Omduth Coceal Dept. of Meteorology, Univ. of Reading, UK.

Email: o.coceal@reading.ac.uk

and

A. Dobre, S.E. Belcher (Reading)T.G. Thomas, Z. Xie, I.P. Castro (Southampton)

Turbulence statistics from DNS and LES - implications for urban canopy models

Interpretation of field experimentsCan we hope to understand this … … using this ?

- CFD/LES/DNS can provide detailed spatial information of any statistics

- But how realistic are the results?

- Compare idealized simulations with less idealized simulations and with field data

Parameterisations & ModellingE.g. Urban canopy models (e.g. Martilli et al., 2002; Coceal & Belcher, 2004 )

- CFD can be used to compute these spatially-averaged quantities - How can they be parameterized?

- Don’t resolve horizontal heterogeneity at the building/street scale- Take horizontal averages: resolve vertical flow structure

h

y

x

Spatial average of Reynolds-averaged momentum equation

€

u = u + ˜ u + u'Triple decomposition of velocity field

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D u

Dt+

1

ρ

∂ p

∂x= −

∂

∂zu'w' −

∂

∂z˜ u ˜ w − D

Outline

Description of numerical simulations

Comparisons with wind-tunnel data

Spatially-averaged statistics for different types of building arrays

Regular arrays with different building layouts Arrays with variable building heights (using results from LES)

Unsteady & organized flow characteristics - comparisons with field data

Direct numerical simulations

• Parallel LES/DNS code developed by T.G. Thomas

• Resolution: 32 x 32 x 32 gridpoints per cube (also 643 gridpoints per cube on a smaller domain)

• Total of 512 x 384 x 256 ~50 million gridpoints for large array

• Periodic boundary conditions in horizontal; flow driven by constant body force

• Largest run took ~3 weeks on 124 processors on SGI Altix

Coceal et al., BLM (2006)Coceal et al., IJC, to appear (2007)

Mean flow is out of screen, 643 gridpoints per cube

Instantaneous windvectors in y-z plane

Compared with data from Cheng and Castro (2003)

and Castro et al. (2006)

Comparisons of DNS with experiment

velocity

stresses

pressure

spectra

Spatially averaged statistics - uniform arrays

Different building layouts, same densityCoceal et al., BLM (2006)

Arrays with random building heights (same density)

0.5hm

Compare results with LES performed by Zhengtong Xie (Southampton)

Spatial averages - mean velocity

Velocities are smaller over the random array. The random array exerts more drag. Spatially-averaged velocities are very similar within arrays.Inflection is much weaker in random array.

Spatial fluctuations vs. spatial average

Qualitatively similar behaviour in the two arraysSpatial fluctuations are very significant within the canopy

Spatial averages - tke and dispersive stress

In the random array, the peaks in tke are less strong, but are still quite pronounced. They occur at the height of the tallest building, not at the mean or modal building height.

Profiles of uw component of dispersive stress are very similar below z=h_m.Dispersive stresses are NOT small within the canopy (also Kanda, 2004).

Buildings of variable heights - TKE

TKE from shear layers shed from vertical edges of tallest building dominates above half the mean building height.

Buildings of variable heights - Umag

Wind speed-up around the tall building in relation to the background flow, especially at lower levels.

Buildings of variable heights - Drag profiles (I)

Tallest building (1.72 times the mean building height) exerts 22% of the total drag! The 5 tallest buildings (out of 16) are together responsible for 65% of the drag.

Buildings of variable heights - Drag profiles (II)

The shapes of the drag profiles are in general similar for many of the tallest buildings (17.2m, 13.6m, 10.0m) except when they are in the vicinity of a taller building. The profile shapes of the shortest buildings (6.4m and 2.8m) are very different - but these buildings do not exert much drag.

Organized motions: Quadrant analysis

Decompose contributions to shear stress <u’w’> according to signs of u’, w’

u’

w’

u’ > 0

w’ > 0

u’ < 0

w’ > 0

u’ < 0

w’ < 0

u’ > 0

w’ < 0

Ejections and sweeps contribute most to the Reynolds stress <u’w’>

They are associated with organized motions

Ejections (Q2)

Sweeps (Q4)

Kanda et al. (2004), Kanda (2006)

Quadrant analysis - ExuberanceExuberance

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Ex =S1 + S3

S2 + S4

Exuberance is a measure of how disorganized the turbulence is

Magnitude of Exuberance is smallest near canopy top in DNS (uniform building heights)

Increases slowly above building canopy, rapidly within canopy

Real field data (Christen, 2005)From DNS

Quadrant analysis - Q2 vs Q4 (I)

Indicates character of the organized motions

Ejection dominance well above the canopy

Sweep dominance close to/within the canopy. Cross-over point is at z = 1.25 h

€

ΔS0 = S4 − S2

Real field data (Christen, 2005)

DNS

ConclusionsEffects of building layout

Mean flow structure and turbulence statistics vary substantially with layout

Effect of packing density significant (Kanda et al., 2004; Santiago et al. 2007)

Effects of random building heights:

Less strong shear layer on average

Inflection in spatially-averaged mean wind profile much less pronounced

Larger drag/roughness length

Below the mean building height, spatial averages are very similar to regular array

Effects of tall buildings:

Strong shear layers associated with tall buildings - high TKE

They exert a large proportion of the drag

They cause significant wind speed-up lower down the canopy

THE END

Fluctuating velocity vectors

Ejections and sweeps are associated with eddy structures

Spatial distribution of ejections and sweeps

Fluctuating windvectors

Unsteady coupling of flow within and above canopy