1. CITES 2005, Novosibirsk Modeling and Simulation of Global Structure of Urban Boundary Layer Kurbatskiy A. F. Institute of Theoretical and Applied Mechanics of SB RAS, Novosibirsk, Russia

2. CITES 2005, Novosibirsk O U T L I N E:  Motivation  Introduction  Urban Boundary Layer  Improved Model for the Turbulent ABL  Urban Heat Island in a Calm and Stably Stratified Environment  Impact of UHI on the Global Structure of the ABL  Impact of the UHI and the UCL on the ABL Structure  Conclusions

3. CITES 2005, Novosibirsk Motivation The aim of lecture consists in a statement of the improved turbulence model for the urban boundary layer and results of its verification in the simple 2D cases.

4. CITES 2005, Novosibirsk Introduction ●Complexity of simulation of urban air quality problems consists in the necessary of resolution the variety spatial-temporal scales over which the phenomena proceed. ●The two most important scales include:  an 'urban' scale of a few tens kilometers (a typical scale of city) where large amounts of contaminants are emitted, and  a 'меsо' scale of a few hundreds of kilometers where secondary contaminants are formed and dispersed.

5. CITES 2005, Novosibirsk Introduction ● In order to compute the mean and turbulent transport and the chemical transformations of pollutants, several meteorological variables, such as wind, turbulent fluxes, temperature etc., it is necessary to known as more as possible precisely. These meteorological variables can be calculated by an improved model for the turbulent ABL. ● The two most important effects of the urbanized surface have an influence on the air flow structure:  Differential heating of the urbanized surfaces which can generate the so-called urban heat island effect.  Drag due to buildings.

6. CITES 2005, Novosibirsk The development of ABL over flat terrain The development of ABL over flat terrain T he potential temperature θ and wind velocity U are shown for the convective and stable boundary layers.

7. CITES 2005, Novosibirsk Urban Boundary Layer

8. CITES 2005, Novosibirsk Improved Turbulence Model for the ABL

9. CITES 2005, Novosibirsk. GOVERNING EQUATIONS FOR TURBULENT PBL

10. CITES 2005, Novosibirsk Turbulence equations

11. CITES 2005, Novosibirsk An updated expressions for the pressure- velocity П ij (= П ij (1) + П ij (2) + П ij (3) ) and the pressure-temperature П iθ (= П iθ (1) + П iθ (2) + П iθ (3) ) correlations Mellor-Yamada model (1982, Mellor, 1973): П ij (1) =C τ -1 b ij П ij (2) ~-ES ij  most of rapid terms are neglected П ij (3) =0  no buoyancy effects are included П iθ (1) =C 1θ h i, П iθ (2) =0, П iθ (3) =C 3θ β, (E=1/2 is TKE; S ij =(U i,j + U j,i )/2)

12. CITES 2005, Novosibirsk An updated expressions for the pressure-velocity П ij (= П ij (1) + П ij (2) + П ij (3) ) and the pressure-temperature П iθ (= П iθ (1) + П iθ (2) + П iθ (3) ) correlations Launder’s model (1975)  Present model (2001) П ij (1) = C 1 τ -1 b ij П ij (2) =-4/3C 2 ES ij - C 2 (Z ij +Σ ij ) П ij (3) = C 3 B ij П iθ (1) = C 1θ τ -1 h i, П iθ (2) =-C 2θ h j U i,j, П iθ (3) = C 3θ β i Σ ij =b ik S ij +S ik b kj -2/3δ ij b km S mk;  The model constants of П ij are C 1, C 2, C 3, C 1θ, C 2θ = C 3θ Zeman and Lumley model (1979)  Canuto et al. model (2002) П ij (1) = C 1 τ -1 b ij П ij (2) =-4/5ES ij - α 1 Σ ij - α 2 Z ij П ij (3) =(1-β 5 )B ij П iθ (1) = C 1θ τ -1 h i, П iθ (2) =-3/4α 3 (S ij +5/3R ij ) h j, П iθ (3) =γ 1 β i Z ij =R ik b kj -b ik R kj ; B ij =β i h j + β j h i - 2/3δ ij β k h k

13. CITES 2005, Novosibirsk Level-3 Algebraic Models for Reynolds Stress and Scalar Fluxes Coupled algebraic system equations for and

14. CITES 2005, Novosibirsk Level-3 Fully Explicit Algebraic Models for Reynolds Stress and Scalar Fluxes : 2D case

15. CITES 2005, Novosibirsk Three-parametric turbulence model

16. CITES 2005, Novosibirsk Air Circulation above an Urban Heat Island in a Calm and Stably Stratified Environment

17. CITES 2005, Novosibirsk Air Circulation above an Urban Heat Island

18. CITES 2005, Novosibirsk Thermal circulation above an urban heat island  Experiment of Lu et al. ( JAM.1997.V.36 )  Computation by three-parametric turbulence model ( Kurbatskii A. JAM. 2001. V.40 )

19. CITES 2005, Novosibirsk (A. F. Kurbatskiy, J. Appl. Meteor. 2001. V. 40. №10)

20. CITES 2005, Novosibirsk Dispersion of passive tracer above UHI in a Calm and Stably Stratified Environment

21. CITES 2005, Novosibirsk Impact of a Urban Heat Island on the Global Structure of the ABL

22. CITES 2005, Novosibirsk 2D case: Computational domain

23. CITES 2005, Novosibirsk Vertical section of horizontal wind speed (U G =1ms -1 )

24. Vertical section of potential temperature and horizontal wind speed  U G =3 ms -1  U G =5 ms -1

25. CITES 2005, Novosibirsk Velocity vectors and isotachs of vertical speed at 12:00 LST

26. CITES 2005, Novosibirsk Vertical section of potential temperature and horizontal wind speed  U G =3 ms -1  U G =5 ms -1

27. CITES 2005, Novosibirsk Height of boundary layer

28. CITES 2005, Novosibirsk Height of boundary layer <u  

29. CITES 2005, Novosibirsk Impact of the UHI and the UCL on the Mesoscale Flow

30. CITES 2005, Novosibirsk Typical Flat Urban Modeling Domain

31. CITES 2005, Novosibirsk Parameterization of Urban Roughness

32. CITES 2005, Novosibirsk Governing Equations for UBL 2D case:

33. CITES 2005, Novosibirsk Turbulent fluxes is the countergradient term

34. CITES 2005, Novosibirsk Three-parametric turbulence model

35. CITES 2005, Novosibirsk Parameterization of Effects of Urban Surfaces on the Airflow [Raupach et al.(1991), Raupach (1992), Vu et al.(2002), Martilli (2002)] The extra terms D A in the Governing Equations are: D U = turbulent momentum flux (roofs and canyon floors) + drag (vertical walls) D θ = turbulent fluxes of sensible heat from roofs and the canyon floor + the temperature fluxes from the walls D E = increasing of conversion of mean kinetic energy into the TKE [ by as, for example, Raupach and Shaw (1982)]  a ‘second’ dissipation linked with the scale of turbulence L=L(z) induced by the presence of the buildings

36. CITES 2005, Novosibirsk Results of Simulation

37. CITES 2005, Novosibirsk Vertical section of potential temperature and horizontal wind speed at 1200 LST  U G =3 ms -1  U G =5 ms -1

38. CITES 2005, Novosibirsk Vector field of horizontal wind speed and isotachs of vertical velocity for 12:00 LST

39. CITES 2005, Novosibirsk Vector field of horizontal wind speed and isotachs for vertical velocity for 12:00 LST

40. CITES 2005, Novosibirsk Vertical section of potential temperature and horizontal wind speed at 1200 LST  U G =3 ms -1  U G =5 ms -1

41. CITES 2005, Novosibirsk Vertical section of potential temperature and horizontal wind speed (3 ms -1 ) for simulation at 1200 LST  Present computation  Computation of Martilli (JAM,2002,V.41, 1247-1266 )

42. CITES 2005, Novosibirsk Vertical section of potential temperature and horizontal wind speed  U G =3 ms -1

43. CITES 2005, Novosibirsk Temperature field above the city

44. CITES 2005, Novosibirsk The Vertical Temperature Profiles

45. CITES 2005, Novosibirsk Vertical section of potential temperature and horizontal wind speed  U G =3 ms -1

46. CITES 2005, Novosibirsk Vertical profiles of ‘local’ friction velocity

47. CITES 2005, Novosibirsk Verticals profiles of ratio u * /U

48. CITES 2005, Novosibirsk Vertical profiles of TKE in the centre city

49. CITES 2005, Novosibirsk Turbulent kinetic energy,

50. CITES 2005, Novosibirsk

51. CONCLUSIONS ■ Using the updated expressions for the pressure-velocity and pressure-temperature correlations, we have derived an improved turbulence model to describe the Urban Boundary Layer. ■ In simple 2D case are investigated the modifications in global structure of the ABL caused by the Urban Heat Island and the Urban Canopy Layer. ■ The comparison between computed results and field observational data on various integrated turbulent characteristics reveals that the improved model can simulate the turbulent transport processes within and above the building canopy with satisfactory accuracy.