Skip to main content
SpringerLink
Log in

Spatial spectra and characteristic horizontal scales of temperature and velocity fluctuations in the convective boundary layer of the atmosphere

  • Published:
Izvestiya, Atmospheric and Oceanic Physics Aims and scope Submit manuscript

Abstract

Using a high-resolution LES numerical model, we calculated the turbulent thermal convection for high ratios of horizontal and vertical sizes of the computational domain (26: 26: 1). The natural analog of the simulated process is a planetary boundary layer (PBL) of the atmosphere growing with height in the background of stably stratified overlying air layers over a horizontally homogeneous heated surface under a weak average wind. We obtained the spectral distributions of variances of fluctuations in potential temperature and velocity components in ranges corresponding to scales from a few tens of meters to a few tens of kilometers. We found energetically significant segments of the spectrum of large-scale fluctuations in the potential temperature for which the power dependences S ∼ k −1/3 and S ∼ k −4/3 are satisfied with good accuracy. We calculated the characteristic spatial scales of horizontal fluctuations in velocity and temperature. We obtained a dependence of these scales on the height of the growing convective PBL. We discuss the characteristic features of large-scale distributions in terms of the self-similarity of the growing boundary layer behavior.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. I. Barenblatt, “Similarity, Self-Similarity, Transitional Asymptotics. Theory and Applications to Geophysical Hydrodynamics,” (Gidrometeoizdat, Moscow, 1982) [In Russian].

    Google Scholar 

  2. A. V. Glazunov, “Large-Eddy Simulation of Turbulence with the Use of a Mixed Dynamic Localized Closure: Part 1. Formulation of the Problem, Model Description, and Diagnostic Numerical Tests,” Izv., Atmos. Ocean. Phys. 45(1), 5–24 (2009).

    Article  Google Scholar 

  3. A. V. Glazunov, “Large-Eddy Simulation of Turbulence with the Use of a Mixed Dynamic Localized Closure: Part 2. Numerical Experiments: Simulating Turbulence in a Channel with Rough Boundaries,” Izv., Atmos. Ocean. Phys. 45(1), 25–36 (2009).

    Article  Google Scholar 

  4. C. C. Zilitenkevich and S. A. Tyuryakov, “Theoretical Models of the Height of the Atmospheric Boundary Layer and Turbulent Entrainment at Its Upper Boundary,” Izv., Atmos. Ocean. Phys. 48(1), 133–140 (2012).

    Article  Google Scholar 

  5. S. S. Zilitinkevich, “Theoretical Model of Penetrating Turbulent Convection,” Izv-vo. AN SSSR, Fiz. Atmos. Okeana 23(6), 593–610 (1987).

    Google Scholar 

  6. N. N. Zubov, Arctic Ices (Izd. Glavsevmorputi, Moscow, 1945) [in Russian].

    Google Scholar 

  7. A. N. Kolmogorov, “Local Structure of Turbulence in Incompressible Fluid at Very Large Reynolds Numbers,” Dokl. Akad. Nauk SSSR 30(4), 99–102 (1941).

    Google Scholar 

  8. A. M. Obukhov, “On the Influence of Archimedean Forces on the Structure of the Temperature Field in a Turbulent Flow,” Dokl. Akad. Nauk SSSR 125(6), 1246–1248 (1959).

    Google Scholar 

  9. E. M. Agee, “Observations from Space and Thermal Convection: A Historical Perspective,” Bull. Am. Meteorol. Soc. 65(9), 938–946 (1984).

    Article  Google Scholar 

  10. B. W. Atkinson and J. W. Zhang, “Mesoscale Shallow Convection in the Atmosphere,” Rev. Geophys. 34(4), 403–431 (1996).

    Article  Google Scholar 

  11. A. K. Betts, “Non-Precipitating Cumulus Convection and Its Parameterization,” Q. J. R. Meteorol. Soc 99(419), 178–196 (1973).

    Article  Google Scholar 

  12. R. Bolgiano, Jr., “Turbulent Spectra in a Stably Stratified Atmosphere,” J. Geophys. Res. 64(12), 2226–2229 (1959).

    Article  Google Scholar 

  13. http://www.brockmann-consult.de/CloudStructures

  14. D. J. Carson, “The Development of a Dry Inversion-Capped Convectively Unstable Boundary Layer,” Q. J. R. Meteorol. Soc. 99(421), 450–467 (1973).

    Article  Google Scholar 

  15. J. W. Deardorff, “Convective Velocity and Temperature Scales for the Unstable Planetary Boundary Layer and for Rayleigh Convection,” J. Atmos. Sci. 27(8), 1211–1213 (1970).

    Article  Google Scholar 

  16. J. W. Deardorff, “Theoretical Expression for the Countergradient Vertical Heat Flux,” J. Geophys. Res. 77(30), 5900–5904 (1972).

    Article  Google Scholar 

  17. S. R. De Roode, P. G. Duynkerke, and H. J. J. Jonker, “Large-Eddy Simulation: How Large Is Large Enough?,” J. Atmos. Sci. 61(4), 403–421 (2004).

    Article  Google Scholar 

  18. M. Germano, “Turbulence: the Filtering Approach,” J. Fluid Mech. 238, 325–336 (1992).

    Article  Google Scholar 

  19. M. Germano, U. Piomelli, P. Moin, and W. H. Cabot, “A Dynamic Subgrid-Scale Eddy Viscosity Model,” Phys. Fluids A 3(7), 1760–1765 (1991).

    Article  Google Scholar 

  20. S. Ghosal, T. S. Lund, P. Moin, and K. Akselvoll, “A Dynamic Localization Model for Large Eddy Simulation of Turbulent Flows,” J. Fluid Mech. 286, 229–255 (1995).

    Article  Google Scholar 

  21. S. Grossman, V. S. L’vov, “Crossover of Spectral Scaling in Thermal Turbulence,” Phys. Rev. E 47(6), 4161–4168 (1993).

    Article  Google Scholar 

  22. A. A. M. Holtslag and C. H. Moeng, “Eddy Diffusivity and Countergradient Transport in the Convective Atmospheric Boundary Layer,” J. Atmos. Sci. 48(14), 1690–1698 (1991).

    Article  Google Scholar 

  23. H. J. J. Jonker, P. G. Duynkerke, and J. W. M. Cuijpers, “Mesoscale Fluctuations in Scalars Generated by Boundary Layer Convection,” J. Atmos. Sci. 56(5), 801–808 (1999).

    Article  Google Scholar 

  24. D. H. Lenschow, “Airplane Measurements of Planetary Boundary Layer Structure,” J. Appl. Meteorol. 9(6), 874–884 (1970).

    Article  Google Scholar 

  25. E. N. Lorenz, “Available Potential Energy and the Maintenance of the General Circulation,” Tellus 7(2), 157–167 (1955).

    Article  Google Scholar 

  26. Y. Morinishi, T. S. Lund, O. V. Vasilyev, and P. Moin, “Fully Conservative Higher Order Finite Difference Schemes for Incompressible Flow,” J. Comp. Phys. 143(1), 90–124 (1998).

    Article  Google Scholar 

  27. K. M. Pankaj and K. V. Mahendra, “Energy Spectra and Fluxes for Rayleigh-Bénard Convection,” Phys. Rev. E 81(5), 1–12 (2009).

    Google Scholar 

  28. P. P. Sullivan and E. G. Patton, “The Effect of Mesh Resolution on Convective Boundary Layer Statistics and Structures Generated by Large-Eddy Simulation,” J. Atmos. Sci. 68(10), 2395–2415 (2011).

    Article  Google Scholar 

  29. H. Tennekes, “A Model for the Dynamics of the Inversion above a Convective Boundary Layer,” J. Atmos. Sci. 30(4), 558–567 (1973).

    Article  Google Scholar 

  30. H. van Dop and G. Verver, “Countergradient Transport Revisited,” J. Atmos. Sci. 58(15), 2240–2247 (2001).

    Article  Google Scholar 

  31. H. Wang and G. Feingold, “Modeling Mesoscale Cellular Structures and Drizzle in Marine Stratocumulus. Part 1: Impact of Drizzle on the Formation and Evolution of Open Cells,” J. Atmos. Sci. 66(11), 3237–3256 (2009).

    Article  Google Scholar 

  32. H. Wang and G. Feingold, “Modeling Mesoscale Cellular Structures and Drizzle in Marine Stratocumulus. Part 2: The Microphysics and Dynamics of the Boundary Region between Open And Closed Cells,” J. Atmos. Sci. 66(11), 3257–3275 (2009).

    Article  Google Scholar 

  33. J. Warner, “Observations of the Eddy Fluxes of Heat and Vapour Over the Sea,” Q. J. R. Meteorol. Soc. 97(414), 540–547 (1971).

    Article  Google Scholar 

  34. S. Zilitinkevich, V. M. Gryanik, V. N. Lykossov, and D. V. Mironov, “Third-Order Transport and Nonlocal Turbulence Closures for Convective Boundary Layers,” J. Atmos. Sci. 56(11), 3463–3477 (1999).

    Article  Google Scholar 

  35. S. S. Zilitinkevich, “Turbulent Penetrative Convection” (Avebury Technical, Aldershot, 1991).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Numerical Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    A. V. Glazunov & V. P. Dymnikov

Authors
  1. A. V. Glazunov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. P. Dymnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Glazunov.

Additional information

Original Russian Text © A.V. Glazunov, V.P. Dymnikov, 2013, published in Izvestiya AN. Fizika Atmosfery i Okeana, 2013, Vol. 49, No. 1, pp. 37–61.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Glazunov, A.V., Dymnikov, V.P. Spatial spectra and characteristic horizontal scales of temperature and velocity fluctuations in the convective boundary layer of the atmosphere. Izv. Atmos. Ocean. Phys. 49, 33–54 (2013). https://doi.org/10.1134/S0001433813010040

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001433813010040

Keywords

Search

Navigation