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Turbulent flow over groups of urban-like obstacles O. Coceal 1, T.G. Thomas 2, I.P. Castro 2 and S.E. Belcher 1 1 Department of Meteorology, University of Reading, U.K. 2 School of Engineering Sciences, University of Southampton, U.K. 1

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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

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Spatial averaging spatial fluctuation from mean turbulent wind speed Compute from LES/DNS data 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)

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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 U top and h) Flow driven by constant body force

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Domain set-up Repeating unit StaggeredAlignedSquare Obstacle density 0.25 Domain sizes: 4h x 4h x 4h, 8h x 8h x 4h, 4h x 4h x 6h

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Grid resolution tests

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Domain size tests (I)

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Domain size tests (II)

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Unsteady flow viz - windvectors

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Unsteady flow very different from mean flow Streamwise vortex structures Streamwise-vertical planeLateral-vertical plane

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Unsteady flow viz - vorticity

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Strong, continuous shear layerInteracting shear layers Enhanced lateral mixingDecoupling of flow ? Streamwise-vertical planeHorizontal plane

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

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Time-mean flow – pressure Pressure on back face more uniform Front faceBack face Side faceTop face Negative pressure on top face

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

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

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

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Spatially-averaged stress budget Very large averaging times needed to average out effects of slow-evolving vortex structures (~ 400 T) Characteristic timescale T = h / u * 50 T400 T

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

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

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

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

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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

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