Skip to main content
SpringerLink
Log in

Calculation of Higher-Order Moments in the Atmospheric Boundary Layer

  • Published:
Journal of Engineering Thermophysics Aims and scope

Abstract

The results of analyzing a number of models to calculate the statistical fourth-order moments of turbulent fluctuations of vertical velocity and temperature, which describe diffusion processes in equations for triple correlations in RANS models, are presented. Correct calculation of higher-order moments allows adequate description of the impact of large-scale vortex structures on the vertical flow of turbulence energy, as well as the impact of chemical reactions (in the case of reactive impurities) and/or phase transitions (moisture condensation and evaporation) in the atmospheric boundary layer.Results of calculations with the use of the quasi-normality hypothesis, a number of empirical formulas. and algebraic models for fourth-order cumulants are comparedwith in situ measurements in the convective boundary layer of the atmosphere. It is shown that the secondorder- closure models, which are much more efficient in numerical implementation than the thirdorder models, predict the behavior of the higher-order moments not worse than the latter.

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. Atmosfernaya turbulentnost’ i modelirovanie rasprostraneniya primesei (Atmospheric Turbulence and Modeling of Impurities., Nistadt, F.T. and Van Dop, X., Eds., Leningrad: Gidrometeoizdat, 1985.

  2. Andre, J.C., De Moor, G., Lacarrere P., Therry, G., and du Vachat, R., Modeling the 24-Hour Evolution of the Mean and Temperature Structures of the Planetary Boundary Layer, J. Atm. Sci., 1978, vol. 35, no. 10, pp. 1861–1883.

    Article  ADS  Google Scholar 

  3. Ilyushin, B.B. and Kurbatskii, A.F., Modeling of Triple Correlations in the Convective Atmospheric Boundary Layer, Izv.AN, Fiz.Atm. Okeana, 1998, vol. 34, no. 6, pp. 640–644.

    Google Scholar 

  4. Ilyushin, B.B. and Kurbatskii, A.F., New Models for Computing Third-Order-Moment Model in the Planetary Boundary Layer,Math. Russian Acad. Sci., Atm. Ocean. Phys., 1998, vol. 34, no. 6, pp. 772–781.

    Google Scholar 

  5. Millionshchikov, M.D.,On the Theory of Homogeneous Isotropic Turbulence, Dokl. ANUSSR, 1941, vol. 32, no. 9, pp. 611–614.

    Google Scholar 

  6. Cheng, Y., Canuto, V.M., and Howard, A.M., Nonlocal Convective PBL Model Based on New Third- and Fourth-Order Moments, J. Atmos. Sci., 2005, vol. 62, pp. 2189–2204.

    Article  ADS  MathSciNet  Google Scholar 

  7. Ilyushin, B.B., Fourth-Order Cumulants Model to Describe Turbulent Transport of Large-Scale Vortex Structures, PMTF, 1999, vol. 40, no. 5, pp. 106–112.

    MATH  Google Scholar 

  8. Ilyushin, B.B., Higher Moment Diffusion in Stably Stratified and Swirled Flows, in Closure Strategies for Turbulent and Transitional Flows, Launder, B.E. and Sandham, N.D., Eds., Cambridge Univ. Press, 2001, pp. 424–448.

    Google Scholar 

  9. Raupach, M.R., Conditional Statistics of Reynolds Stress in Rough-Wall and Smooth-Wall Turbulent Boundary Layers, J. Fluid Mech., 1981, vol. 108, pp. 363–382.

    Article  ADS  MATH  Google Scholar 

  10. Cha,M., Chong, and Pitsch, H., Higher-Order Singly-ConditionalMoment-ClosureModeling Approaches to Turbulent Combustion, Combust. TheoryModel., 2002, vol. 6, iss. 3, pp. 425–437.

    Article  ADS  Google Scholar 

  11. Zhang, K., Fu, R., Shaikh, M.J., Ghan, S., Wang, M., Leung, L.R., Dickinson, R.E., and Marengo, J., Influence of Superparameterization and a Higher-Order Turbulence Closure on Rainfall Bias over Amazonia in Community Atmosphere Model Version 5, J. Geophys. Res.: Atm., 2017, vol. 122, no. 18, pp. 9879–9902.

    ADS  Google Scholar 

  12. Jovanovic, J., Durst, F., and Johansson, T.G., Statistical Analysis of the Dynamic Equations for Higher- OrderMoments in TurbulentWall Bounded Flows, Phys. Fluids A, 1993, vol. 5, no. 11, pp. 2886–2900.

    Article  ADS  MATH  Google Scholar 

  13. Gryanik, V.M. and Hartmann, J., A Turbulence Closure for the Convective Boundary Layer Based on a Two- ScaleMass-Flux Approach, J. Atmos. Sci., 2002, vol. 59, pp. 2729–2744.

    Article  ADS  Google Scholar 

  14. Hartmann, J. et al., Arctic Radiation and Turbulence Interaction Study (ARTIST), no. 305, Alfred Wegener Institute for Polar and Marine Research Report on Polar Research, Germany: Bremerhaven, 1999.

    Google Scholar 

  15. Daly, B.J. and Harlow, B.E., Transport Equations in Turbulence, Phys. Fluids, 1970, vol. 13, pp. 2634–2649.

    Article  ADS  Google Scholar 

  16. Hanjalic, K. and Launder, B.E., A Reynolds Stress Model of Turbulence and Its Application to Thin Shear Flows, J. Fluid Mech., 1972, vol. 52, no. 4, pp. 609–638.

    Article  ADS  MATH  Google Scholar 

  17. Deardorff, J.W., Closure of Second- and Third-Moment Rate Equation in Homogeneous Turbulence, Phys. Fluids, 1978, vol. 21, pp. 525–530.

    Article  ADS  MATH  Google Scholar 

  18. Ilyushin, B.B., Modeling Daily Evolution of the Atmospheric Boundary Layer, Izv. AN, Fiz. Atm. Okeana, 2014, vol. 50, no. 3, pp. 282–292.

    Google Scholar 

  19. Mironov, D.V., Gryanik, V.M., Moeng, C.-H., Olbers, D.J., and Warncke, T.H.,Vertical Turbulence Structure and Second-Moment Budgets in Convection with Rotation: A Large Eddy Simulation Study, Quart. J. Roy. Meteor. Soc., 2000, vol. 126, pp. 477–516.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 1, Novosibirsk, 630090, Russia

    B. B. Ilyushin

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    B. B. Ilyushin

Authors
  1. B. B. Ilyushin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. B. Ilyushin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ilyushin, B.B. Calculation of Higher-Order Moments in the Atmospheric Boundary Layer. J. Engin. Thermophys. 27, 339–344 (2018). https://doi.org/10.1134/S1810232818030098

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1810232818030098

Search

Navigation