MISA LogoTITLE: Simulation of the atmospheric turbulent air flow within and above roughness layer

BY: B.S.Mastryukov, A.V.Ivanov - Moscow State Institute of Steel & Alloys

DATE: 1999-2000




  1. Solution of air pollution problems in town conditions requires the development of effective methods for turbulent air flow modeling taking into account its interaction with buildings and other obstacles. Nowadays there are a lot of successful examples of gases dispersion simulations in buildings complex and towns, but correct set-up of boundary conditions for the perturbed incoming air flow in such cases still remains difficult. Possible way to set-up more realistic boundary conditions at inlet regions is described here.

  2. PHOENICS was used to provide the vertical profiles of the turbulent air flow characteristics including velocity components, temperature, turbulent kinetic energy and rate of its dissipation within and above roughness layer which can represents built-up areas as well as a plant community.

  3. To simulate the atmospheric boundary layer including one within various types of roughness layers we based upon the works performed by A.M.Popov /1/ and G.I.Voronov at al /2/ in which the main principles and governing equations were formulated for the first time. After some modifications their ideas were implemented in PHOENICS computer code.

  4. The model particularity was that the model was formulated and solved for the atmospheric boundary layer as a whole that also allowed us to consider the boundary layer without roughness layer in particular case.

  5. A roughness layer was considered as a porosity layer with the uniform vertical structure what is typical of a industrial built-up, and also with the nonuniform vertical structure what is typical of real downtown districts and a plant community.

  6. As roughness layer characteristics were considered: porosity (D) (and its variation with the layer height), the number of obstacles per ground unit area that describes 'dispersity' (N) of a layer, the maximum height of a layer (H).

  7. The following assumptions were made to develop the model:

    1. Case was described as steady one;

    2. Atmospheric boundary layer was considered as uniform in horizontal directions;

    3. Porosity layer, in turn, was also accepted as statistically uniform and isotropic in horizontal directions;

    4. Porosity layer characteristics were determined with use the concept of a layer which contained identical obstacles (cylinders, cones, pyramids) uniformly distributed on the ground;

    5. Air density as well as specific heat capacity were constant;

    6. Turbulent heat conductivity equation for the airflow was numerically solved within roughness layer only. Above roughness layer the temperature distribution was prescribed on the basis of the heat flux value at the top of porosity layer;

    7. Influence of moisture transfer on heat transfer was negligible;

    8. Model obstacles in porosity layer were considered as 'thin bodies' with respect to heat transfer.

  8. The dynamic part of the model contained motion equations for two velocity vector components as well as the balance equation for turbulent kinetic energy. Each equation included additional source terms. The k-l model was used for the closure of the turbulent equations set with mixing length within porosity layer not being able to exceed certain limited value. The last one was determined as a function of porosity and 'dispersity' of layer at each height within roughness layer.

  9. The part of the model dealing with heat transfer contained heat conductivity equation for the air flow within roughness layer with the source term which described the additional air heating or cooling resulting from the thermal interaction with obstacles, equations for upward and downward longwave radiation transfer and formulae for the sun shortwave radiation extension within porosity layer. Moreover, the influence of urban heat sources was taken into account. The heat balance equations for the ground and obstacles surfaces were additionally adopted in the model. In the boundary condition for downward longwave radiation the additional radiation flux from the cloud base was also taken into account.

  10. The boundary layer height was considered as an internal parameter of the model.

  11. The GROUND coding was extensively used to represent a great variety of source terms in the equations for all dependent variables. The source terms for cases described must represent: drag force and vortex generation effects induced by obstacles and also additional heat sources (moisture sources are optional especially for plant communities but they were not included in the current version of the model).

  12. The atmospheric turbulent flow parameters within roughness layer can be predicted in wide range of the atmospheric stability depending on the local time and cloud presence.

  13. The height of computational domain was chosen to be larger than possible top height of the atmospheric boundary layer at any conditions and was equal 4500 m. The nonuniform grid including 720 cells was used. The first 200 cells were placed within lower 100 m layer of the atmosphere. Within porosity layer the grid was uniform with distance between nodes being equal 0,5 m.

Pictures are as follows:


  1. Comparison of the computed results with well known data from field and wind tunnel experiments carried out in a built-up, a plant community and artificial obstacles published by more than ten authors, shows that formulated model is quite adequate in presenting both a quantitative and qualitative picture of the turbulent flow within various types of roughness layer.

  2. The dependencies of 10 m height wind speed and 10 m height eddy viscosity coefficient upon the external parameters and the industrial built-up characteristics were obtained. These data allowed to establish that layer density rate had dominate influence upon above mentioned parameters as well as upon the flow characteristics profiles shape. The layer density rate was characterized by two regimes: 'free-blown layer' regime and 'density layer' regime. The change between these regimes was expressed by extremum presence in the dependencies of wind speed and eddy viscosity coefficient at 10 m height upon internal roughness layer parameters. The layer density rate was not only dependent on its internal parameters but also was dependent on the atmospheric stability.

  3. The urban heat sources within various types of built-up were found to influence to a large extent on wind, turbulence and temperature regimes of the airflow within a built-up. This influence grown up with decreasing of geostrophic wind speed and with increasing of surface area density of buildings (with decreasing of porosity and/or increasing of 'dispersity' of a built-up).

  4. The grid independence test has been done by means of two times decreasing in distances between nodes. Using more fine grid showed that difference in estimation of wind speed under neutral stratification did not exceed 3% and took place in the lowest part of porosity layer, near the ground in the first node. At the height 5 m above the ground within porosity layer the difference was equal 0,15% and did not exceed this value within the rest of the atmospheric boundary layer. Put it another way the solution on the refined grid had negligible differences from the solution obtained with using the main grid spacing.

  5. The results dealing with behaviour of wind speed, eddy viscosity coefficient, turbulent kinetic energy and so forth in the atmospheric boundary layer obtained by means of the developed model form plausible picture which represents observed particularities of these quantities distributions rather good. For example, the effect of so called 'nocturnal jet' and increased mean wind direction shear through the atmospheric boundary layer under stable stratification can be recognized. Roughness layer presence also increases mean wind direction shear through the lowest part of the atmospheric boundary layer which can amount up to 90 degree.

  6. The model developed also can be used for solution of the wide range of applicable cases including meteorology, forestry, agriculture, aviation, air pollution problem, risk assessment (see evaporation of liquid spill) and so on.


  1. A.M.Popov. Modelling of the planetary boundary layer taking into account the roughness layer / Izvestia AN USSR: Phisika atmosphery i okeana (News of AN USSR: Physics of atmosphere and ocean), 1975, v. 11, No 6, pp. 574-581. (in Russian, abstract in English is available).

  2. G.I.Voronov, A.M.Krigel. The structure of the turbulent flow in the vegetative canopy / Vestnik s.-h. Nauki (Messenger of agriculture science), 1986, No 3 (354), pp. 131-134. (in Russian, abstract in English is available).

  3. A.S.Gavrilov. On the atmospheric boundary layer structure above a terrain with arbitrary roughness properties / Meteorologia i hidrologia (Meteorology and Hydrology), 1973, No 12, pp. 35-42. (in Russian).

  4. H.R.Oliver. Wind profiles in and above a forest canopy / Quart. J. Roy. Meteorol. Soc., 1971, v. 97, No 414, pp. 548-553.

  5. A.S.Dubov, L.P.Bykova, S.V.Marunich. Turbulence in plant community. - Leningrad. Gidrometeoizdat, 1978. - 183 p. (in Russian).

  6. S.V.Marunich. Turbulence characteristics in the forest conditions according to gradient and structural observations / Trudy GGI (Proceedings of GGI), 1971, No 198, pp. 154-165. (in Russian).

  7. J.L.Wright, K.W.Brown. Comparison of momentum and energy balance methods of computing vertical transfer within a crop / Agronom. J., 1967, v. 59, No 5, pp. 427-432.

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