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Turbulent circulation above the surface heat source in a stably stratified environment

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Thermophysics and Aeromechanics Aims and scope

Abstract

The results of the numerical modeling of turbulent structure of the penetrating convection above the urban heat island with a small aspect ratio in a stably stratified medium at rest are presented. The gradient diffusion representations for turbulent momentum and heat fluxes are used, which depend on three parameters — the turbulence kinetic energy, the velocity of its spectral expenditure, and the dispersion of temperature fluctuations. These parameters are found from the closed differential equations of balance in the RANS approach of turbulence description. The distributions of averaged velocity and temperature fields as well as turbulent characteristics agree well with measurement data.

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References

  1. J. Lu, P. Arya, W.H. Snyder, and R.E. Lawson, A laboratory study of the urban heat island in a calm and stably stratified environment. Part I, II, J. Appl. Meteor., 1997, Vol. 36, No. 10, P. 1377–1402.

    Article  ADS  Google Scholar 

  2. G.E. Willis and J.W. Deardorff, A laboratory model of the unstable planetary boundary layer, J. Atmos. Sci., 1974, Vol. 31, P. 1297–1307.

    Article  ADS  Google Scholar 

  3. A.F. Kurbatskiy and L.I. Kurbatskaya, Three-parameter model of turbulence for the atmospheric boundary layer over an urbanized surface, Izvestiya. Atmospheric and Oceanic Phys., 2006, Vol. 42, No. 4, P. 439–455.

    Article  ADS  Google Scholar 

  4. D.W. Byun and S.P.S. Araya, A two-dimensional mesoscale numerical model an urban mixed layer. I. Model formulation, surface energy budget, and mixed layer dynamic, Atmospheric Environment, 1990, Vol. 24A, No. 4, P. 829–844.

    Article  ADS  Google Scholar 

  5. R.A. Pielke, Mesoscale meteorological modeling. 2nd edition, Academic Press, New York, 2002.

    Google Scholar 

  6. A.F. Kurbatsky, Modeling of Non-local Turbulent Transfer of Momentum and Heat, Nauka, Novosibirsk, 1988.

    Google Scholar 

  7. C.G. Speziale, Modeling of turbulent transport equations, in: T.B. Gatski, M.Y. Hussaini, J.L. Lumley (Eds.), Simulation and Modeling of Turbulent Flows, Oxford University Press, Oxford, 1996.

    Google Scholar 

  8. Y. Cheng, V.M. Canuto, and A.M. Howard, An improved model for the turbulent PBL, J. Atmos. Sci., 2002, Vol. 59, No. 9, P. 1550–1565.

    Article  ADS  Google Scholar 

  9. T.P. Sommer and R.M.C. So, On the modeling of homogeneous turbulence in a stably stratified flow, Phys. Fluids, 1995, Vol. 7, No. 11, P. 2766–2777.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. L.H. Jin, R.M.C. So, and T.B. Gatski, Equilibrium states of turbulent homogeneous buoyant flows, J. Fluid Mech., 2003, Vol. 482, P. 207–233.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. C. Beguier, I. Dekeyser, and B.E. Launder, Ratio of scalar and velocity dissipation time scales in shear flow temperature, Phys. Fluids, 1978, Vol. 21, No. 3, P. 307–310.

    Article  ADS  Google Scholar 

  12. Y.A. Panofsky, Y. Tennekes, D.Y. Lenshow, and J.C. Wyngaard, The characteristics of turbulent velocity components in the surface layer under convective conditions, Boundary Layer Meteor., 1977, Vol. 11, P. 353–361.

    Article  ADS  Google Scholar 

  13. J.A. Businger, J.C. Wyngaard, Y. Izumi, and E.F. Bradley, Flux profile relationship in the atmospheric surface layer, J. Atmos. Sci., 1971, Vol. 28, P. 181–189.

    Article  ADS  Google Scholar 

  14. J.-F. Louis, A parametric model of vertical eddy fluxes in the atmosphere, Boundary-Layer Meteor., 1979, Vol. 17, No. 2, P. 187–202.

    Article  ADS  MathSciNet  Google Scholar 

  15. A.S. Monin and A.M. Yaglom, Statistical Fluid Mechanics. Vol. 1: Mechanics of Turbulence, MIT Press, Cambridge, Mass., 1971.

    Google Scholar 

  16. J.C. Andre, G. de Moor, F. Laccarere, G. Therry, and R. du Vachat, Modeling the 24-hour evolution of the mean and turbulent structures of the planetary boundary layer, J. Atmos. Sci., 1978, Vol. 35, P. 1861–1883.

    Article  ADS  Google Scholar 

  17. P.G. Duynkerke, Application of the e-ε turbulence closure model to the neutral and stable atmospheric boundary layer, J. Atmos. Sci., 1988, Vol. 45, No. 5, P. 865–879.

    Article  ADS  Google Scholar 

  18. P. Roache, Computational Fluid Dynamics, Hermosa, Albuquerque, New Mexico, 1976.

    Google Scholar 

  19. O. Zeman and J.L. Lumley, Buoyancy effects in entraining turbulent boundary layers: a second-order closure study, in: F. Durst, B.E. Launder, F.W. Schmidt, and J.H. Whitelaw (Eds.), Turbulent Shear Flows I, Springer, Berlin, Heidelberg, 1979, P. 295–306.

    Chapter  Google Scholar 

  20. A.A.A. Andren, TKE dissipation model for the atmospheric boundary layer, Boundary Layer Meteor., 1992, Vol. 56, P. 207–221.

    Article  ADS  Google Scholar 

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Correspondence to A. F. Kurbatskii.

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The work was financially supported by the Russian Foundation for Basic Research (Grant No. 13-05-00006 and partially No. 14-01-00125) and Program for Basic Research of SB RAS No. II. 2П.

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Kurbatskii, A.F., Kurbatskaya, L.I. Turbulent circulation above the surface heat source in a stably stratified environment. Thermophys. Aeromech. 23, 677–692 (2016). https://doi.org/10.1134/S0869864316050061

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  • DOI: https://doi.org/10.1134/S0869864316050061

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