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Models of eddy viscosity for numerical simulation of horizontally inhomogeneous, neutral surface-layer flow

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Abstract

Modification of a turbulent flow due to a change from a smooth to a rough surface has been studied by means of a stream function-vorticity model. Results of four models of eddy viscosity (or turbulent exchange coefficient) K mhave been compared. The models are: (1) K m = l2S, where l is the mixing length and S is the deformation of mean flow; (2) K m ∼ E/S, which is based on the assumption that turbulent momentum flux is proportional to turbulent kinetic energy E; (3) K m ∼ lE1/2, the so called Prandtl-Kolmogoroff approach; and (4) K m ∼ E2/ɛ, the E — ɛ closure, where ɛ is the dissipation of turbulent kinetic energy.

It is found that net-production, i.e., the difference of production and dissipation of turbulent kinetic energy counteracts the influence of mean shear on turbulent shear stress and diminishes turbulent shear stress. The reduction of mixing-length, being predicted by Model 4 only, adds to this attenuation. As a consequence, in Models 2 and 4, loss of horizontal mean momentum is concentrated close to the ground, which results in an inflexion point in the logarithmic, vertical profile of horizontal mean velocity. By contrast, in Models 1 and 3, modification of turbulent shear stress reaches larger heights causing deeper internal boundary layers. Concerning the existence of an inflexion point in U(lnz), the depth of the internal boundary layer for mean velocity, and the modification of bottom shear stress, Model 4 comes closest to experimental data.

A remarkable difference of Models 1, 2, 3 and Model 4 is that only Model 4 predicts a very slow relaxation of eddy viscosity which can be attributed to the reduction of mixing-length.

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References

  • Beljaars, A. C. M.: 1982, ‘The Derivation of Fluxes from Profiles in Perturbed Areas’, Boundary-Layer Meteorol. 24, 35–55.

    Google Scholar 

  • Beljaars, A. C. M., Schotanus, P., and Nieuwstadt, F. T. M.: 1983, ‘Surface Layer Similarity Under Nonuniform Fetch Conditions’, J. Climate App. Meteorol. 22, 1800–1810.

    Google Scholar 

  • Beljaars, A. C. M., Walmsley, J. L., and Taylor, P. A.: 1987, ‘A Mixed Spectral Finite-Difference Model for Neutrally Stratified Boundary-Layer Flow over Roughness Changes and Topography’, Boundary-Layer Meteorol. 38, 273–303.

    Google Scholar 

  • Bradley, E. F.: 1968, ‘A Micrometeorological Study of Velocity Profiles and Surface Drag in the Region Modified by a Change in Surface Roughness’, Quart. J. Roy. Meteorol. Soc. 94, 361–379.

    Google Scholar 

  • Claussen, M.: 1985, ‘A Model of Turbulence Spectra in the Atmospheric Surface Layer’, Boundary-Layer Meteorol. 33, 151–172.

    Google Scholar 

  • Claussen, M.: 1987, ‘The Flow in a Turbulent Boundary Layer Upstream of a Change in Surface Roughness’, Boundary-Layer Meteorol. 40, 31–86.

    Google Scholar 

  • Duynkerke, P. G.: 1987, ‘An Application of the E-ɛ Turbulence Closure Model to the Neutral and Stable Atmospheric Boundary Layer’, J. Atmos. Sci. (in press).

  • Elliott, W. P.: 1958, ‘The Growth of the Atmospheric Internal Boundary’, Trans. A. G. U. 39, 1048–1054.

    Google Scholar 

  • Hasse, L.: 1978, ‘Parameterization of the Dissipation Term in Second-Order Closure Modelling of the Planetary Boundary Layer Under Conditions of Forced Convection’, Contr. Atmos. Phys. 51, 166–173.

    Google Scholar 

  • Hinze, H. O.: 1975, Turbulence, McGraw-Hill Book Co., New York, 790 p.

    Google Scholar 

  • Jackson, P. S. and Hunt, J. C. R.: 1975, ‘Turbulent Wind Flow Over a Low Hill’, Quart. J. Roy. Meteorol. Soc. 101, 929–955.

    Google Scholar 

  • Lo, A. K.-F.: 1986, ‘On the Boundary-Layer Flow Over a Canadian Archipelago Polynia’, Boundary-Layer Meteorol. 35, 53–71.

    Google Scholar 

  • Lumley, J. L. and Panofsky, H. A.: 1964, The Structure of Atmospheric Turbulence, Interscience Publ., New York, 239 p.

    Google Scholar 

  • Mellor, G. L. and Yamada, T.: 1982, ‘Development of a Turbulence Closure for Geophysical Fluid Problems’, Rev. Geophys. Space Phys. 20, 851–875.

    Google Scholar 

  • Miyake, M.: 1965, Transformation of the Atmospheric Boundary Layer Over Inhomogeneous Surfaces, Scientific Report, Univ. of Wash., Seattle, 63 p.

    Google Scholar 

  • Panofsky, H. A. and Dutton, J. A.: 1984, Atmospheric Turbulence, John Wiley and Sons, Toronto, 397 p.

    Google Scholar 

  • Peterson, E. W.: 1969, ‘Modification of Mean Flow and Turbulent Energy by a Change in Surface Roughness Under Condition of Neutral Stability’, Quart. J. Roy. Meteorol. Soc. 95, 561–575.

    Google Scholar 

  • Rao, K. S., Wyngaard, J. C. and Coté, O. R.: 1974, ‘The Structure of the Internal Boundary Layer Over a Sudden Change of Surface Roughness’, J. Atmos. Sci. 31, 738–746.

    Google Scholar 

  • Shir, C. C.: 1972, ‘A Numerical Computation of Air Flow Over a Sudden Change of Surface Roughness’, J. Atmos. Sci. 29, 304–310.

    Google Scholar 

  • Taylor, P. A.: 1970, ‘A Model of Airflow Above Changes in Surface Heat Flux Temperature and Roughness, for Neutral and Unstable Conditions’, Boundary-Layer Meteorol. 1, 18–39.

    Google Scholar 

  • Walmsley, J. L., Taylor, P. A., and Keith, T.: 1986, ‘A Simple Model of Neutrally Stratified Boundary-Layer Flow Over Complex Terrain with Surface Roughness Modulations (MS3DJH/3R)’, Boundary-Layer Meteorol. 36, 157–186.

    Google Scholar 

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Claussen, M. Models of eddy viscosity for numerical simulation of horizontally inhomogeneous, neutral surface-layer flow. Boundary-Layer Meteorol 42, 337–369 (1988). https://doi.org/10.1007/BF00121590

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