Large-eddy simulation of turbulent flow in a street canyon

Transcription

1 Q. J. R. Meteorol. Soc. (2004), 130, pp doi: /qj Large-eddy simulation of turbulent flow in a street canyon By ZHIQIANG CUI 1, XIAOMING CAI 1 and CHRIS J. BAKER 2 1 School of Geography, Earth and Environmental Sciences, The University of Birmingham, UK 2 School of Engineering, The University of Birmingham, UK (Received 3 July 2002; revised 10 November 2003) SUMMARY The turbulent flow inside an idealized urban street canyon with an aspect ratio of one is studied by means of large-eddy simulation. The Regional Atmospheric Modelling System is configured to simulate the turbulent flow in a neutrally stratified atmosphere with the initial wind perpendicular to the street canyon axis. The mean velocity components, resolved-scale turbulent kinetic energy (RS-TKE), the skewness and kurtosis of the resolved-scale velocity components (u along the canyon and w vertically) are compared with wind-tunnel measurements. The comparison indicates that a reasonable agreement is achieved. The simulation slightly underestimates the intensity of the primary eddy. It is found that distribution of the RS-TKE is very asymmetric: high in the vicinity of the downstream wall, and uniformly low in the vicinity of the upstream wall. The analyses of skewness and kurtosis indicate that there is a layer just below the rooftop in the canyon where ejection events dominate. Quadrant analysis of resolved-scale velocity fluctuations, u and w, under the rooftop at the centre of the canyon reveals that the exchange of momentum across the canyon top is contributed unevenly by different events. Weak ejection events dominate the frequency of occurrences, but fewer strong sweep events contribute the majority of the total momentum transfer. The features of momentum transfer are further investigated by analysing the spatial temporal variations of u,w,andu w at the roof level. It is found that the variation of these variables is highly intermittent and is associated with multi-scale turbulent events. The period of eddies containing high RS-TKE is attributed to the Kelvin Helmhotz instabilities. These results improve our understanding of the turbulent structure in street canyon flow. KEYWORDS: Intermittency Momentum flux Street canyon flow Turbulence 1. INTRODUCTION Dispersion of atmospheric pollutants within a street canyon has been considered a difficult research topic. One of the primary obstacles is the poor understanding of the unsteady and intermittent wind field inside the canyon. Previous studies on street canyon flow using field experiments, wind-tunnel experiments and numerical simulations, have provided a qualitative classification of the flow regimes within street canyons. It is found that the flow regimes are mainly determined by the aspect ratio of W, the canyon width, to H, the building height, in a neutral stratified atmospheric boundary layer (ABL) for winds roughly perpendicular to the canyon (Oke 1987; Hunter et al. 1992; Sini et al. 1996). Three regimes are identified: skimming flow, wake interference flow and isolated roughness flow. For a narrow canyon (W/H < 1.5) one or more vortices may be trapped within the canyon, with the majority of the external flow skimming above the top of the canyon. If two rows of buildings are further apart but still not very distant (1.5 <W/H <8 9), the downwind building is in the wake of the upwind building and interaction of flows induced by the two rows of buildings takes place. If the canyon is wide enough (W/H >8 9), the individual building elements act as isolated roughness elements, and the interaction of the induced flow by the buildings is negligible. Vortex structure within a canyon is also related to the aspect ratio; there may be two counterrotating vortices (W/H < 0.6), one main vortex (0.6 <W/H<5), or two co-rotating vortices (W/H > 5). It is noted that the threshold values for vortex structure are different from those for flow regime, e.g. the one-vortex case spanning two regimes (Sini et al. 1996). Other factors have minor effects on the flow regimes, but will obviously change Corresponding author: School of Geography, Earth and Environmental Sciences, The University of Birmingham, Edgebaston, Birmingham B15 2TT, UK. zxc633@geesmail.bham.ac.uk c Royal Meteorological Society,

2 1374 Z. CUI et al. the wind fields within canyons, e.g. the aspect ratio of building length or width to height, wind speed above canyon top, roof shape, upwind building configuration, static stability, etc. DePaul and Sheih (1986) suggested that the critical ambient wind speed necessary to produce one vortex is about 1.2 m s 1. Rafailidis (1997) found that the effect of the building density on rooftop wind speed is relatively weak, but that it is strongly influenced by the roof shape. Uehara et al. (2000) examined the effects of atmospheric stability on flow in urban street canyons, and found that cavity eddies that arose in the street canyon tended to be weak when the atmosphere was stable and vice versa. Gayev and Savory (1999) found that the presence of complex flow patterns within the roughness sub-layer is associated with the internal roughness, i.e. roughness associated with obstacles such as small buildings, kiosks, trees and stationary vehicles within the canyon. Louka et al. (2000) found that under light wind conditions the mean recirculation within the street canyon was weaker than the unsteady turbulent fluctuations, suggesting that transient processes dominate the wind fields. In order to understand the turbulent characteristics inside a street canyon, several field measurement programmes have been conducted (e.g. Depaul and Sheih 1986; Qin and Kot 1993; Rotach 1995; Kousa et al. 2001; Vachon et al. 2001; Ketzel et al. 2002; Kastner-Klein et al. 2003). Although such experiments provide the ultimate real data, there are a number of weaknesses: low spatial resolutions, uncontrollable meteorological conditions, and complex building configurations. Wind-tunnel experiments, however, are much better in these aspects. Because of this, several such studies have been carried out for street canyon flows (e.g. Hoydysh and Dabberdt 1988; Kastner-Klein and Plate 1999). One great advantage of wind-tunnel experiments is that the upstream boundary conditions can be controlled. In addition, the configuration of canyons is simple and, usually, the case of an aspect ratio of one is employed. These advantages make it feasible to use the data to validate a numerical model. A clear disadvantage of windtunnel experiments is that their spatial resolution is usually very low and, in most cases, they only provide data at a few stations. In contrast to experiments, numerical simulations can provide high-resolution results not only in time but also in space, and hence depict a complete picture of the canyon flow. To date, nearly all the comprehensive applications of computational fluid dynamics (CFD) techniques to the street canyon case are based on the Reynoldsaveraged equations, one example being the k ε model (where k is the turbulent kinetic energy, and ε is the turbulent dissipation rate). Such models have the disadvantage of not being able to predict the unsteadiness and intermittency mentioned above. Largeeddy simulation (LES), however, provides a potential path to reproduce the unsteady and intermittent wind fields in a street canyon. Several previous LESs of street canyon flow have been reported; for example, Ca et al. (1995) and Chabni et al. (1998) conducted a two-dimensional (2D) LES. Wood (2000) discussed some requirements for a rational LES in complex terrain, in his case over hills. A rational LES requires three-dimensionality, a nearly isotropic grid, a large enough domain, a small enough grid spacing, and a sufficiently long simulation time. Therefore, such a LES must be 3D in order to correctly capture the turbulence dynamics. Recently, a 3D LES of a street canyon type of flow was conducted by Liu and Barth (2002), with their primary interest being in the scalar transport. The top of the domain is placed at the level of half a building height (0.5H ) above the rooftop. This configuration, however, limits the development of eddies with sizes larger than 0.5H in the so-called free surface layer and, inevitably, represents less turbulent kinetic energy (TKE) above the rooftop. On the other hand, validation of the model is focused on the mean concentration and variance of the scalar and the scalar fluxes, rather than the flow features in a street

3 SIMULATION OF TURBULENT FLOW IN A STREET CANYON 1375 canyon. To compensate for this, Liu and Barth (2002) validated the dynamics of their LES for lid-driven cubic cavity flow data from a wind-tunnel experiment. The quantities in the validation included mean velocities, turbulence intensities, and Reynolds stresses along the vertical and horizontal centrelines on the mid-plane. So far, there has not been a report in the literature of validation of a LES of a street canyon flow against data of wind and turbulence. In this study, a 3D LES of street canyon flow with an aspect ratio of W/H = 1is investigated as a part of the National Environment Research Council funded project Experimental Quantification and Modelling of the Dispersion of Particles in Urban Street Canyons. The focus of this paper is to compare the LES results against recently conducted wind-tunnel measurements of street canyon flows (involving comparison of mean velocities, TKE, skewness and kurtosis at five stations in the canyon) and to examine the temporally averaged structures of the canyon flow. This comparison is carried out to justify the use of the LES-predicted unsteady wind fields as input to a dispersion model to estimate the concentration of air pollutants within the canyon and the pollutant flux across the canyon roof, and to investigate the effects of different roof shapes. These calculations will be reported in future papers. 2. EXPERIMENTAL DESIGN In the simulations, an idealized street canyon with an aspect ratio of unity is configured so that the LES results can be compared with wind-tunnel measurements of similar configuration. Brown et al. (2000, hereafter BLDL2000) conducted highresolution measurements of the three components of the mean and turbulent velocity statistics in and above a 2D array of model buildings in the US Environmental Protection Agency s meteorological wind-tunnel. In the measurements, seven rectangular blocks (0.15 m 0.15 m 3.8 m), i.e. six street canyons, were placed in the wind-tunnel with their long face perpendicular to the flow and with W/H = 1. The variables measured include mean velocity, turbulence intensity, skewness and kurtosis. Their results were compared with another wind-tunnel experiment carried out in Europe (Kastner-Klein et al. 2000), which is configured in a similar way but with only three canyons; it has been shown that the two experiments are in good agreement with each other in the first canyon. BLDL2000 and Kastner-Klein et al. (2000) have shown that for W/H = 1the profiles of mean wind and TKE inside a canyon gradually approach an equilibrium as the flow goes to a further downwind canyon. The data at the sixth canyon represent very well the equilibrium profiles in remaining canyons further downwind. In order to compare with the LES results presented in this study, the data from BLDL2000 meet the requirement because the LES adopts cyclic boundary conditions for dynamics components (see below) and this automatically implies a setting with an infinite number of buildings. Table 1 shows the designs of the simulations, where: N x,n y, and N z are the numbers of grid points in x (across-canyon), y (along-canyon) and z (vertical) directions, respectively; x and y are the resolutions in x and y directions; z 1 is the lowest grid spacing in the z direction; and C s is the Smagorinsky constant. As an example, the configuration in Case CSV is explained as follows: the resolution is 0.3 m in the x-direction and 0.5 m in the y-direction; in the vertical (z-direction) there are 91 levels, of which 61 are equally spaced with resolution z = 0.3 m within the canyon and 30 more are stretched above the canyon to 94 m with the grid spacing gradually increasing to about 5 m at the top. This configuration gives a street canyon whose width and height are both 18 m. The grid mesh is close to isotropic inside or just above the canyon in order

4 1376 Z. CUI et al. TABLE 1. E XPERIMENTAL DESIGN Simulations Parameter CSV CSV81 CS08 CS12 LW1 LW2 N x x (m) N y y (m) N z z 1 (m) C s Initial wind Logarithmic Logarithmic Logarithmic Logarithmic Linear Linear profile U max = 2.6 U max = 2.6 U max = 2.6 U max = 2.6 U max = 2.6 U max = 3.9 (m s 1 ) (m s 1 ) (m s 1 ) (m s 1 ) (m s 1 ) (m s 1 ) See text for details. to ensure that no artificial structure is imposed on eddies. In total there are grid points. Some further explanations are needed to clarify the designs. In Case CSV, C s is taken as 0.08 when < 1.1 and 0.12 when 1.1, in order to get more turbulent flow in the canyon. In Case CSV81, C s is taken as 0.08 for < 0.9 and 0.1 for > 1.1; for a linear interpolation between the two values is specified. The building width in Case CSV81 is half of the canyon width. In the two LW experiments, the initial wind profiles are linear rather than logarithmic; the maximum wind speed at the top of the domain is so specified that for Case LW1 it matches that of Case CS08, and for Case LW2 the total momentum above the roof top matches that of Case CS08. In all these simulations, the flow is initially in the x-direction above the rooftop, with zero velocity values inside the canyon. The static stability of the atmosphere is neutral. The lateral boundary conditions for velocity components u, v and w (in the x-, y- andz-directions, respectively) are cyclic, and this implies that the canyon is infinitely long in the y-direction and that there are an infinite number of canyons in the x-direction. BLDL2000 found that the transition features are very clear in the first and the second canyons. Furthermore, the first canyon represents the case where a canyon is adjacent to an open area; in this case an internal boundary layer (IBL) is developed when the air moves towards the built-up area in a real atmosphere (Stull 1988). Therefore, most wind-tunnel experiments include an IBL, but the current LES does not. The two factors, i.e. transition of the turbulent structure and the existence of an IBL, make it impossible to carry out a direct comparison. Fortunately, BLDL2000 found that the TKE and the mean flow within street canyons reached equilibrium at the third or fourth canyon. The LES results in this study are compared with the measurements taken in the sixth canyon of BLDL2000. The numerical model employed in this study is the Regional Atmospheric Modelling System (RAMS). Pielke et al. (1992) gives a comprehensive review of RAMS capabilities. The applications of the RAMS to LES of the ABL can be found in Cai and Steyn (1996) and Cai (1999). The RAMS was originally designed to simulate atmospheric circulations spanning from mesoscale down to microscale. Nicholls et al. (1992, 1993) simulated the wind field around a building with vertical walls. The essence of the building model is that the normal velocity is set to zero at roofs and walls, and the tangential velocity follows the logarithmic law all the time. For the simulation of turbulent street canyon flow, the Smagorinsky eddy viscosity model is used to parametrize small eddies which cannot be explicitly resolved by

5 SIMULATION OF TURBULENT FLOW IN A STREET CANYON 1377 the RAMS. In tensor notation the Smagorinsky model is: τ ij 1 3 δ ij τ kk = 2νS ij, (1) S ij = 1 2 (u i,j + u j,i ), (2) ν = l 2S 2 ij S ij, (3) where the indices i or j refer to the coordinates i, j, k = 1, 2, 3(x, y, z, respectively); τ ij is the subgrid-scale (SGS) stress tensor; ν is the SGS turbulent viscosity; δ ij is the Kronecker symbol; S ij is the rate-of-strain tensor for the resolved-scale (RS); and l is the turbulent characteristic length-scale which is given by: C s = l/( x y z) 1/3. (4) Too large a value of C s provides excessive dissipation, but too small a value may carry numerical errors. The range of C s in Table 1 is consistent with that in previous LESs of ABL flows (Mason and Thompson 1987) and of cavity flow (Jordan and Ragab 1994). For Cases CSV, CSV81, CS08 and CS12 the simulations are conducted for about 20 turnover times (with respect to the main eddy in the canyon; one turnover time is about 3 minutes), while for Cases LW1 and LW2 the simulations are conducted for about 10 turnover times because of the requirement to test sensitivity to the initial wind profile. The results of the later half duration were analysed. Due to the limited capacity of the hard disks and the large size of output files, two methods are used to sample the simulation results: (i) for Case CSV, to output all variables at a 2D slice with y = 0ata frequency of 1 Hz; and (ii) for other cases, to output all variables in the whole domain at a frequency of 5 Hz. In order to compensate for the low frequency of sampling for the latter method we make use of the turbulent information along the y-axis, based on the assumption that the flow is homogeneous along the y-axis and is stationary during the course of analysis. Because of the low frequency of sampling, the RS-TKEs so calculated do not include the contribution from turbulent eddies of higher frequencies. The procedures of statistical analysis for the case are described below. The secondmoment RS quantities, denoted by: q ϕψ (x, z) = ϕ ψ t,y (x, z), (5) have been calculated from LES results, where t,y denotes an average along the y-direction and over time at (x, z),i.e. 1 t1 Ly ϕ t,y = ϕ(t,x,y,z)dy dt, (6) (t 1 t 0 )L y t 0 0 (where L y is the domain size in the y direction) and ϕ is the fluctuation of ϕ about ϕ t,y. In particular, mean wind components are: u = u t,y and w = w t,y, (7) and RS-TKE is: E rs = 1 2 (q uu + q vv + q ww ). (8) The LES results shown here are derived from the whole domain (for all y) based on the averaging procedures mentioned above. Good statistics are obtained for the LES results based on such a method of processing model output in space. The duration of about ten turnover times is also sufficient for good statistics. For other runs, analysis is not carried out along the y-direction because only the output on a central plane is saved due to limitations of computer resources.

6 Z. CUI et al. (a) = u/<u> (b) = 0.25 u/<u> (c) =0 u/<u> (d) =0.25 u/<u> (e) =0.4 u/<u> Figure 1. Comparison of u/ u of large-eddy simulations (LESs) with the wind-tunnel measurements of BLDL2000. Circles denote the wind-tunnel data and curves indicate the LES results: thick solid lines Case CSV81, thin solid lines CSV, short-dashed lines CS08, dotted lines CS12, dash-dotted lines LW1, longdashed lines LW2. Panels (a) (e) present the results at locations where = 0.4, 0.25, 0.0, 0.25, and 0.4, respectively. See text for details. 3. RESULTS (a) Comparison of LES results Figure 1 presents the comparison of normalized u (temporally averaged acrosscanyon wind component) at five locations in the canyon for all runs in Table 1. All those runs produce very similar results. The first location ( = 0.4) is near the upstream wall at which = 0.5, and the following four locations are at = 0.25, 0, 0.25 and 0.4, respectively. In the figure, u is normalized by u, the averaged value of u between = atall five locations. the LES predicts the streamwise flow in the upper part of the canyon at all the five locations, and also the reversed flow in the lower part as shown by the wind-tunnel experiment. Some further details are also produced by the LES; for example, the variation of wind shear strength across the canyon top with downstream distance. At = 0.4 and across the rooftop, the LES results show a clear kink, indicating a shear layer at that level. This feature was also noted in the windtunnel results of BLDL2000. Unfortunately, the vertical resolution of the measurements does not enable this shear-layer to be resolved. The profiles become smoother across the rooftop at locations further downstream as more extensive turbulent mixing occurs. In general, the profiles of the temporally averaged u-component derived from the LES are in good agreement with those from the wind-tunnel experiments of BLDL2000, except

7 (a) = SIMULATION OF TURBULENT FLOW IN A STREET CANYON 1379 (b) = (c) = (d) = w/<u> w/<u> w/<u> w/<u> w/<u> (e) = Figure 2. As Fig. 1 but for w/ u. that the temporally averaged flow intensity inside the canyon is slightly underestimated by the LES, especially for the coarse-resolution runs. Figure 2, similarly, shows results from the comparison of w/ u (the normalized temporally averaged vertical wind component). In general, the LES slightly underestimates the magnitude of the vertical velocity, most noticeably for the coarse-resolution runs. This is clearer in the downstream site at = 0.4 (Fig. 2(e)) which shows an underestimation of about 20%. Several reasons are given to explain this. Firstly, for economic reasons, the LES adopts a limited domain size enforced by cyclic boundary conditions, and this only allows those eddies whose sizes are smaller than half the domain size, e.g. 18 m, to be developed. In other words, any eddies larger than half of the canyon width are not represented by the model. This is not the case in the wind-tunnel experiments, in which maximum eddies are confined by the dimension of the crosssection of the tunnel, and those eddies whose sizes are larger than canyon width could be induced by the roughness elements and instability of flow in upstream locations. These extra eddies could contribute to more intensive momentum transfer from the mean wind to inside the canyon, and hence a stronger primary vortex. Secondly, the LES does not have refined mesh structure near the roof level where a strong wind shear and associated instability are present. The consequence could be insufficient numbers of small eddies in the region and an insufficient amount of momentum transfer. Thirdly, one may also attribute the underestimation to scaling, because using the maximum u/ u inside the canyon as the scaling velocity yields a nearly perfect match (not shown). However, the flow inside the canyon is driven by the turbulent flow outside, and the strength and variation of the circulation inside the canyon is closely related to the wind shear just

8 1380 Z. CUI et al. above the canyon. This is the reason behind the selection of velocity scaling of u. In the analysis of the LES of a cavity flow by Liu and Barth (2002) the speed of the moving lid at the top of the cavity is used to normalize the flow variables, and their results seemed to match observations very well. However, this velocity-scale is not well defined in the present case of street canyon flow. The issue of normalization has been discussed by Soulhac (2000) who used different velocity-scales for the flow inside and outside the canyon. In his study, the velocity profiles above the canyon are scaled by the wind speed at infinite height, but those inside the canyon are scaled by a characteristic velocity which is a solution of a (quadratic) conservation equation of TKE. Hitherto, a simple and straightforward scaling method has not been revealed for the street canyon flow problem. In addition to the temporally averaged velocities, TKE is an important parameter to assess the quality of simulation. The comparison of RS-TKE, denoted by E rs,isshown in Fig. 3, scaled by E rs, the mean RS-TKE averaged in = at all five sites. Some features that are found in the wind-tunnel experiment are also reproduced by the LESs. For example, the flow outside the canyon possesses much larger TKE values than the flow inside the canyon, and RS-TKE in the vicinity of the downstream wall is much higher than that in the vicinity the upstream wall. In general, a reasonably good agreement is achieved between the LES and the wind-tunnel experiment. The most noticeable discrepancy is found at = 0.4. In most runs RS-TKE inside the canyon is slightly underestimated, especially in the upper part of the canyon. Possible reasons may be related to the SGS model itself in the RAMS, including: (i) SGS TKE is not taken into account in the LES results (Mason and Thompson 1987), and (ii) the Smagorinsky SGS model has too much dissipation in the near-wall region (Piomelli and Balaras 2002); in addition, the low sampling frequency loses some RS-TKE. For Case CSV81 better agreement is obtained, related partly to the procedure described in section 2, which takes the fluctuations along the y-direction into consideration. In the lowerpartoftheprofile at = 0.4 for Case CSV, however, the RS-TKE derived from Case CSV is larger than measured data, and this is caused by active, unsteady corner eddies. For Case CSV81, the LES underestimates the RS-TKE in the lower part of the canyon. The effects of C s on the RS-TKE at = 0.4 are clearly seen in Fig. 3(j): Case CS08 produces larger RS-TKE than Case CS12. Although the normalized RS- TKE in the coarse-resolution runs (Figs. 3(f) to (j)) seems to agree well with that in the wind-tunnel experiment, the absolute values of RS-TKE are smaller than those in the fine-resolution runs (Cases CSV and CSV81). Consequently, the exchange between the relatively high-momentum air above the canyon and the relatively low-momentum air inside the canyon is not as active as that in the fine-resolution runs. Therefore, the circulations driven by the air outside the canyon in the coarse-resolution runs are weaker. The normalized w at = 0.25 and 0.25 are weaker for the coarse-resolution runs in Fig. 2. Figure 4 shows the dimensionless turbulence intensities inside and above the canyon. In general, the results in the lower and middle parts of the canyon are in agreement with those shown in Liu and Barth (2002): the streamwise turbulence intensity is larger along the downstream wall, smaller along the upstream wall, and locally larger around the corner between ground-level and the upstream wall; the vertical turbulence intensity is larger along the downstream wall, smaller along the upstream wall, and locally larger around the corner between the ground-level and the downstream wall. Figure 10 of Liu and Barth (2002) shows two larger maxima at roof level, while our LES results indicate that the flow is more turbulent above the rooftop. This results from the configuration difference in the two studies, as mentioned in the introduction; their

9 SIMULATION OF TURBULENT FLOW IN A STREET CANYON 1381 (a) = 0.4 (b) = 0.25 (c) =0.0 (d) =0.25 (e) =0.4 () (f) = 0.4 (g) = 0.25 (h) =0.0 (i) =0.25 (j) =0.4 () (k) = 0.4 (l) = 0.25 (m) =0.0 (n) =0.25 (o) =0.4 () E rs /<E rs > E rs /<E rs > E rs /<E rs > E rs /<E rs > E rs /<E rs > Figure 3. Comparison of normalized RS-TKE, E rs / E rs, of large-eddy simulations (LES) with the wind-tunnel measurements of BLDL Circles denote the wind-tunnel data and curves indicate the LES results: (a) (e) thin solid lines Case CSV and thick solid line CSV81; (f) (j) thick solid lines Case CS08 and thin solid lines CS12; and (k) (o) thick solid lines Case LW1 and thin solid lines LW2. Panels from left to right present the results at the locations where = 0.4, 0.25, 0.0, 0.25, and 0.4, respectively. See text for details. vertical extent of the domain is 1.5H, while ours is 5.2H. Obviously, the latter allows larger eddies to be developed above the rooftop and the flow there is more turbulent. The results shown in Figs. 1 and 2 indicate that the temporally averaged wind fields are relatively independent of the resolution, the initial wind profile, and the Smagorinsky constant. However, the RS-TKE fields (Fig. 3) are sensitive to these parameters. Theoretical studies suggest that even if the higher moments are not perfectly predicted in a LES, it still allows the correct prediction of temporally averaged fields (Meneveau 1993). The findings are consistent with the previous study by Cai et al. (1995), who found that the turbulent intensity increases with increasing grid point numbers and with decreasing Smagorinsky constant. In short, Case CSV81 gives the

10 1382 Z. CUI et al (a) (b) Figure 4. Spatial variation of the dimensionless turbulence intensities in the street canyon for Case CSV81: (a) streamwise quu 1/2 / u and (b) vertical qww/ u. 1/2 See text for details. best overall performance: the temporally averaged fields are close to the wind-tunnel measurements and the RS-TKE is reasonably reproduced. For turbulent flow the third and the fourth moments, i.e. skewness and kurtosis are also important quantities for judging the quality of simulation of the control run. For a set of univariate data f 1,f 2,...,f N, the formula for skewness is: N (f i f) 3 i=1 s f = (N 1)σf 3, (9) where f is the mean, σ f is the standard deviation, and N is the number of data points. Skewness measures the direction and degree of asymmetry of the distribution of the data; the skewness for a symmetric distribution is zero. Negative values for the skewness indicate a distribution that is weighted towards the negative direction and vice-versa. Equation (9) is used to calculate, by the procedure in Eqs. (5) (8), the u-skewness, s u,andw-skewness, s w. In Figs. 5 and 6, s u and s w are compared with the experimental measurements. For s u, Fig. 5 shows that the LES results are generally in a good agreement with observations in most places. At (, ) = (0.25, 0.6), the difference is large. Two likely possibilities are related to the significant fluctuation of s u from the wind-tunnel data: one concerns too small values of σ u, which is bound by TKE values shown in Fig. 3(d); and the other is related to the statistical procedure. The values of s u from the wind-tunnel experiment are calculated at a single point, and this procedure may not produce good statistics. The effect of the procedures on s u can be seen in Fig. 5. The profiles of s u from the LES are quite smooth for Cases CSV81, CS08, CS12, LW1 and LW2. In contrast, the profiles of s u for Case CSV are not smooth, because the calculated s u is based on the output on the central plane. The lack of smoothness is also found in s w, k u,andk w for Case CSV. It is, therefore, suggested that large amounts of data are needed for good statistics of high order moments. For s w, as shown in Fig. 6, the five sets of LES results are generally in better agreement than those for s u, and reproduce several interesting features in s w found in the experiment. The negative values of skewness between = 0.8 and 1.0 are reproduced by LES as in the experiment. At = 0.4, the curvatures of s w above = 0.8 in high-resolution simulations (Cases CSV81 and CSV) are related to corner eddies (shown later in Fig. 12). At = 0.4 the curvatures in the profiles are similar both in wind-tunnel experiments and in the LES although

11 SIMULATION OF TURBULENT FLOW IN A STREET CANYON 1383 (a) = 0.4 (b) = 0.25 (c) =0.0 (d) =0.25 (e) = s u s u s u s u s u Figure 5. Comparison of the skewness of u, s u, with the wind-tunnel data of BLDL2000; (a) (e) present the results at locations of of 0.4, 0.25, 0.0, 0.25, and 0.4, respectively. Circles denote the wind-tunnel data and curves indicate the large-eddy simulation results: thick solid lines Case CSV81, thin solid lines CSV, short dashed lines CS08, dotted lines CS12, dash-dotted lines LW1, long-dashed lines LW2, respectively. See text for details. the amplitudes are different. More details of physical interpretations of the results are discussed later. Similarly, the formula for kurtosis, a measurement of the degree peaking or flatness of a distribution, is: N (f i f) 4 i=1 k f = (N 1)σf 4. (10) For a normal distribution k f = 3; excess kurtosis is therefore defined as k f 3. Positive excess kurtosis indicates a peaked distribution, whilst negative excess kurtosis indicates a flat distribution, relative to normal. The kurtosis of u and w (i.e. k u and k w ) are compared with the experimental measurements in Figs. 7 and 8, respectively. For k u, at the three locations in the upstream part of the canyon, i.e. at = 0.4, 0.25, and 0, the values of k u do not deviate much from that of the normal distribution both for LES and for the wind-tunnel experiment. An exception is that the values of k u derived from LES are large just below the rooftop for three locations: = 0.25, 0, and Unfortunately, wind-tunnel data are not able to confirmthis due to the low spatial resolution. At = 0.25and +0.4, the difference between the LES results and the observed data are noticeable at middle levels. For k w, as shown in Fig. 8, the results of the comparison are better, but

12 1384 Z. CUI et al. (a) = 0.4 (b) = 0.25 (c) =0.0 (d) =0.25 (e) = s w s w s w s w s w Figure 6. As Fig. 5 but for s w, the skewness of w. the w-distribution shows peakedness in the middle part of the canyon at = 0in the wind-tunnel measurement. At = 0.4, k w in the upper part of the canyon is larger in the LES. It is noted that s w 0 above rooftop both from the LES and from the wind-tunnel experiment. The distribution of the w-component from the LES is nearly Gaussian, while it is symmetric and peaked from the wind-tunnel experiment. In contrast, s u and k u agree well above the rooftop both from the LES and from the wind-tunnel experiment. The results suggest that the ambient flow properties are slightly different in the vertical direction. This seems to be related to the different ways by which turbulence is generated; turbulence was generated by small roughness elements over the fetch in the wind-tunnel experiment, but in the LES it was generated by the nonlinear development of perturbations in the infinitely recycled flow. The profiles of s u and s w in Figs. 5 and 6 show strong signals of skewness in the canyon. Figures 5(b), (c) and (d) indicate that there is a layer of significant positive s u just below the rooftop, whose thickness increases downstream. In this layer the distribution of the u-component turbulence skews in a positive direction, i.e. its mean value is typically greater than its median, which in turn is greater than its mode. Therefore, for most events u<u, but their magnitudes are smaller than the ones for the few events in which u>u. In contrast, as shown in Fig. 6, there is a layer, of significant negative s w just below the rooftop. For most events, w>w, but their magnitudes are smaller than those for the few events in which w<w. The features of s u and s w can be related to ejection and sweep events, which are important in turbulence studies (Shaw et al. 1983). For an ejection event u<u and w>w, whilst for a sweep event, u>u and w<w. The results shown in Figs. 5 and 6 indicate there are more ejection events and fewer sweep events in a layer just below the rooftop. Both ejection and sweep

13 SIMULATION OF TURBULENT FLOW IN A STREET CANYON 1385 (a) = 0.4 (b) = 0.25 (c) =0.0 (d) =0.25 (e) = k u k u k u k u k u Figure 7. As Fig. 5 but for k u, the kurtosis of u. events contribute to the negative Reynolds stress, i.e. to turbulence production, since the temporally averaged wind speed increases with height. There are also outward (where u > u and w > w) and inward (where u < u and w < w) interaction events. These events contribute to the turbulence destruction. In Figs. 7 and 8, k u and k w have large values of positive excess kurtosis in the layer corresponding to the significant s u and s w layer, respectively, below the rooftop shown in Figs. 5 and 6. This means that the distribution of u has a tall narrow peak at which u<u, and the distribution of w has a tall narrow peak at which w>w. Therefore, ejection events dominate the turbulent processes just below the rooftop in the canyon. To demonstrate this, the fluctuations u and w at (, ) = (0, 0.98) are analysed; the results are displayed in Fig. 9. In Fig. 9(a), the scatter plot shows that a long tail stretches towards the fourth quadrant (sweep events) in which u > 0andw < 0, as the analyses of skewness and kurtosis indicate. It is shown that the relationship between u and w is highly nonlinear and complex. The numbers of events of outward interaction (u > 0andw > 0), ejection (u < 0andw > 0), inward interaction (u < 0andw < 0), and sweep (u > 0and w < 0) are 17.56%, 37.56%, 21.75% and 23.13%, respectively, of the total events. The dominant events in frequency are ejections (Fig. 9(b)). However, the contribution from sweep events is the largest part of the total momentum flux and it exceeds the sum of contributions from the other three processes, as shown in Fig. 9(c). These results are in agreement with those in the full-scale observations of Rotach (1993) and Oikawa and Meng (1995). In summary, the results presented in this section demonstrate that temporally averaged flow structure, RS-TKE, skewness and kurtosis have been captured in the LES, both qualitatively and quantitatively. The LES and wind-tunnel measurements are in

14 1386 Z. CUI et al. (a) = 0.4 (b) = 0.25 (c) =0.0 (d) =0.25 (e) = k w k w k w k w k w Figure 8. As Fig. 5 but for k w, the kurtosis of w. reasonably good agreement. The results demonstrate the capability of RAMS with LES in the study of street canyon flow. (b) The flow structure Field and laboratory studies only provide high-temporal-resolution data, but the LES can produce high-resolution output both in time and space. The temporally averaged structure of the canyon flow is presented in this section. Figure 10 shows the vectors of (u, w) within the canyon. The general picture of the canyon flow is in agreement with the previous results using k ε models (e.g. Sini et al. 1996, Baik and Kim 1999), i.e. there is one primary eddy (PE) inside the canyon. The centre of the PE does not coincide with the canyon centre, it is located slightly to the right at x = 0.03 and towards the upper part of canyon at z = Figure 11 shows the profile of u( ) at = 0 and that of w() at = 0.5. The maximum speed of the reversed flow is 0.4 m s 1, and is similar to that near the top of the canyon. The downdraught flow in the vicinity of the downstream wall is 0.45 m s 1, stronger than the updraught in the vicinity of the upstream wall which is about 0.3 m s 1. The results of BLDL2000 and Soulhac (2000) showed the same feature. From the viewpoint of mass conservation, the area of the updraught should be larger than that of the downdraught, and the centre of the PE should shift towards the downstream wall, as is indeed the case. In Fig. 10, a weak eddy residing around street level and near the downstream wall is just visible. This corner eddy is also evident in Figs. 12(a) and (c), which show instantaneous vectors (u, w) and the fluctuation vectors of (u,w ) on the central plane of the domain at two different times. The corner eddies result from air

15 SIMULATION OF TURBULENT FLOW IN A STREET CANYON 1387 (a) (b) (c) outward ejection inward sweep outward ejection inward sweep w u Figure 9. Analysis of turbulent events at (, y/h, ) = (0, 0, 0.98) for Case CSV: (a) scatter plot of u against w ; (b) percentage frequency of occurrence of the four events outward interaction, ejection, inward interaction and sweep; and (c) u w (m 2 s 2 ) contributed from these same four events. See text for details. flowing over the bluff canyon corner (e.g. Ghia et al. 1982). By viewing an animation of the flow it is found that the eddy exists permanently, although its size varies with time so as to contribute to large values of RS-TKE shown in Fig. 3(e). Therefore, it is a persistent feature. In contrast, the lower- and upper-corner eddies in the vicinity of the upstream wall are transient. Also, at rooftop the sweep can clearly be seen in Fig. 12(b) in the vicinity the upstream wall, and ejection in Fig. 12(d) in the vicinity

16 1388 Z. CUI et al ms Figure 10. Temporally averaged wind vectors on the central plane in the street canyon at y = 0 for Case CSV. See text for details u w Figure 11. The profiles of u (solid curve; m s 1 ) at (, y/h) = (0, 0) and w (dashed curve; m s 1 ) at (y/h, ) = (0, 0.5) for Case CSV. See text for details.

17 SIMULATION OF TURBULENT FLOW IN A STREET CANYON 1389 (a) (b) ms ms (c) (d) ms ms Figure 12. Snapshots of: (a) wind vectors (u, w) at time t = 315 s, (b) fluctuation vectors (u,w ) at t = 315 s, (c) wind vectors (u, w) at t = 214 s, and (d) fluctuation vectors (u,w ) at t = 214 s, on the central plane of the street canyon at y = 0 for Case CSV. See text for details. of the downstream wall. On these figures, the PE is a dominant feature. By comparing the figures, the flapping of wind at the rooftop is evident. This transient feature of the canyon flow has not been apparent in the previous numerical studies that employed Reynolds-average equations. Figure 13 shows the RS-TKE on the central plane of the canyon. The RS-TKE is higher outside the canyon, and a zone of high RS-TKE above the roof tilts downward to the downstream wall, dipping down along this wall. Baik and Kim (1999) presented TKE in their k ε modelling of street canyon flow, and their non-compared results also showed a similar feature. In most parts of the canyon the RS-TKE is relatively uniform. Another feature is that the RS-TKE has a secondary maximum value in the vicinity of the lower downstream corner, suggesting the effects of the unstable corner eddy discussed above. The picture of the RS-TKE indicates the advection of turbulence as well as the generation of turbulence in the vicinity of the downstream wall. To investigate the intermittency of the street canyon flow, the spatial temporal variation of u, w, and the momentum flux, u w, at the rooftop ( = 1) for Case CSV during the first half of the analysis period (450 s) is presented in Fig. 14, in which

18 Z. CUI et al. Ŧ1.0 Ŧ Figure 13. Temporally averaged resolved-scale turbulent kinetic energy (RS-TKE, m2 s 2 ) on the central plane of the street canyon at y = 0 for Case CSV. See text for details. (a) (c) (b) time (sec) time (sec) time (sec) 0.4 Ŧ Ŧ Ŧ Ŧ0.4 Ŧ0.2 Ŧ0.6 Ŧ0.4 Ŧ0.4 Ŧ Ŧ0.4 Ŧ Ŧ0.4 Ŧ Figure 14. Spatial temporal variation of: (a) u (m s 1 ), (b) w (m s 1 ), and (c) u w (m2 s 2 ) at rooftop level ( = 1.0) for Case CSV from time t = 0 to t = 450 s. See text for details.

19 SIMULATION OF TURBULENT FLOW IN A STREET CANYON 1391 Period(sec) Time(sec) Figure 15. The normalized local wavelet power spectrum of u w at (, ) = (0, 1) by using the Morlet wavelet. The values in the key are magnified by 100 for clearer drawing. The left axis is the Fourier period (s), and the bottom axis is time (s). The region under the dashed line indicates the cone of influence, where edge effects become important. See text for details. the amplitudes of a variable are represented by different grey scales. The turbulent flow gives rise to highly intermittent features of these variables. Negative values of u w correspond to either sweep or ejection events, and the positive values correspond to either inward or outward interactions. A striking feature in Fig. 14 is the existence of very bright stripes, which appear on an irregular basis with time. Manual examination of the velocity fluctuation fields indicates that most of the verybright stripes are associated with strong sweep events, and few with strong ejection events. Strong sweep events can travel most of the canyon rooftop with varying amplitudes, and the manifestation of those processes is the long stripes stretching across most of the horizontal axis. An example is the one around time t = 315 s. The corresponding (u,w ) at this time-step is shown in Fig. 12(b), and the sweep is clearly seen just downstream of the upstream wall at rooftop. Strong ejection events seem to occur in the vicinity of the downstream wall. Figure 12(d) shows the (u,w ) field at t = 214 s, and the ejection is found near the downstream wall. The technique of wavelet analysis is used to identify the dominant modes of the variability of u w. In this paper the scheme described by Torrence and Compo (1998) is adopted; Fig. 15 shows the normalized local wavelet power spectrum of u w at (, ) = (0, 1) by using the Morlet wavelet. The ordinate is the Fourier periods, and the abscissa is time. The region below the dashed line (i.e. near the long periods end) indicates the cone of influence, where the edge effects become important; therefore, results above the line are meaningful. In this figure most of the power is concentrated within the band 4 16 s. This time-scale fits quite well with that of eddies produced by Kelvin Helmhotzinstability: if thedepthof theshearlayer neartherooftop, δz, is of the order of 1 m, the difference in mean wind, δu, for this case is of the order of 1 m s 1, the time-scale of the turnover time of an eddy is 2πδz/δu 8 s. It is noted that there

20 1392 Z. CUI et al. is appreciable power at longer periods around 1 2, 1, 2, and 4 minutes. These time-scales are not easily interpreted. The advection time-scale across the domain has an order of magnitude of about 1 2 minute, which may explain the power at this value. The intermittency of the street canyon flow indicates that strong exchanges of fresh and polluted air take place across the rooftop. The problem of quantifying air pollution inside an urban street canyon will require simulations with a coupled LES dispersion model in our future research. 4. CONCLUSIONS For this paper, a LES of turbulent street canyon flow with an aspect ratio of unity has been conducted. The primary objectives are to compare the LES results with windtunnel experiments and to present the simulated turbulent structures, with a particular focus on those near the roof-level. The simulation results were compared with recent wind-tunnel measurements of Brown et al. (2000) at five stations in a canyon. The variables compared include the mean velocities u and w, RS-TKE, skewness and kurtosis. Among these variables, the mean flow fields and the RS-TKE are in good agreement, and the skewness and kurtosis are in reasonably good agreement with the observations. In addition, the LES reproduces many flow features as found in the wind-tunnel experiments. The flow is predicted as a PE inside the canyon, which is slightly asymmetric about the geometric centre of the canyon. The mean vertical wind component shows a strong downdraught along the downstream wall and a weak updraught along the upstream wall. The RS-TKE has large values along the downstream wall, indicating that the flow is more turbulent there. Quadrant analysis of resolved-scale velocity fluctuations, u and w, under the rooftop at the centre of the canyon reveals that the exchange of momentum across the canyon top is contributed to unevenly by different events. Weak ejection events dominate the frequency of occurrences, but a few strong sweep events contribute the majority of the total momentum transfer. The features of momentum transfer are further investigated by analysing the spatial temporal variations of u, w and u w at the roof level. It is found that the variation of these variables is highly intermittent and is associated with multi-scale turbulent events. The periods of the dominating modes are identified by means of wavelet analysis. The smallest period of eddies containing high TKE is attributed to Kelvin Helmhotz instabilities. These results improve our understanding of the turbulent structure in the street canyon flow. An extension of the current research into turbulent street canyon flow will be focused on air pollution problems and involve the coupling of a LES model with a dispersion model in the future. ACKNOWLEDGEMENTS This study is sponsored by Natural Environmental Research Council of the UK (GST/02/2602). The authors wish to thank Dr M. Brown of Los Alamos National Laboratory for providing the wind-tunnel measurements. Thanks also go to Professor Roger Pielke of the Atmospheric Sciences Department at Colorado State University and Dr Craig Tremback of ATMET for providing the numerical code CSU-RAMS, version 2a, which was developed under the support of the National Science Foundation (NSF) and the Army Research Offices (ARO).

21 SIMULATION OF TURBULENT FLOW IN A STREET CANYON 1393 REFERENCES Baik, J. and Kim, J A numerical study of flow and pollutant dispersion characteristics in urban street canyons. J. Appl. Meteorol., 38, Brown, M. J., Lawson, R. E., Decroix, D. S. and Lee, R. L Mean flow and turbulence measurements around a 2-D array of buildings in a wind tunnel. Proceedings of the 11th joint AMS/AWMA conference on applied air pollution meteorology. January 2000, Long Beach, CA, USA 1995 Characteristics of wind-fields in a street canyon. J. Wind Eng. Ind. Aerodyn., 57, Ca,V.T.,Asaeda,T.,Ito,M.and Armfield, S. Cai, X.-M Large-eddy simulation of the convective boundary layer over an idealized patchy urban surface. Q. J. R. Meteorol. Soc., 125, Cai, X.-M. and Steyn, D. G The Von Karman constant determined by large eddy simulation. Boundary-Layer Meteorol., 78, Cai, X.-M., Steyn, D. G. and Gartshore, I. S. Chabni, A., Le Quere, P., Tenaud, C. and Laatar, H Resolved-scale turbulence in the atmospheric surface-layer from a large-eddy simulation. Boundary-Layer Meteorol., 75, Modelling of pollutant dispersion in urban street canyons by means of a large-eddy simulation approach. Int. J. Vehicle Design, 20, Depaul, F. T. and Sheih, C. M Measurements of wind velocities in a street canyon. Atmos. Environ., 20, Gayev, Y. A. and Savory, E Influence of street obstructions on flow processes within urban canyons. J. Wind Eng. Ind. Aerodyn., 82, Ghia,U.,Ghia,K.N.and Shin, C. T. Hoydysh, W. G. and Dabberdt, W. F. Hunter, L. J., John, G. T. and Watson, I. D High-Re solutions for incompressible flow using the Navier Stokes equations and a multigrid method. J. Comput. Phys., 48, Kinematics and dispersion characteristics of flows in asymmetric street canyons. Atmos. Environ., 22, An investigation of three-dimensional characteristics of flow regimes within the urban canyon. Atmos. Environ., 26, Jordan, S. A. and Ragab, S. A On the unsteady and turbulent characteristics of the threedimensional shear-driven cavity flow. J. Fluids Eng., 116, Kastner-Klein, P. and Plate, E. J Wind-tunnel study of concentration fields in street canyons. Atmos. Environ., 33, Kastner-Klein, P., Rotach, M. W., Brown, M. J., Fedorovich, E. and Lawson, R. E. Kastner-Klein, P., Fedorovich, E., Kelzel, M., Berkpwicz, R. and Britter, R. Ketzel, M., Berkowicz, R., Müller, W. J. and Lohmeyer, A. Kousa, A., Kukkonen, J., Karppinen, A., Aarnio, P. and Koskentalo, T Spatial variability of mean flow and turbulence fields in street canyons. Proceedings of the third AMS symposium on the urban environment, August, Davis, CA, USA 2003 The modelling of turbulence from traffic in urban dispersion models Part II: Evaluation against laboratory and fullscale concentration measurements in street canyons. Environ. Fluid Mech., 3, Dependence of street canyon concentrations on above-roof wind speed implications for numerical modelling. Int. J. Environ. and Pollut., 17, Statistical and diagnostic evaluation of a new-generation urban dispersion modelling system against an extensive dataset in the Helsinki Area. Atmos. Environ., 35, Liu, C. and Barth, M. C Large-eddy simulation of flow and scalar transport in a modelled street canyon. J. Appl. Meteorol., 41, Coupling between air flow in streets and the well-developed boundary layer aloft. Atmos. Environ., 34, Louka, P., Belcher, S. E. and Harrison, R. G. Mason, P. J. and Thompson, D. J Large-eddy simulations of the neutral-static-stability planetary boundary. Q. J. R. Meteorol. Soc., 113, Meneveau, C Statistics of turbulence subgrid-scale stresses: Necessary conditions and experimental tests. Phys. Fluids, 6, Nicholls, M. E., Pielk, R. A. and Meroney, R. N. Nicholls,M.E.,Pielk,R.A., Eastman, J. L., Finley, C. A., Lyons, W. A., Tremback, C. J., Walko, R. L. and Cotton, W. R Large eddy simulation of microburst winds flowing around a building. Proceedings of the first international symposium on computing and wind engineering. Tokyo, Japan 1993 Application of the RAMS numerical model to dispersion over urban areas. Pp in Wind climate in cities. Eds. J. E. Cermak, A. G. Davenport, E. J. Plate and D. X. Viegas, Kluwer Academic Publishers, Dordrecht, the Netherlands