evaluate several closure approximations that model the turbulent stresses in the Reynolds averaged momentum equations. Two first-order closure equations proposed by O’Brien and by Large, McWilliams, and Doney were tested; both models approximate the eddy diffusivity as a function of height using cubic polynomials. Of these two models, the O’Brien model, which requires data both at the surface layer and at the top of the boundary layer, proved superior. The higher-order k–ε model also agreed well with DNS results and more accurately represented the eddy diffusivity in this rotational flow.

Current affiliation: United Launch Alliance, Littleton, Colorado.

Corresponding author address: Sedat Biringen, Aerospace Engineering Sciences, CB 429, University of Colorado, Boulder, CO 80309. E-mail: biringen@colorado.edu
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  • Balsley, B. B., R. G. Frehlich, M. L. Jensen, and Y. Meillier, 2003: Extreme gradients in the nocturnal boundary layer: Structure, evolution, and potential causes. J. Atmos. Sci., 60, 2496–2508.

    • Search Google Scholar
    • Export Citation

  • Beljaars, A. C. M., J. L. Walmsley, and P. A. Taylor, 1987: A mixed spectral finite-difference model for neutrally stratified boundary layer flow over roughness changes and topography. Bound.-Layer Meteor., 38, 273–303.

    • Search Google Scholar
    • Export Citation

  • Blackadar, A. K., 1962: The vertical distribution of wind and turbulent exchange in a neutral atmosphere. J. Geophys. Res., 67, 3095–3102.

    • Search Google Scholar
    • Export Citation

  • Caldwell, D. R., C. W. van Atta, and K. N. Helland, 1972: A laboratory study of the turbulent Ekman layer. Geophys. Fluid Dyn., 3, 125–160.

    • Search Google Scholar
    • Export Citation

  • Coleman, G. N., 1999: Similarity statistics from a direct numerical simulation of the neutrally stratified planetary boundary layer. J. Atmos. Sci., 56, 891–900.

    • Search Google Scholar
    • Export Citation

  • Deardorff, J. W., 1966: The counter-gradient heat flux in the lower atmosphere and in the laboratory. J. Atmos. Sci., 23, 503–506.

  • Detering, H. W., and D. Etling, 1985: Application of the E–ε turbulence model to the atmospheric boundary layer. Bound.-Layer Meteor., 33, 113–133.

    • Search Google Scholar
    • Export Citation

  • Hess, G. D., and J. R. Garratt, 2002a: Evaluating models of the neutral, barotropic planetary boundary layer using integral measures: Part I. Overview. Bound.-Layer Meteor., 104, 333–358.

    • Search Google Scholar
    • Export Citation

  • Hess, G. D., and J. R. Garratt, 2002b: Evaluating models of the neutral, barotropic planetary boundary layer using integral measures: Part II. Modelling observed conditions. Bound.-Layer Meteor., 104, 359–369.

    • Search Google Scholar
    • Export Citation

  • Jones, W. P., and B. E. Launder, 1972: The prediction of laminarization with a two-equation model of turbulence. Int. J. Heat Mass Transfer, 15, 301–314.

    • Search Google Scholar
    • Export Citation

  • Jones, W. P., and B. E. Launder, 1973: The calculation of low Reynolds number phenomena with a two-equation model of turbulence. Int. J. Heat Mass Transfer, 16, 1119–1130.

    • Search Google Scholar
    • Export Citation

  • Kantha, L., 2006: Comments on ‘Second-order turbulence closure models for geophysical boundary layers: A review of recent work.’ Cont. Shelf Res., 26, 819–822.

    • Search Google Scholar
    • Export Citation

  • Keller, L. V., and A. A. Friedmann, 1924: Differentialgleichung für die turbulente Bewegung einer Kompressiblen Flüssigkeit. Proc. First Int. Congress on Applied Mechanics, Delft, Netherlands, 394–405.

    • Search Google Scholar
    • Export Citation

  • Kitada, T., 1987: Turbulence structure of sea breeze front and its implication in air pollution transport–application of k–ε turbulence model. Bound.-Layer Meteor., 41, 217–239.

    • Search Google Scholar
    • Export Citation

  • Lappen, C.-L., D. Randall, and T. Yamaguchi, 2010: A higher-order closure model with an explicit PBL top. J. Atmos. Sci., 67, 834–850.

    • Search Google Scholar
    • Export Citation

  • Large, W. G., J. C. McWilliams, and S. C. Doney, 1994: Oceanic vertical mixing: A review and a model with a nonlocal k-profile boundary layer parameterization. Rev. Geophys., 32, 363–403.

    • Search Google Scholar
    • Export Citation

  • Mansour, N. M., J. Kim, and P. Moin, 1988: Reynolds-stress and dissipation-rate budgets in a turbulent channel flow. J. Fluid Mech., 194, 15–44.

    • Search Google Scholar
    • Export Citation

  • Marlatt, S., S. Waggy, and S. Biringen, 2010: Direct numerical simulation of the turbulent Ekman layer: Turbulent energy budgets. J. Thermophys. Heat Transfer, 24, 544–555.

    • Search Google Scholar
    • Export Citation

  • Miyashita, K., K. Iwamoto, and H. Kawamura, 2006: Direct numerical simulation of the neutrally stratified turbulent Ekman boundary layer. J. Earth Simulator, 6, 3–15.

    • Search Google Scholar
    • Export Citation

  • O’Brien, J. J., 1970: A note on the vertical structure of the eddy exchange coefficient in the planetary boundary layer. J. Atmos. Sci., 27, 1213–1215.

    • Search Google Scholar
    • Export Citation

  • Panofsky, H. A., and J. A. Dutton, 1984: Atmospheric Turbulence: Models and Methods for Engineering Application. John Wiley & Sons, 397 pp.

    • Search Google Scholar
    • Export Citation

  • Reynolds, O., 1895: On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Philos. Trans. Roy. Soc. London, 186A, 123–164.

    • Search Google Scholar
    • Export Citation

  • Spalart, P. R., G. N. Coleman, and R. Johnstone, 2008: Direct numerical simulation of the Ekman layer: A step in Reynolds number, and cautious support for a log law with a shifted origin. Phys. Fluids, 20, 101507, doi:10.1063/1.3005858.

    • Search Google Scholar
    • Export Citation

  • Spalart, P. R., G. N. Coleman, and R. Johnstone, 2009: Retraction: “Direct numerical simulation of the Ekman layer: A step in Reynolds number, and cautious support for a log law with a shifted origin.” Phys. Fluids, 21, 109901, doi:10.1063/1.3247176.

    • Search Google Scholar
    • Export Citation

  • Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology. Kluwer Academic, 666 pp.

  • Taylor, J. R., and S. Sarkar, 2008: Direct and large eddy simulations of a bottom Ekman layer under an external stratification. Int. J. Heat Fluid Flow, 29, 721–732.

    • Search Google Scholar
    • Export Citation

  • Troen, I. B., and L. Mahrt, 1986: A simple model of the atmospheric boundary layer; sensitivity to surface evaporation. Bound.-Layer Meteor., 37, 129–148.

    • Search Google Scholar
    • Export Citation

  • Umlauf, L., and H. Burchard, 2005: Second-order turbulence closure models for geophysical boundary layers: A review of recent work. Cont. Shelf Res., 25, 795–827.

    • Search Google Scholar
    • Export Citation

  • Waggy, S., S. Marlatt, and S. Biringen, 2011: Direct numerical simulation of the turbulent Ekman layer: Instantaneous flow structures. J. Thermophys. Heat Transfer, 25, 309–318.

    • Search Google Scholar
    • Export Citation

  • White, F. M., 1991: Viscous Fluid Flow. McGraw-Hill, 614 pp.

  • Zilitinkevich, S. S., and I. N. Esau, 2002: On integral measures of the neutral barotropic planetary boundary layer. Bound.-Layer Meteor., 104, 371–379.

    • Search Google Scholar
    • Export Citation
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