1. Turbulent flow over groups of urban-like obstacles
O. Coceal1, T.G. Thomas2, I.P. Castro2 and S.E. Belcher1
1Department of Meteorology, University of Reading, U.K.
2School of Engineering Sciences, University of Southampton, U.K. 1

2. Motivation and Aims Modelling flow and dispersion in urban areas
Wider application, e.g. in engineering
Aims
To perform high resolution simulations – no turbulence modelling, no tuning
To validate simulations against a high quality dataset
To compute 1-d momentum balance for canopy of cubical roughness, and
compare with vegetation canopies
compare with rough walls in general
To compare flow within canopy with that above & understand their coupling
To investigate effect of layout of the obstacles

3. Spatial averaging spatial fluctuation from mean turbulent wind speed
Spatial average of Reynolds-averaged momentum equation
is spatial average of Reynolds stress
is dispersive stress
is distributed drag term
is spatially averaged mean wind speed
See e.g. Raupach & Shaw (1982), Finnigan (2000)
Compute from LES/DNS data

4. Numerical method Multiblock LES/DNS code developed by T.G. Thomas
Resolutions:
DNS at 64 x 64 x 64 grid points per cube (256 x 256 x 256 grid points)
32 x 32 x 32 grid points per cube (128 x 128 x 128 grid points)
16 x 16 x 16 grid points per cube (64 x 64 x64 grid points)
Boundary conditions:
free slip at top
no slip at bottom and cube surfaces
periodic in streamwise and lateral directions
Reynolds number = 5000 (based on Utop and h)
Flow driven by constant body force

5. Domain set-up Domain sizes: 4h x 4h x 4h, 8h x 8h x 4h, 4h x 4h x 6h
Staggered
Aligned
Square
Obstacle density 0.25
Repeating unit

6. Grid resolution tests

7. Domain size tests (I)

8. Domain size tests (II)

9. Unsteady flow viz - windvectors

10. Unsteady flow viz - windvectors
Streamwise-vertical plane
Lateral-vertical plane
Streamwise vortex structures
Unsteady flow very different from mean flow

11. Unsteady flow viz - vorticity

12. Unsteady flow viz - vorticity
Streamwise-vertical plane
Horizontal plane
Strong, continuous shear layer
Interacting shear layers
Decoupling of flow ?
Enhanced lateral mixing

13. Time-mean flow - windvectors
Robust recirculation upstream of cube
Staggered array
No recirculation bubble behind cube
Divergence point near ground
Steady vortex in canyon
Square array
More two-dimensional in nature

14. Time-mean flow – pressure
Front face
Back face
Pressure on back face more uniform
Side face
Top face
Negative pressure on top face

15. Pressure drag profile
Compared with data from Cheng and Castro (2003)

16. Mean velocity profiles
Compared with data from Cheng and Castro (2003)

17. Spatially-averaged stress budget
Dispersive stress negligible above canopy cf Finnigan (1985) Cheng and Castro (2003)
Dispersive stress significant within canopy

18. Spatially-averaged stress budget
Characteristic timescale T = h / u*
Very large averaging times needed to average out effects of slow-evolving vortex structures (~ 400 T)

19. Stress budget – effect of layout
Dispersive stress changes sign for aligned/square arrays
Due to recirculation (cf Poggi et al., 2004)

20. Reynolds and dispersive stresses
Aligned array
Stress measurements above array Cheng and Castro (2003)
Dispersive stresses of order 1% of total stress above array

21. Mean velocity and drag profiles
Spatially-averaged mean velocity profile
Well predicted with few sampling points
Much lower for staggered array
Much lower for aligned/square arrays - sheltering
Sectional drag coefficient

22. Mixing length profile Velocity profile logarithmic above canopy
Mixing length minimum at top of canopy
Blocking of eddies by shear layer
Velocity profile not exponential in canopy

23. Conclusions
High resolution DNS of flow over cubes – excellent agreement with data
Vortex structures both above and within array
unsteady flow very different from mean flow
Strong shear layer at top of array
decouples flow within array from that within
Time-mean flow structure depends on layout
vortex in canyon for aligned/square arrays
no recirculation bubble for staggered array
Dispersive stress small above array, large within
Log profile above arrays
Mean flow and turbulence structure is different from plant canopies