Boundary-Layer Meteorology

, Volume 138, Issue 1, pp 61–75 | Cite as

On the Time Evolution of the Turbulent Kinetic Energy Spectrum for Decaying Turbulence in the Convective Boundary Layer

  • A. G. Goulart
  • B. E. J. Bodmann
  • M. T. M. B. de Vilhena
  • P. M. M. Soares
  • D. M. Moreira


Our focus is the time evolution of the turbulent kinetic energy for decaying turbulence in the convective boundary layer. The theoretical model with buoyancy and inertial transfer terms has been extended by a source term due to mechanical energy and validated against large-eddy simulation data. The mechanical effects in a boundary layer of height z i at a convective surface-layer height z = 0.05z i are significant in the time evolution of the vertical component of the spectrum, i.e. they enhance the decay time scale by more than an order of magnitude. Our findings suggest that shear effects seem to feedback to eddies with smaller wavenumbers, preserving the original shape of the spectrum, and preventing the spectrum from shifting towards shorter wavelengths. This occurs in the case where thermal effects only are considered.


Convective boundary layer Turbulent kinetic energy Vertical non-homogeneous turbulence field 


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  1. Batchelor GK (1949) Diffusion in a field of homogeneous turbulence. I Eulerian analysis. Aust J Sci Res 2: 437–450Google Scholar
  2. Batchelor GK (1953) The theory of homogeneous turbulence. Cambridge University, Cambridge, UK, p 197Google Scholar
  3. Cuijpers JWM, Bechtold P (1995) A simple parameterization of cloud water related variables for use in boundary layer models. J Atmos Sci 52(13): 2486–2490CrossRefGoogle Scholar
  4. Frisch U (1995) Turbulence. Cambridge University Press, Cambridge, UK, p 296Google Scholar
  5. Goulart A, Degrazia G, Rizza U, Anfossi D (2003) A theoretical model for the study of the convective turbulence decay and comparison witch LES data. Boundary-Layer Meteorol 107: 143–155CrossRefGoogle Scholar
  6. Goulart A, Vilhena MTMB, Degrazia G, Flores D (2007) Temporal, lateral and longitudinal eddy diffusivities for a decaying turbulence in the convective boundary layer. Ecol Model 204: 516–522CrossRefGoogle Scholar
  7. Heydarian M, Mullineaux N (1989) Solution of parabolic partial differential equations. Appl Math Model 5: 448–449CrossRefGoogle Scholar
  8. Hinze JO (1975) Turbulence. McGraw Hill, London, p 790Google Scholar
  9. Kaimal JC (1978) Horizontal velocity spectra in an unstable surface layer. J Atmos Sci 35(11): 18–23CrossRefGoogle Scholar
  10. Kristensen L, Lenschow D, Kirkegaard P, Courtney M (1989) The spectral velocity tensor for homogeneous boundary-layer turbulence. Boundary-Layer Meteorol 47: 149–193CrossRefGoogle Scholar
  11. Moeng CH, Sullivan PP (1994) A comparison of shear-and buoyancy-driven planetary boundary layer flows. J Atmos Sci 51: 999–1022CrossRefGoogle Scholar
  12. Monin AS, Obukhov AM (1954) Osnovnye zakonomernosti turbulentnogo peremeshivanija v prizemnom sloe atmosfery (Basic laws of turbulent mixing in the atmosphere near the ground). Trudy Geofiz Inst AN SSSR 24(151): 163–187Google Scholar
  13. Monin AS, Yaglom AM (1975) Statistical fluid mechanics: mechanics of turbulence, vol 2. MIT Press, Cambridge, p 874Google Scholar
  14. Nieuwstadt FTM, Brost RA (1986) The decay of convective turbulence. J Atmos Sci 43: 532–546CrossRefGoogle Scholar
  15. Obukhov AM (1946) Turbulentnost v temperaturnorodnoj atmosfere (Turbulence in an atmosphere with a non-uniform temperature). Trudy Inst Theor Geofiz AN SSSR 1: 95–115Google Scholar
  16. Pao YH (1965) Structure of turbulent velocity and scalar fields at large wave numbers. Phys Fluids 8: 1063–1075CrossRefGoogle Scholar
  17. Siebesma AP, Cuijpers JWM (1995) Evaluation of parametric assumptions for shallow cumulus convection. J Atmos Sci 52: 650–666CrossRefGoogle Scholar
  18. Sorbjan Z (1989) Structure of the atmospheric boundary layer. Prentice-Hall, Englewood Cliffs, NJ, p 317Google Scholar
  19. Sorbjan Z (1997) Decay of convective turbulence revisited. Boundary-Layer Meteorol 82: 501–515CrossRefGoogle Scholar
  20. Stull RB (1988) An introduction to boundary layer meteorology. Kluwer, Boston, p 670Google Scholar
  21. Tennekes H, Lumley JL (1994) A first course in turbulence. MIT Press, Cambridge, p 300Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • A. G. Goulart
    • 1
  • B. E. J. Bodmann
    • 2
  • M. T. M. B. de Vilhena
    • 2
  • P. M. M. Soares
    • 3
  • D. M. Moreira
    • 4
  1. 1.Federal University of the PampaAlegreteBrazil
  2. 2.Federal University of Rio Grande do SulPorto AlegreBrazil
  3. 3.University of LisbonCampo Grande, LisbonPortugal
  4. 4.Federal University of the PampaBagéBrazil

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