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Three-dimensional numerical study of turbulence in an entraining mixed layer

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Abstract

The mean structure calculated by a three-dimensional numerical model of a heated planetary boundary layer, in simulation of DAY 33 of the Australian Wangara data, has been previously described. The present study supplements it by describing properties of the calculated turbulence.

A major finding is the importance of entrainment upon turbulence statistics relating to specific humidity, relative to those for potential temperature. The variances, skewness and spectra of velocity, temperature and humidity are presented, as are budget equations for kinetic energy, temperature and humidity variances and heat/moisture fluxes. These are interpreted with regard to the relative importance of the surface flux vs the flux due to entrainment at the top of the mixed layer, and in regard to the structure which would occur if the entrainment were to vanish.

The Rotte-type closure assumption is tested for the correlation between the pressure fluctuation and the vertical gradient of vertical velocity, potential temperature, or specific humidity, and found to be qualitatively correct except near the top of the mixed layer.

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References

  • Batchelor, G. K.: 1953, The Theory of Homogeneous Turbulence, University Press, Cambridge, 197 pp.

    Google Scholar 

  • Clarke, R. H., Dyer, A. J., Brook, R. R., Reid, D. G., and Troup, A. J.: 1971, ‘The Wangara Experiment: Boundary Layer Data’, CSIRO Div. of Meteorol. Phys., Tech. Paper No. 19, 340 pp.

  • Crow, S. C.: 1968, ‘Viscoelastic Properties of Fine-Grained Incompressible Turbulence’, J. Fluid Mech. 33, 1–20.

    Google Scholar 

  • Deardorff, J. W.: 1972a (D1), ‘Numerical Investigation of Neutral and Unstable Planetary Boundary Layers’, J. Atmospheric Sci. 29, 91–115.

    Google Scholar 

  • Deardorff, J. W.: 1972b, ‘On the Magnitude of the Subgrid Scale Eddy Coefficient’, J. Comp. Phys. 7, 120–133.

    Google Scholar 

  • Deardorff, J. W.: 1973, ‘The Use of Subgrid Transport Equations in a Three-Dimensional Model of Atmospheric Turbulence’, J. Fluids Eng., Sept., 429–438.

  • Deardorff, J. W.: 1974 (D2), ‘Three-Dimensional Numerical Study of the Height and Mean Structure of a Heated Planetary Boundary Layer’, Boundary-Layer Meteorol. 7, 81–106.

    Google Scholar 

  • Lenschow, D. H.: 1970, ‘Airplane Measurements of Planetary Boundary Layer Structure’, J. Appl. Meteorol. 9, 874–884.

    Google Scholar 

  • Lenschow, D. H.: 1974, ‘Model of the Height Variation of the Turbulence Kinetic Energy Budget in the Unstable Planetary Boundary Layer’, J. Atmospheric Sci. 31, 465–474.

    Google Scholar 

  • Lewellen, W. S. and Teske, M.: 1973, ‘Prediction of the Monin-Obukhov Similarity Functions from an Invariant Model of Turbulence’, J. Atmospheric Sci. 30, 1340–1345.

    Google Scholar 

  • Lilly, D. K.: 1967, ‘The Representation of Small-Scale Turbulence in Numerical Simulation Experiments’, in Proceedings of the IBM Scientific Computing Symposium on Environmental Sciences, White Plains, N.Y.

    Google Scholar 

  • Lumley, J. and Khajeh-Nouri, B.: 1974, ‘Computational Modeling of Turbulent Transport, in Turbulent Diffusion in Environmental Pollution’, (Adv. Geophys. 18), F. N. Frenkiel and R. E. Munn, (eds.), Academic Press, Inc., New York.

    Google Scholar 

  • Mellor, G. L.: 1973, ‘Analytic Prediction of the Properties of Stratified Planetary Boundary Layers’, J. Atmospheric Sci. 30, 1061–1069.

    Google Scholar 

  • Phelps, G. T. and Pond, S.: 1971, ‘Spectra of the Temperature and Humidity Fluctuations and of the Fluxes of Moisture and Sensible Heat in the Marine Boundary Layer’, J. Atmospheric Sci. 28, 918–928.

    Google Scholar 

  • Rotta, J.: 1951, ‘Statistische Theorie Nichthomogener Turbulenz’, Z. Phys. 129, 547–572.

    Google Scholar 

  • Telford, J. W. and Warner, J.: 1964, ‘Fluxes of Heat and Vapor in the Lower Atmosphere derived from Aircraft Observations’, J. Atmospheric Sci. 21, 539–548.

    Google Scholar 

  • Willis, G. and Deardorff, J. W.: 1974, ‘A Laboratory Model of the Unstable Planetary Boundary Layer’, to appear in J. Atmospheric Sci. 31.

  • Wyngaard, J. C.: 1973, ‘On Surface-Layer Turbulence’, in Workshop in Micrometeorology, D. A. Haugen (ed.), American Meteorological Society, Boston, Mass., pp. 101–149.

    Google Scholar 

  • Wyngaard, J. C. and Coté, O. R.: 1971, ‘The Budgets of Turbulent Kinetic Energy and Temperature Variance in the Atmospheric Surface Layer’, J. Atmospheric Sci. 28, 190–201.

    Google Scholar 

  • Wyngaard, J. C., Coté, O. R., and Izumi, Y.: 1971, ‘Local Free Convection, Similarity, and the Budgets of Shear Stress and Heat Flux’, J. Atmospheric Sci. 28, 1171–1182.

    Google Scholar 

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NCAR is sponsored by the National Science Foundation (U.S.A.).

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Deardorff, J.W. Three-dimensional numerical study of turbulence in an entraining mixed layer. Boundary-Layer Meteorol 7, 199–226 (1974). https://doi.org/10.1007/BF00227913

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