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Some aspects of the turbulent stable boundary layer

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Abstract

We consider the structure of the stable boundary layer using the concept of local scaling. In this scaling approach turbulence variables, non-dimensionalized with measurements taken at the same height, can be expressed as a function of a single parameter z/Λ, where z is the height and Λ a local Obukhov length. One of the consequences is that locally scaled variables become constant above the surface layer. This behavior is illustrated with observations of the Richardson number. With local scaling as a closure hypothesis we then formulate a model of the stable boundary layer. Its solution for steady-state conditions is given. One result we obtain is the well-known Zilitinkevich equation for the boundary-layer height. A comparison of this equation with observations results in a reasonable agreement. Also we discuss some alternative expressions for the stable boundary-layer height and compare them with observations. Another result of our model is an explicit profile for the K-coefficient as a quadratic function of height. We discuss the consequences of this expression for the dispersion of a point source emission. We find that the time scale of diffusion in this case is about 5 hours.

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References

  • André, J.C.: 1983, ‘On the variability of the nocturnal boundary-layer depth’, J. Atmos. Sci. 40, 2309–2311.

    Google Scholar 

  • André, J.C. and Mahrt, L.: 1982, ‘The nocturnal surface inversion and influence of clear-air radiative cooling’, J. Atmos. Sci. 39, 864–878.

    Google Scholar 

  • Arya, S.P.S.: 1981: ‘Parameterizing the height of the stable atmospheric boundary layer’, J. Appl. Meteorol. 20, 1192–1202.

    Google Scholar 

  • Brost, R.A. and Wyngaard, J.C.: 1978, ‘A model study of the stably stratified planetary boundary layer’, J. Atmos. Sci. 35, 1427–1440.

    Google Scholar 

  • Businger, J.A., Wyngaard, J.C., Izumi, Y., and Bradley, F.F.: 1971, ‘Flux profile relationships in the atmospheric surface layer’, J. Atmos. Sci. 28, 181–189.

    Google Scholar 

  • Businger, J.A.: 1982, ‘Equations and concepts’, Atmospheric Turbulence and Air Pollution Modelling, F.T.M. Nieuwstadt and H. van Dop (eds.) D. Reidel Publishing Company, Dordrecht, Holland.

    Google Scholar 

  • Caughey, S.J. and Readings, C.J.: 1975, ‘An observation of waves and turbulence in the earth's boundary layer’, Boundary-Layer Meteorol. 9, 279–296.

    Google Scholar 

  • Caughey, S.J., Wyngaard, J.C. and Kaimal, J.C.: 1979, ‘Turbulence in the evolving stable boundary layer’, J. Atmos. Sci., 36, 1041–1052.

    Google Scholar 

  • Dyer, A.J.: 1974, ‘A Review of flux-profile relationships’, Boundary-Layer Meteorol. 7, 363–372.

    Google Scholar 

  • Einaudi, F. and Finnigan, J.J.: 1981, ‘The interaction between an internal gravity wave and the planetary boundary layer. Part I: The linear analysis’, Quart. J. Roy. Meteorol. Soc. 107, 793–806.

    Google Scholar 

  • Garratt, J.R. and Brost, R.A.: 1981, ‘Radiative cooling effects within and above the nocturnal boundary layer’, J. Atmos. Sci., 2730–2746.

  • Garratt, J.R.: 1982a, ‘Observations in the nocturnal boundary layer’, Boundary-Layer Meteorol. 22, 21–48.

    Google Scholar 

  • Garratt, J.R.: 1982b, ‘Surface fluxes and the nocturnal boundary-layer height’, J. Appl. Meteorol. 21, 725–729.

    Google Scholar 

  • Hunt, J.C.R.: 1982, ‘Diffusion in the stable boundary layer’, Atmospheric Turbulence and Air Pollution Modelling, F.T.M. Nieuwstadt and H. van Dop (eds.) D. Reidel Publishing Company, Dordrecht Holland.

    Google Scholar 

  • Hunt, J.C.R., Kaimal, J.C., Gaynor, J.E. and Korrell, A.: 1983, ‘Observations of turbulence structure in stable layers at the Boulder Atmospheric Observatory’. Studies of Nocturnal Stable Layers at BAO, J.C. Kaimal (ed.), NOAA/ERL, Boulder.

    Google Scholar 

  • Keisuke, F., Masamomoto, N., and Ueda, H.: 1983, ‘A laboratory experiment on momentum and heat transfer in the stratified surface layer’, Quart. J. R. Meteorol. Soc. 109, 661–676.

    Google Scholar 

  • Kerman, B.R.: 1979, ‘A similarity model for maximum ground-level concentration in a height-invariant, stably stratified atmospheric boundary layer’, Boundary-Layer Meteorol. 17, 297–313.

    Google Scholar 

  • Kondo, J., Kanechika, O. and Yasuda, N.: 1978, ‘Heat and momentum transfer under strong stability in the atmospheric surface layer’, J. Atmos. Sci. 35, 1012–1021.

    Google Scholar 

  • Mahrt, L.: 1981, ‘Modelling the depth of the stable boundary-layer’, Boundary-Layer Meteorol. 21, 3–19.

    Google Scholar 

  • Mahrt, L. and Heald, R.C.: 1979, ‘Comments on determining height of the nocturnal boundary layer’, J. Appl. Meteorol. 36, 383.

    Google Scholar 

  • Mahrt, L., Heald, R.C., Lenschow, D.H. and Stankov, B.B.: 1979, ‘An observational study of the structure of the nocturnal boundary layer’, Boundary-Layer Meteorol. 17, 247–264.

    Google Scholar 

  • Mahrt, L., André, J.C. and Heald, R.C.: 1982, ‘On the depth of the nocturnal boundary layer’, J. Appl. Meteorol. 21, 90–92.

    Google Scholar 

  • McPhee, M.: 1981, ‘An analytic similarity theory for the planetary boundary layer stabilized by surface buoyancy’, Boundary-Layer Meteorol. 21, 325–339.

    Google Scholar 

  • Monin, A.S. and Yaglom, A.M.: 1971, ‘Statistical Fluid Mechanics. Vol. I’, M.I.T. Press, Cambridge, Mass.

    Google Scholar 

  • Nai-Ping, L., Neff, W.D. and Kaimal, J.C.: 1983, ‘Wave and turbulence structure in a disturbed nocturnal inversion’, Boundary-Layer Meteorol. 26, 141–155.

    Google Scholar 

  • Nieuwstadt, F.T.M.: 1981, ‘The steady-state height and resistance laws of the nocturnal boundary layer: Theory compared with Cabauw observations’, Boundary-Layer Meteorol. 20, 3–17.

    Google Scholar 

  • Nieuwstadt, F.T.M.: 1984a, ‘The turbulent structure of the stable nocturnal boundary layer’, submitted to J. Atmos. Sci.

  • Nieuwstadt, F.T.M.: 1984b, ‘A model for the stationary, stable boundary layer’, Proceedings of the conference on Models of Turbulence and Diffusion in Stably Stratified Regions of the Natural Environment, March 1983, Cambridge.

  • Nieuwstadt, F.T.M. and Tennekes, H.: 1981, ‘A rate equation for the nocturnal boundary-layer height’, J. Atmos. Sci. 38, 1418–1428.

    Google Scholar 

  • Pearson, H.J., Putlock, J.S. and Hunt, J.C.R.: 1983, ‘A statistical model of fluid-element motions and vertical diffusion in a homogeneous statified turbulent flow’, J. Fluid Mech. 129, 219–249.

    Google Scholar 

  • Rao, K.S. and Snodgrass, H.F.: 1979, ‘Some parameterizations of the nocturnal boundary layer’, Boundary-Layer Meteorol. 17, 15–28.

    Google Scholar 

  • Smeda, M.: 1979, ‘Incorporation of planetary boundary-layer processes into numerical forecasting models’, Boundary-Layer Meteorol. 16, 115–129.

    Google Scholar 

  • Stull, R.B.: 1983a, ‘A heat-flux history length scale for the nocturnal boundary layer’, Tellus 35A, 219–230.

    Google Scholar 

  • Stull, R.B.: 1983b, ‘Integral scales for the nocturnal boundary layer part 2: heat budget, transport, and energy implications’, J. Climate Appl. Meteor. 22, 1932–1941.

    Google Scholar 

  • Tennekes, H.: 1982, ‘Similarity relations, scaling laws and spectral dynamics’, Atmospheric Turbulence and Air Pollution Modelling, F.T.M. Nieuwstadt and H. van Dop (eds.) D. Reidel Publishing Company, Dordrecht, Holland.

    Google Scholar 

  • Ueda, H., Mitsumoto, S., and Komori, S.: 1981, ‘Buoyancy effects on the turbulent transport processes in the lower atmosphere’, Quart. J. R. Meteorol. Soc. 107, 561–578.

    Google Scholar 

  • Van Ulden, A.P. and Holtslag, A.A.M.: 1983, ‘The stability of the atmospheric surface layer’, Preprint volume 6th symposium on turbulence and diffusion, March 1983, Boston, American Meteorological Society.

    Google Scholar 

  • Venkatram, A.: 1980, ‘Estimating the Monin-Obukhov length in the stable boundary layer for dispersion calculations’, Boundary-Layer Meteorol. 19, 481–485.

    Google Scholar 

  • Wetzel, P.: 1982, ‘Toward parameterization of the stably boundary layer’, J. Appl. Meteorol. 21, 7–13.

    Google Scholar 

  • Wyngaard, J.C.: 1973, ‘On surface layer turbulence’, Workshop on Micrometeorology. D.A. Haugen (ed.), American Meteorological Society, Boston.

    Google Scholar 

  • Yamada, T.: 1979, ‘PBL similarity profiles determined from a level-2 turbulence closure model’, Boundary-Layer Meteorol. 17, 333–351.

    Google Scholar 

  • Yamamoto, S., Yokoyama, O. and Gamo, M.: 1979, ‘Observational study on the turbulent structure of the atmospheric boundary layer under stable conditions’, J. Meteorol. Soc. Japan 57, 423–431.

    Google Scholar 

  • Yu, T.: 1978, ‘Determining height of the nocturnal boundary layer’, J. Appl. Meteorol. 17, 28–33.

    Google Scholar 

  • Zeman, O.: 1979, ‘Parameterization of the dynamics of stable boundary layers and nocturnal jets’, J. Atmos. Sci. 36, 792–804.

    Google Scholar 

  • Zilitinkevich, S.S.: 1972, ‘On the determination of the height of the Ekman boundary layer’, Boundary-Layer Meteorol. 3, 141–145.

    Google Scholar 

Download references

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Authors and Affiliations

  1. Royal Netherlands Meteorological Institute, De Bilt, The Netherlands

    F. T. M. Nieuwstadt

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  1. F. T. M. Nieuwstadt
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Nieuwstadt, F.T.M. Some aspects of the turbulent stable boundary layer. Boundary-Layer Meteorol 30, 31–55 (1984). https://doi.org/10.1007/BF00121948

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