Abstract
A modified three-parameter model of turbulence for a thermally stratified atmospheric boundary layer (ABL) is presented. The model is based on tensor-invariant parametrizations for the pressure-strain and pressure-temperature correlations that are more complete than the parametrizations used in the Mellor-Yamada model of level 3.0. The turbulent momentum and heat fluxes are calculated with explicit algebraic models obtained with the aid of symbol algebra from the transport equations for momentum and heat fluxes in the approximation of weakly equilibrium turbulence. The turbulent transport of heat and momentum fluxes is assumed to be negligibly small in this approximation. The three-parameter E − ε − <ϑ2> model of thermally stratified turbulence is employed to obtain closed-form algebraic expressions for the fluxes. A computational test of a 24-h ABL evolution is implemented for an idealized two-dimensional region. Comparison of the computed results with the available observational data and other numerical models shows that the proposed model is able to reproduce both the most important structural features of the turbulence in an urban canopy layer near the urbanized ABL surface and the effect of urban roughness on a global structure of the fields of wind and temperature over a city. The results of the computational test for the new model indicate that the motion of air in the urban canopy layer is strongly influenced by mechanical factors (buildings) and thermal stratification.
Similar content being viewed by others
References
M. Roth, “Review of Atmospheric Turbulence over Cites,” Q. J. R. Meteorol. Soc. 126, 941–990 (2000).
H. J. S. Fernando, S. M. Lee, J. Anderson, et al., “Urban Fluid Mechanics: Air Circulation and Contaminant Dispersion in Cites,” Environ. Fluid Mech. 1, 107–164 (2001).
T. C. Vu, Y. Ashie, and T. Asaeda, “A Turbulence Closure Model for the Atmospheric Boundary Layer Including Urban Canopy,” Boundary-Layer Meteorol. 102, 459–490 (2002).
B. E. Launder, “On the Effects of Gravitational Field on the Turbulent Transport of Heat and Momentum,” J. Fluid Mech. 67, 569–581 (1975).
A. Martilli, “An Urban Exchange Parameterization for Mesoscale Models,” Boundary-Layer Meteorol. 104, 261–304 (2002).
M. R. Raupach, R. A. Antonia, and S. Rajagoplan, “Rough-Wall Turbulent Boundary Layers,” Appl. Mech. Rev. 44, 79–90 (1991).
A. F. Kurbatskii, “Computational Modeling of the Turbulent Penetrative Convection above the Urban Heat Island in a Stably Stratified Environment,” J. Appl. Meteorol. 40, 1748–1761 (2001).
A. F. Kurbatskii and L. I. Kurbatskaya, “Penetrative Turbulent Convection over a Heat Island in a Stably Stratified Environment,” Izv. Akad. Nauk, Fiz. Atm. Okeana 37, 149–161 (2001) [Izv., Atmos. Ocean. Phys. 37, 135–146 (2001)].
A. N. Kolmogorov, “Equations of Turbulent Motion of an Incompressible Fluid,” Izv. Akad. Nauk SSSR, Ser. Fizicheskaya 6(1–2), 56–58 (1942).
G. L. Mellor and T. Yamada, “A Hierarchy of Turbulence Closure Models for Planetary Boundary Layer,” J. Atmos. Sci. 31, 1791–1806 (1974).
G. L. Mellor and T. Yamada, “Development of a Turbulence Closure Model for Geophysical Fluid Problems,” Rev. Geophys. Space Phys. 20, 851–875 (1982).
Y. Cheng, V. M. Canuto, and A. M. Howard, “An Improved Model for the Turbulent PBL,” J. Atmos. Sci. 59, 1500–1565 (2002).
O. Zeman and J. L. Lumley, “Buoyancy Effects in Entraining Turbulent Boundary Layers: A Second-Order Closure Study,” in Turbulent Shear Flows, Ed. by F. Durst et al. (Springer, Berlin, 1979), Vol. 1, pp. 295–302.
B. E. Launder, G. Reece, and W. Rodi, “Progress in the Development of a Reynolds-Stress Turbulent Closure,” J. Fluid Mech. 68, 537–566 (1975).
B. E. Launder, in Simulation and Modeling of Turbulent Flows, Ed. by T. D. Gatski et al. (Oxford Univ. Press, New York, 1996).
S. S. Girimaji and S. Balachandar, “Analysis and Modeling of Buoyancy-Generated Turbulence Using Numerical Data,” Int. J. Heat Mass Transfer 41, 915–929 (1998).
T. P. Sommer and R. M. C. So, “On the Modeling of Homogeneous Turbulence in a Stably Stratified Flow,” Phys. Fluids 7, 2766–2777 (1995).
A. Andren, “Evaluation of a Turbulence Closure Scheme for Air-Pollution Applications,” J. Appl. Meteorol. 29, 224–239 (1990).
A. Andren, “A TKE-Dissipation Model for the Atmospheric Boundary Layer,” Boundary-Layer Meteorol. 56, 207–221 (1990).
A. F. Kurbatskii and A. V. Kazakov, “Explicit Algebraic Model of Turbulent Heat Transfer for a Developed Flow in a Rotating Round Pipe,” Thermophys. Aeromech. 6, 231–240 (1999).
P. Roche, Computational Fluid Dynamics (Hermosa, Albuquerque, 1976; Mir, Moscow, 1980).
M. W. Rotach, “Turbulence within and above an Urban Canopy,” ETH Dissertation, 9439 (1991).
M. W. Rotach, “Turbulence Closure to a Rough Urban Surface. Part I: Reynolds Stress,” Boundary-Layer Meteorol. 65, 1–28 (1993).
M. W. Rotach, “Turbulence Closure to a Rough Urban Surface. Part II,” Boundary-Layer Meteorol. 65, 1–28 (1993).
M. W. Rotach, “Profiles of Turbulence Statistics in and above an Urban Street Canyon,” Atmos. Environ. 29, 1473–1486 (1995).
S. Oikawa and Y. Meng, “Turbulence Characteristics and Organized Motion in a Suburban Roughness Sublayer,” Boundary-Layer Meteorol. 74, 289–312 (1995).
C. Feigenwinter, The Vertical Structure of Turbulence above an Urban Canopy, PhD Thesis (Univ. of Basel, 1999).
I. Uno and S. Wakamatsu, “Observed Structure of the Nocturnal Urban Boundary Layer and Its Evolution into a Convective Mixed Layer,” Atmos. Environ. B 26, 45–57 (1992).
P. Louka, S. E. Belcher, and R. G. Harrison, “Coupling between Air Flow in Streets and the Well Developed Boundary Layer Aloft,” Atmos. Environ. 34, 2613–2621 (2000).
A. M. Spanton and M. L. Williams, “A Comparison of the Structure of the Atmospheric Boundary Layers in Central London and a Rural/Suburban Site Using Acoustic Sounding,” Atmos. Environ. 22, 211–223 (1988).
R. Bornstein and D. S. Johnson, “Urban-Rural Wind Velocity Differences,” Atmos. Environ. 11, 597–604 (1977).
A. F. Kurbatskii, “Numerical Study of the Effect of a Surface Heat Spot on the Structure of the Planetary Boundary Layer,” Teplofiz. Aeromekh. 12(1), 41–60 (2005).
M. M. Gibson and B. E. Launder, “Ground Effects on Pressure Fluctuation in the Atmospheric Boundary Layer,” J. Fluid Mech. 86, 491–511 (1978).
J. L. Lumley and P. Monsfield, “Second Order Modeling of Turbulent Transport in the Surface Mixed Layer,” Boundary-Layer Meteorol. 30, 109–142 (1984).
M. R. Raupach, “Drag and Drag Partition on Rough Surfaces,” Boundary-Layer Meteorol. 60, 375–395 (1992).
M. R. Raupach and R. H. Show, “Averaging Procedure for Flow within Vegetation Canopies,” Boundary-Layer Meteorol. 22, 79–90 (1982).
H. Hiraoka, T. Maruyama, Y. Nakamura, and J. Katsura, “A Study on Modeling of Turbulent Flows within Plant and Urban Canopies. Formalization of Turbulence Model. Part 1,” J. Archit. Plann. Eng. 406, 1–9.
T. Yamada and G. Mellor, “A Simulation of the Wangara Atmospheric Boundary Layer Data,” J. Atmos. Sci. 32, 2309–2329 (1975).
J. C. Andre, G. De Moor, P. Lacarrere, et al., “Modeling the 24-hour Evolution of the Mean and Turbulent Structures of the Planetary Boundary Layer,” J. Atmos. Sci. 35, 1861–1883 (1978).
Author information
Authors and Affiliations
Additional information
Original Russian Text © A.F. Kurbatskii, L.I. Kurbatskaya, 2006, published in Izvestiya AN. Fizika Atmosfery i Okeana, 2006, Vol. 42, No. 4, pp. 476–494.
Rights and permissions
About this article
Cite this article
Kurbatskii, A.F., Kurbatskaya, L.I. Three-parameter model of turbulence for the atmospheric boundary layer over an urbanized surface. Izv. Atmos. Ocean. Phys. 42, 439–455 (2006). https://doi.org/10.1134/S0001433806040049
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1134/S0001433806040049