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A numerical study of the convective boundary layer

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Abstract

Computations of the buoyantly unstable Ekman layer are performed at low Reynolds number. The turbulent fields are obtained directly by solving the three-dimensional time-dependent Navier-Stokes equations (using the Boussinesq approximation to account for buoyancy effects), and no turbulence model is needed. Two levels of heating are considered, one quite vigorous, the other more moderate. Statistics for the vigorously heated case are found to agree reasonably well with laboratory, field, and large-eddy simulation results, when Deardorff's mixed-layer scaling is used. No indication of large-scale longitudinal roll cells is found in this convection-dominated flow, for which the inversion height to Obukhov length scale ratio −z i /L *=26. However, when heating is more moderate (so that −z i /L *=2), evidence of coherent rolls is present. About 10% of the total turbulent kinetic energy and turbulent heat flux, and 20% of the Reynolds shear stress, are estimated to be a direct consequence of the observed cells.

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References

  • Abramowitz, M. and Stegun, A. (eds.): 1972,Handbook of Mathematical Functions. National Bureau of Standards Appl. Math. Series 55. Also published by Dover.

  • Brown, R. A.: 1974,Analytical Methods in Planetary Boundary-layer Modelling. Wiley.

  • Brown, R. A.: 1980, ‘Longitudinal Instabilities and Secondary Flows in the Planetary Boundary Layer: A Review’,Rev. Geophys. Space Phys. 18, 683–697.

    Google Scholar 

  • Businger, J. A.: 1982, ‘Equations and Concepts’, in F. T. M. Nieuwstadt and H. Van Dop (eds.),Atmospheric Turbulence and Air Pollution Modelling, Chap. 1, D. Reidel.

  • Caughey, S. J.: 1982, ‘Observed Characteristics of the Atmospheric Boundary Layer. Equations and Concepts’, in F. T. M. Nieuwstadt and H. Van Dop (eds.),Atmospheric Turbulence and Air Pollution Modelling, Chap. 4, D. Reidel.

  • Chlond, A.: 1992, ‘Three-Dimensional Simulation of Cloud Street Development During a Cold Air Outbreak’,Boundary-Layer Meteorol. 58, 161–200.

    Google Scholar 

  • Chrobok, G., Raasch, S. and Etling, D.: 1992, ‘Comparison of Local and Non-Local Turbulence Closure Methods for the Case of a Cold Air Outbreak’,Boundary-Layer Meteorol. 58, 69–90.

    Google Scholar 

  • Coleman, G. N., Ferziger, J. H. and Spalart, P. R.: 1990a, ‘A Numerical Study of the Turbulent Ekman Layer’,J. Fluid Mech. 213, 313–348 (referred to herein as CFSa).

    Google Scholar 

  • Coleman, G. N., Ferziger, J. H. and Spalart, P. R.: 1990b,A. Numerical Study of the Stratified Turbulent Ekman Layer, Dept. of Mech. Engrg., Stanford University, Thermosciences Div. Report TF-48 (referred to herein as CFSb).

  • Coleman, G. N., Ferziger, J. H. and Spalart, P. R.: 1992, ‘Direct Simulation of the Stably Stratified Turbulent Ekman Layer’,J. Fluid Mech. 244, 677–712. Corrigendum:J. Fluid Mech. 252, 271.

    Google Scholar 

  • Deardorff, J. W.: 1966, ‘The Counter-Gradient Heat Flux in the Lower Atmosphere and in the Laboratory’,J. Atmos. Sci. 23, 503–506.

    Google Scholar 

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

    Google Scholar 

  • Deardorff, J. W. and Willis, G. E.: 1985, ‘Further Results from a Laboratory Model of the Convective Boundary Layer’,Boundary-Layer Meteorol. 32, 205–236.

    Google Scholar 

  • Etling, D. and Raasch, S.: 1987, ‘Numerical Simulation of Vortex Roll Development During a Cold Air Outbreak’,Dyn. Atmos. Oceans. 10, 277–290.

    Google Scholar 

  • Gedzelman, S. D.: 1980,The Science and Wonders of the Atmosphere, Wiley.

  • Grossman, R. L.: 1982, ‘An Analysis of Vertical Velocity Spectra Obtained in the BOMEX Fair-Weather, Trade-Wind Boundary Layer’,Boundary-Layer Meteorol. 23, 323–357.

    Google Scholar 

  • Holton, J. R.: 1979,An Introduction to Dynamic Meteorology, Academic Press.

  • Hunt, J. C. R., Kaimal, J. C. and Gaynor, J. E.: 1988, ‘Eddy Structure in the Convective Boundary Layer — New Measurements and Concepts’,Q. J. R. Meteorol. Soc. 114, 827–858.

    Google Scholar 

  • Leibovich, S. and Lele, S. K.: 1985, ‘The influence of the Horizontal Component of Earth's Angular Velocity on the Instability of the Ekman Layer’,J. Fluid Mech. 150, 41–87.

    Google Scholar 

  • LeMone, M. A.: 1973, ‘The Structure and Dynamics of Horizontal Roll Vortices in the Planetary Boundary Layer’,J. Atmos. Sci. 30, 1077–1091.

    Google Scholar 

  • Lenschow, D. H., Wyngaard, J. C. and Pennell, W. T.: 1980, ‘Mean-Field and Second-Moment Budgets in a Baroclinic, Convective Boundary Layer’,J. Atmos. Sci. 37, 1313–1326.

    Google Scholar 

  • Ludwig, F. L.: 1993, ‘Analysis of Patterns of Atmospheric Motions at Different Scales’, Ph.D. Thesis, Dept. of Civil Engrg., Stanford University.

  • Mason, P. J. and Sykes, R. I.: 1982, ‘A Two-Dimensional Numerical Study of Horizontal Roll Vortices in an Inversion Capped Planetary Boundary Layer’,Q. J. R. Meteorol. Soc. 108, 801–823.

    Google Scholar 

  • Mason, P. J. and Thomson, D. J.: 1987, ‘Large-Eddy Simulations of the Neutral-Static-Stability Planetary Boundary Layer’,Q. J. R. Meteorol. Soc. 113, 413–443.

    Google Scholar 

  • Mason, P. J.: 1989, ‘Large-Eddy Simulation of the Convective Atmospheric Boundary Layer’,J. Atmos. Sci. 46, 1492–1516.

    Google Scholar 

  • Moeng, C.-H. and Wyngaard, J. C.: 1984, ‘Statistics of Conservative Scalars in the Convective Boundary Layer’,J. Atmos. Sci. 41, 3161–3169.

    Google Scholar 

  • Moeng, C.-H. and Wyngaard, J. C.: 1989, ‘Evaluations of Turbulent Transport and Dissipation Closures in Second-Order Modeling’,J. Atmos. Sci. 46, 2311–2330.

    Google Scholar 

  • Müller, D., Etling, D., Kottmeier, Ch. and Roth, R.: 1985, ‘On the Occurrence of Cloud Streets over Northern Germany’,Q. J. R. Meteorol. Soc. 111, 761–772.

    Google Scholar 

  • Nieuwstadt, F. T. M., Mason, P. J., Moeng, C.-H. and Schumann, U.: 1991, Large-Eddy Simulation of the Convective Boundary Layer: A Comparison of Four Computer codes.Proc. 8th Symp. on Turbulent Shear Flows, Munich, Germany, September 9–11, 1991.

  • Padofsky, H. A. and Dutton, J. A.: 1984,Atmospheric Turbulence — Models and Methods for Engineering Applications, Wiley.

  • Raasch, S.: 1990, ‘Numerical Simulation of the Development of the Convective Boundary Layer During a Cold Air Outbreak’,Boundary-Layer Meteorol. 52, 349–375.

    Google Scholar 

  • Schmidt, H. and Schumann, U.: 1989, ‘Coherent Structure of the Convective Boundary Layer Derived from Large-Eddy Simulations’,J. Fluid Mech. 200, 511–562.

    Google Scholar 

  • Sorbjan, Z.: 1991, ‘Evaluation of Local Similarity in the Convective Boundary Layer’,J. Appl. Meteorol. 30, 1565–1583.

    Google Scholar 

  • Spalart, P. R.: 1988, ‘Direct Simulation of a Turbulent Boundary Layer up toR ⊖=1410’,J. Fluid Mech. 187, 61–98.

    Google Scholar 

  • Spalart, P. R.: 1989, ‘Theoretical and Numerical Study of a Three-Dimensional Turbulent Boundary Layer’,J. Fluid Mech. 205, 319–340.

    Google Scholar 

  • Spalart, P. R., Moser, R. D. and Rogers, M. M.: 1991, ‘Spectral Methods for the Navier-Stokes Equations with One Infinite and Two Periodic Directions’,J. Comp. Phys. 96, 297–324.

    Google Scholar 

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

  • Sykes, R. I., Lewellen, W. S., and Henn, D. S.: 1990, ‘Numerical Simulation of the Boundary-Layer Eddy Structure During the Cold Air Outhreak of GALE IOP 2’,Mon. Wea. Rev. 118, 363–374.

    Google Scholar 

  • Walter, B. A. and Overland, J. E.: 1984, ‘Observations of Longitudinal Rolls in a Near Neutral Atmosphere’,Mon. Wea. Rev. 112, 200–208.

    Google Scholar 

  • Willis, G. E. and Deardorff, J. W.: 1974, ‘A Laboratory Model of the Unstable Planetary Boundary Layer’,J. Atmos. Sci. 31, 1297–1307.

    Google Scholar 

  • Wyngaard, J. C. and Brost, R. A.: 1984, ‘Top-Down and Bottom-Up Diffusion of a Scalar in the Convective Boundary Layer’,J. Atmos. Sci. 41, 102–112.

    Google Scholar 

  • Wyngaard, J. C.: 1992, ‘Atmospheric Turbulence’,Ann. Rev. Fluid Mech. 24, 205–233.

    Google Scholar 

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Author notes

  1. G. N. Coleman

    Present address: Mechanical, Aerospace and Nuclear Engineering Department, University of California, 90024, Los Angeles, California, USA

  2. P. R. Spalart

    Present address: Boeing Commercial Airplane Group, 98124, Seattle, Washington, USA

Authors and Affiliations

  1. Department of Mechanical Engineering, Stanford University, 94305, Stanford, California, USA

    G. N. Coleman & J. H. Ferziger

  2. NASA Ames Research Center, 94035, Moffett Field, California, USA

    P. R. Spalart

Authors
  1. G. N. Coleman
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  2. J. H. Ferziger
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  3. P. R. Spalart
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Coleman, G.N., Ferziger, J.H. & Spalart, P.R. A numerical study of the convective boundary layer. Boundary-Layer Meteorol 70, 247–272 (1994). https://doi.org/10.1007/BF00709121

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