A New Wall Shear Stress Model for Atmospheric Boundary Layer Simulations

Marcus Hultmark Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey

Search for other papers by Marcus Hultmark in
Current site
Google Scholar
PubMed
Close
,
Marc Calaf School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

Search for other papers by Marc Calaf in
Current site
Google Scholar
PubMed
Close
, and
Marc B. Parlange School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

Search for other papers by Marc B. Parlange in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

A new wall shear stress model to be used as a wall boundary condition for large-eddy simulations of the atmospheric boundary layer is proposed. The new model computes the wall shear stress and the vertical derivatives of the streamwise velocity component by means of a modified, instantaneous, and local law-of-the-wall formulation. By formulating a correction for the modeled shear stress, using experimental findings of a logarithmic region in the streamwise turbulent fluctuations, the need for a filter is eliminated. This allows one to model the wall shear stress locally, and at the same time accurately recover the correct average value. The proposed model has been applied to both unique high Reynolds number experimental data and a suite of large-eddy simulations, and compared to previous models. It is shown that the proposed model performs equally well or better than the previous filtered models. A nonfiltered model, such as the one proposed, is an essential first step in developing a universal wall shear stress model that can be used for flow over heterogeneous surfaces, studies of diurnal cycles, or analyses of flow over complex terrain.

Current affiliation: Department of Mechanical Engineering, University of Utah, Salt Lake City, Utah.

Corresponding author address: Marcus Hultmark, Department of Mechanical and Aerospace Engineering, Princeton University, D222 Engineering Quadrangle, Olden Street, Princeton, NJ 08544. E-mail: hultmark@princeton.edu

Abstract

A new wall shear stress model to be used as a wall boundary condition for large-eddy simulations of the atmospheric boundary layer is proposed. The new model computes the wall shear stress and the vertical derivatives of the streamwise velocity component by means of a modified, instantaneous, and local law-of-the-wall formulation. By formulating a correction for the modeled shear stress, using experimental findings of a logarithmic region in the streamwise turbulent fluctuations, the need for a filter is eliminated. This allows one to model the wall shear stress locally, and at the same time accurately recover the correct average value. The proposed model has been applied to both unique high Reynolds number experimental data and a suite of large-eddy simulations, and compared to previous models. It is shown that the proposed model performs equally well or better than the previous filtered models. A nonfiltered model, such as the one proposed, is an essential first step in developing a universal wall shear stress model that can be used for flow over heterogeneous surfaces, studies of diurnal cycles, or analyses of flow over complex terrain.

Current affiliation: Department of Mechanical Engineering, University of Utah, Salt Lake City, Utah.

Corresponding author address: Marcus Hultmark, Department of Mechanical and Aerospace Engineering, Princeton University, D222 Engineering Quadrangle, Olden Street, Princeton, NJ 08544. E-mail: hultmark@princeton.edu
Save
  • Albertson, J. D., and M. B. Parlange, 1999a: Natural integration of scalar fluxes from complex terrain. Adv. Water Resour., 23, 239252.

    • Search Google Scholar
    • Export Citation
  • Albertson, J. D., and M. B. Parlange, 1999b: Surface length scales and shear stress: Implications for land-atmosphere interaction over complex terrain. Water Resour. Res., 35, 21212132.

    • Search Google Scholar
    • Export Citation
  • Alfredsson, P. H., A. V. Johansson, J. H. Haritonidis, and H. Eckelmann, 1988: The fluctuating wall-shear stress and the velocity field in the viscous sublayer. Phys. Fluids, 31, 10261033.

    • Search Google Scholar
    • Export Citation
  • Avissar, R., E. W. Eloranta, K. Gürer, and G. J. Tripoli, 1998: An evaluation of the large-eddy simulation option of the regional atmospheric modeling system in simulating a convective boundary layer: A FIFE case study. J. Atmos. Sci., 55, 11091130.

    • Search Google Scholar
    • Export Citation
  • Bailey, S. C. C., and Coauthors, 2010: Turbulence measurements using a nanoscale thermal anemometry probe. J. Fluid Mech., 663, 160179.

    • Search Google Scholar
    • Export Citation
  • Belcher, S. E., I. N. Harman, and J. J. Finnigan, 2012: The wind in the willows: Flows in forest canopies in complex terrain. Annu. Rev. Fluid Mech., 44, 479504, doi:10.1146/annurev-fluid-120710-101036.

    • Search Google Scholar
    • Export Citation
  • Bou-Zeid, E., C. Meneveau, and M. B. Parlange, 2004: Large-eddy simulation of neutral atmospheric boundary layer flow over heterogeneous surfaces: Blending height and effective surface roughness. Water Resour. Res., 40, W02505, doi:10.1029/2003WR002475.

    • Search Google Scholar
    • Export Citation
  • Bou-Zeid, E., C. Meneveau, and M. B. Parlange, 2005: A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys. Fluids,17, 025105, doi:10.1063/1.1839152.

  • Bou-Zeid, E., M. Parlange, and C. Meneveau, 2007: On the parametrization of surface roughness at regional scales. J. Atmos. Sci., 64, 216227.

    • 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
  • Chew, Y. T., B. C. Khoo, C. P. Lim, and C. J. Theo, 1998: Dynamic response of a hot-wire anemometer. Part II: A flush-mounted hot-wire and hot-film probes for wall shear stress measurements. Meas. Sci. Technol., 9, 765778.

    • Search Google Scholar
    • Export Citation
  • Gong, W., P. Taylor, and A. Dörnbrack, 1996: Turbulent boundary-layer flow over fixed aerodynamically rough two-dimensional sinusoidal waves. J. Fluid Mech., 312, 137.

    • Search Google Scholar
    • Export Citation
  • Grötzbach, G., 1987: Direct numerical and large eddy simulations of turbulent channel flows. Complex Flow Phenomena and Modeling, N. P. Cheremisinoff, Ed., Vol. 6, Encyclopedia of Fluid Mechanics, Gulf Publishing, 1337–1391.

  • Hobson, J., N. Wood, and A. Brown, 1999: Large-eddy simulations of neutrally stratified flow over surfaces with spatially varying roughness length. Quart. J. Roy. Meteor. Soc., 125, 19371958.

    • Search Google Scholar
    • Export Citation
  • Hultmark, M., M. Vallikivi, S. C. C. Bailey, and A. J. Smits, 2012: Turbulent pipe flow at extreme Reynolds numbers. Phys. Rev. Lett.,108, 094501, doi:10.1103/PhysRevLett.108.094501.

  • Hultmark, M., M. Vallikivi, S. C. C. Bailey, and A. J. Smits, 2013: Logarithmic scaling of turbulence in smooth and rough-walled pipe flow. J. Fluid Mech., 728, 376395.

    • Search Google Scholar
    • Export Citation
  • Khoo, B. C., Y. T. Chew, C. P. Lim, and C. J. Teo, 1998: Dynamic response of a hot-wire anemometer. Part I: A marginally elevated hot-wire probe for near-wall velocity measurements. Meas. Sci. Technol., 9, 751763.

    • Search Google Scholar
    • Export Citation
  • Landau, L., and E. Lifshitz, 1959: Fluid Mechanics. Pergamon Press, 536 pp.

  • Marusic, I., and W. D. C. Heuer, 2007: Reynolds number invariance of the structure inclination angle in wall turbulence. Phys. Rev. Lett.,99, 114504, doi:10.1103/PhysRevLett.99.114504.

  • Marusic, I., G. J. Kunkel, and F. Porté-Agel, 2001: Experimental study of wall boundary conditions for large-eddy simulation. J. Fluid Mech., 446, 309320.

    • Search Google Scholar
    • Export Citation
  • Millikan, C. B., 1939: A critical discussion of turbulent flows in channels and circular tubes. Proceedings of the Fifth International Congress on Applied Mechanics, J. P. Den Hartog and H. Peters, Eds., Wiley, 386–932.

  • Moeng, C.-H., 1984: A large-eddy-simulation model for the study of planetary boundary-layer turbulence. J. Atmos. Sci., 41, 20522062.

    • Search Google Scholar
    • Export Citation
  • Monin, A., and A. Obukhov, 1954: Basic laws of turbulence mixing in the surface layer of the atmosphere. Tr. Geofiz. Inst., Akad. Nauk SSSR, 24, 163187.

    • Search Google Scholar
    • Export Citation
  • Piomelli, U., J. Ferziger, P. Moin, and J. Kim, 1989: New approximate boundary conditions for large eddy simulations of wall-bounded flows. Phys. Fluids, 1A, 1061, doi:10.1063/1.857397.

    • Search Google Scholar
    • Export Citation
  • Porté-Agel, F., C. Meneveau, and M. B. Parlange, 2000: A scale-dependent dynamic model for large-eddy simulation: Application to a neutral atmospheric boundary layer. J. Fluid Mech., 415, 261284.

    • Search Google Scholar
    • Export Citation
  • Porté-Agel, F., M. Pahlow, C. Meneveau, and M. B. Parlange, 2001: Atmospheric stability effect on subgrid-scale physics for large-eddy simulation. Adv. Water Resour., 24, 10851102.

    • Search Google Scholar
    • Export Citation
  • Prandtl, L., 1925: Bericht über Untersuchungen zur ausgebildeten Turbulenz. Z. Angew. Math. Mech., 5, 136139.

  • Prandtl, L., 1932: Zur turbulenten Strömung in Röhren und längs Platten. Ergeb. Aerodyn. Versuchsanst., 4, 1829.

  • Schumann, U., 1975: Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys., 18, 376404.

    • Search Google Scholar
    • Export Citation
  • Schumann, U., 1990: Large-eddy simulation of the up-slope boundary layer. Quart. J. Roy. Meteor. Soc., 116, 637670.

  • Shaw, R., and U. Schumann, 1992: Large-eddy simulation of turbulent flow above and within a forest. Bound.-Layer Meteor., 61, 4764.

  • Smits, A. J., J. Monty, M. Hultmark, S. C. C. Bailey, M. Hutchins, and I. Marusic, 2011: Spatial resolution correction for turbulence measurements. J. Fluid Mech., 676, 4153.

    • 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, 169187.

    • Search Google Scholar
    • Export Citation
  • Tennekes, H., and J. L. Lumley, 1972: A First Course in Turbulence. MIT Press, 300 pp.

  • Townsend, A. A., 1976: The Structure of Turbulent Shear Flow. 2nd ed. Cambridge University Press, 429 pp.

  • Vallikivi, M., M. Hultmark, S. C. C. Bailey, and A. J. Smits, 2011: Turbulence measurements in pipe flow using a nano-scale thermal anemometry probe. Exp. Fluids, 51, 15211527.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 456 179 14
PDF Downloads 396 149 17