Turbulent flow over groups of urban-like obstacles

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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. 1Email: o.coceal@reading.ac.uk www.met.rdg.ac.uk/bl_met

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

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

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

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

Grid resolution tests

Domain size tests (I)

Domain size tests (II)

Unsteady flow viz - windvectors

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

Unsteady flow viz - vorticity

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

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

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

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

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

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

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)

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

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

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

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

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