# Pollutant Dispersion in Boundary Layers Exposed to Rural-to-Urban Transitions: Varying the Spanwise Length Scale of the Roughness

## Abstract

Both large-eddy simulations (LES) and water-tunnel experiments, using simultaneous stereoscopic particle image velocimetry and laser-induced fluorescence, have been used to investigate pollutant dispersion mechanisms in regions where the surface changes from rural to urban roughness. The urban roughness was characterized by an array of rectangular obstacles in an in-line arrangement. The streamwise length scale of the roughness was kept constant, while the spanwise length scale was varied by varying the obstacle aspect ratio *l* / *h* between 1 and 8, where *l* is the spanwise dimension of the obstacles and *h* is the height of the obstacles. Additionally, the case of two-dimensional roughness (riblets) was considered in LES. A smooth-wall turbulent boundary layer of depth 10*h* was used as the approaching flow, and a line source of passive tracer was placed 2*h* upstream of the urban canopy. The experimental and numerical results show good agreement, while minor discrepancies are readily explained. It is found that for \(l/h=2\) the drag induced by the urban canopy is largest of all considered cases, and is caused by a large-scale secondary flow. In addition, due to the roughness transition the vertical advective pollutant flux is the main ventilation mechanism in the first three streets. Furthermore, by means of linear stochastic estimation the mean flow structure is identified that is responsible for street-canyon ventilation for the sixth street and onwards. Moreover, it is shown that the vertical length scale of this structure increases with increasing aspect ratio of the obstacles in the canopy, while the streamwise length scale does not show a similar trend.

### Keywords

Large-eddy simulation Laser-induced fluorescence Pollutant dispersion Roughness transition Stereoscopic particle image velocimetry## 1 Introduction

Because there is a worldwide increase in urbanization, more pollutant emission sources, such as from power generation, households and traffic, are present near populated areas. As a consequence, the demand for accurate urban air quality predictions is rising, which requires proper understanding of the dispersion of pollutants in the urban environment. Investigations of the urban boundary layer are often made for fully-developed flow over areas with uniform properties. For example, Cheng and Castro (2002b) carried out experiments on turbulent boundary layers where the complete bottom wall of the wind tunnel was covered with cubical roughness elements, thereby representing the flow over an urban area. In multiple simulation studies the fully-developed character of the flow is implicitly assumed by employing periodic boundary conditions in the horizontal directions (e.g., Coceal et al. 2006; Michioka et al. 2014; Boppana et al. 2014). However, in reality the surface roughness changes, e.g. from rural to urban regions, and the boundary layer has to adapt to this roughness transition. There are only a few recent numerical studies on turbulent flow over an explicitly resolved roughness transition (Lee et al. 2011; Cheng and Porté-Agel 2015), where mostly cubical roughness elements or riblets are considered. In addition, experimental investigations with results up to the roughness elements are scarce, and if a roughness transition is considered it is to determine when the boundary layer retains an equilibrium state, without investigating pollutant dispersion (Cheng and Castro 2002a).

In order to obtain insight in pollutant dispersion mechanisms, Michioka et al. (2014) performed large-eddy simulations (LES) on fully-developed flow over an array of obstacles with various aspect ratios *l* / *h*, where *l* is the spanwise obstacle length and *h* is the obstacle height. They conclude that for fully-developed conditions the turbulent pollutant flux is the main contributor to street-canyon ventilation, although the ratio of the turbulent to the advective pollutant flux does change slightly for different aspect ratios. Tomas et al. (2016) show that up to 14*h* downstream of a rural-to-urban roughness transition the advective pollutant flux remains significant. Furthermore, Michioka et al. (2011, 2014) conclude that street-canyon ventilation mostly takes place when low momentum regions pass over the canyon, and they suggest that these regions are of small scale compared to the coherent structures in the outer region and are generated close to the top of the canopy.

What is the influence of the aspect ratio

*l*/*h*on flow over a rural-to-urban transition, in terms of velocity statistics, internal boundary-layer depth, surface forces, and pollutant dispersion?What are the dominant mechanisms of pollutant removal from street canyons and how do these mechanisms change in the transition region?

## 2 Materials and Methods

### 2.1 Considered Cases

In both the experiments and the simulations a smooth-wall turbulent boundary layer was generated that approached an urban roughness geometry consisting of an array of obstacles. The Reynolds number of the approaching flow, \(Re_\tau = u_\tau \delta _{99} / \nu \), based on the fluid kinematic viscosity \(\nu \), the friction velocity \(u_\tau =\sqrt{\nu \partial u /\partial z}\), and the boundary-layer depth \(\delta _{99}\), was \(2.0\times 10^3\) in both cases. Figure 1a shows the top view and the side view of both the experimental set-up (black lines) and the domain used in the LES (blue lines). The location \(x=0\) corresponds to the upstream walls of the first row of obstacles, while the plane \(y=0\) lies in the middle of the domain at the symmetry plane of the obstacles. A uniform street layout of obstacles placed in an in-line arrangement was considered to capture the basic characteristics of urban areas. The parameter that was varied is the obstacle aspect ratio *l* / *h*; aspect ratios of 1, 2, 3.5, 5, 8, and \(\infty \) were simulated by LES, while aspect ratios of 1, 5, and 8 were investigated in the experiments. Figure 1b shows the top view of the different cases, which are indicated by AR1, AR2, AR3.5, AR5, AR8, and 2D. For each case two ‘streets’ are shown that consist of an obstacle row and a ‘street canyon’, which indicates a canyon in spanwise direction unless stated otherwise. In all cases the width of the obstacles as well as the width of all street canyons was equal to *h*. Consequently, the plan area density \(\lambda _\text {p} = A_\text {p}/A_\text {t}\) was equal to the frontal area density \(\lambda _\text {f} = A_\text {f}/A_\text {t}\), where \(A_\text {t}\) is the total area viewed from the top, \(A_\text {p}\) is the total area covered with obstacles and \(A_\text {f}\) is the total frontal area of the obstacles. \(\lambda =\lambda _\text {f}=\lambda _\text {p}\) was between 0.25 (case AR1) and 0.5 (case 2D), and all cases were in the skimming flow regime (Oke 1988). In addition, a line source of passive tracer was placed in front of the urban environment to simulate an emission from a highway as is often found near urban regions. Its location was 2*h* upstream of the first row of obstacles. In the experiments the tracer was released from the ground surface, while in the simulations the source was located at \(z/h=0.2\). After these properties of the test cases were determined, the experiments and simulations were done independently.

### 2.2 Experimental Set-Up

#### 2.2.1 Layout

The transparent test section of the water tunnel has a length of 5.0 m and a cross section of \(0.6\times 0.6\)\( m ^2\), which enables good access for optical measurement techniques, as in the currently employed PIV and LIF techniques.

The urban model was placed approximately 3.9 m downstream of the spires. It was constructed from blocks made of Plexiglass with cross-sectional dimensions of \(0.02\times 0.02\)\( m ^2\) and lengths of 0.02, 0.10, and 0.16 m for cases AR1, AR5, and AR8, respectively. The model contained eight street canyons in streamwise direction. Based on initial results from LES (Tomas et al. 2016), this was deemed to be sufficient to capture the flow development up to the region where the flow in the street canyons becomes similar.

To perform simultaneous velocity and concentration measurements above and partly inside the canopy, a stereoscopic PIV set-up was combined with a planar LIF set-up, as shown in Fig. 2. For the stereoscopic PIV measurements, the flow was seeded with 10 \(\mu \)m diameter neutrally buoyant tracer particles (Sphericell). The \(y=0\) plane was illuminated with a twin-cavity double pulsed Nd:YAG laser (Spectra-Physics Quanta Ray), resulting in a field-of-view of approximately \(0.43\times 0.25\)\( m ^2\) (\(x\times z\)). Dedicated optics were used to form a thin laser sheet with a thickness of approximately 1 mm in the measurement area. The particle images were recorded using two high resolution CCD cameras with a \(4872\times 3248\) pixel format (Image LX 16M, LaVision). Both PIV cameras were equipped with Micro-Nikkor F105mm objectives with an aperture number of 8. Additionally, both cameras were equipped with Scheimpflug adapters (Prasad and Jensen 1995) to allow for large viewing angles while keeping the particle images in focus. The total separation angle between the PIV cameras was set to \(56^{\circ }\). To enable measurements partly inside the canopy, both cameras had a small vertical inclination of about \(10^{\circ }\), with a third camera (Image LX 16M, LaVision) added to perform the planar LIF measurements. This camera was also equipped with a Micro-Nikkor F 105mm objective with an aperture number set to 2.8. A lower aperture number was chosen to collect a larger amount of the fluorescent signal. To provide a better view into the canopy this camera had a slight vertical inclination of \(10^{\circ }\), thereby eliminating the need for a Scheimpflug adapter. In order to separate the scattered light by the tracer particles (PIV) and the fluorescent signal (LIF), shortpass optical filters (PIV cameras) and a longpass optical filter (LIF camera) were employed (Westerweel et al. 2009).

#### 2.2.2 PIV Measurements

Data acquisition, image calibration, and analysis of the PIV images was performed using the commercial software package Davis 8.3. A custom-made calibration target was used to digitally backproject the distorted PIV images to remove the perspective deformation in stereoscopic viewing. The PIV images were interrogated with a multi-pass interrogation technique, where the final interrogation windows had a size of \(24\times 24\) pixels, corresponding to a spatial resolution of 0.1h, with 75% overlap between the neighbouring windows. The fraction of spurious vectors was found to be <2%; these could be reliably detected using a median test (Westerweel and Scarano 2005) and replaced by linear interpolation. Each dataset consisted of at least 1500 instantaneous velocity/concentration fields acquired at a temporal resolution of 1.44 Hz. This low acquisition frequency ensured that subsequent samples could be considered as statistically uncorrelated. As a result, reliable and accurate first-order and second-order statistics could be obtained.

#### 2.2.3 LIF Measurements

As the laser operated at a frequency-doubled wavelength of 532 nm, Rhodamine WT (Rh-WT) was selected as the fluorescent dye, which has spectral characteristics similar to the more commonly used Rhodamine B (Rh-B). However, it is much less toxic (Crimaldi 2008). Although Rh-WT is a temperature sensitive fluorescent tracer (Smart and Laidlaw 1977), the effect of temperature variations was negligible, because the water temperature varied by <1 \(^{\circ }\)C. The Schmidt number (\(Sc = \nu /D\), where *D* is the mass diffusivity) of Rh-WT in the experiments was approximately \(2.5\times 10^3\). Furthermore, the effective resolution of the concentration fields was 0.004*h* in both directions. The dye was injected 2*h* upstream of the first row of obstacles as a uniform line source, that consisted of a porous metal plate with size \(0.01\times 0.40\)\( m ^2\) (\(L_x \times L_y\)), which was mounted flush with the ground plate. A concentrated solution Rh-WT (10 mg \( l ^{-1}\)) was injected at a constant flow rate of 3 ml \( s ^{-1}\) by means of a syringe pump system, that resulted in an average vertical injection velocity of about \(0.75\times 10^{-3}\) m \( s ^{-1}\) or \(3\times 10^{-3}\,U_\infty \), where \(U_\infty \) is the freestream velocity.

After each experiment, a calibration of the LIF images, i.e. the conversion of raw digital images to concentration fields, was done by placing a small Plexiglas container of size \(0.45\times 0.12\times 0.04\)\( m ^3\) in the measurement domain, with different known uniform concentrations. This yielded a calibration curve for measured pixel grey values to concentrations for each pixel in the measurement domain. Care was taken to perform all experiments under so-called ‘optically thin’ conditions. Accordingly, the attenuation of the laser sheet due to the presence of Rh-WT was negligible, and the conversion of raw images to concentration fields simplified significantly (Crimaldi 2008; Krug et al. 2014). The raw images were converted to a concentration field after subtraction of a background image based on linearly interpolating the background image that was taken before and after each measurement to account for the increase in background levels due to the dye introduced during each measurement. In addition, a rescaling procedure was applied to compensate for the pulse-to-pulse variations (with a standard deviation of about 3% of the mean intensity) that are inherently present in the laser beam of the Nd:YAG laser. Finally, the concentration fluxes are obtained by interpolating the velocity field onto the high resolution LIF grid by bicubic interpolation.

### 2.3 Numerical Set-Up

The LES set-up is the same as in Tomas et al. (2016) except that in the current study only neutrally buoyant conditions are considered and that several obstacle aspect ratios are studied. Here, the main characteristics of the simulations are given, while further details can be found in Tomas et al. (2016).

#### 2.3.1 Governing Equations and Numerical Method

The code developed is based on the Dutch Atmospheric Large-Eddy Simulation (DALES) code (Heus et al. 2010), where the main modifications are the addition of an immersed boundary method (Pourquie et al. 2009), the implementation of inflow/outflow boundary conditions, and the application of the eddy-viscosity SGS model of Vreman (2004). This model has the advantage over the standard Smagorinsky–Lilly model (Smagorinsky 1963; Lilly 1962) that no wall damping is required to reduce the SGS viscosity near walls. The equations of motion are solved using second-order central differencing for the spatial derivatives and an explicit third-order Runge–Kutta method for time integration. For the scalar concentration field the second-order \(\kappa \) scheme is used to ensure monotonicity (Hundsdorfer et al. 1995). The simulations are wall-resolved, so no use is made of wall functions. The Schmidt number *Sc* was 0.71, and \(Sc_\mathrm{sgs}\) was set to 0.9, equal to the turbulent Prandtl number found in the major part of the turbulent boundary layer in direct numerical simulation (DNS) studies by Jonker et al. (2013). The code has been used previously to simulate turbulent flow over a surface-mounted fence, showing good agreement with experimental data (Tomas et al. 2015a, b).

#### 2.3.2 Domain and Boundary Conditions

Figure 1 shows the LES domain in blue together with the applied number of grid cells in each direction. Vertical grid stretching was used such that each (cubical) obstacle was covered with \(20\times 20\times 48\) (\(x \times y \times z\)) cells. At the ground and the obstacle walls no-slip conditions were applied. The velocity and the concentration fields were assumed to be periodic in the spanwise direction. Furthermore, the smooth-wall turbulent boundary layer imposed at the inlet was generated in a separate ‘driver’ simulation using the rescaling method proposed by Lund et al. (1998). At the outlet a convective outflow boundary condition was applied for both velocity and concentration. Furthermore, at the top wall free-slip conditions were assumed for the horizontal velocity components. In addition, a small vertical outflow velocity was applied that corresponds to the outflow velocity used in the driver simulation to achieve a zero pressure-gradient boundary layer. The computational grid, boundary conditions, as well as the inflow turbulent boundary layer are the same as for the neutrally buoyant case described by Tomas et al. (2016), in which further details are given.

#### 2.3.3 Statistics

*T*was used, where \(T=h/U_h\) and \(U_h\) is a velocity scale defined in the next section. The simulations ran for at least 780

*T*before statistics were computed, which was long enough to assure a steady state. Statistics were computed for a duration of at least 780

*T*with a sampling interval of 0.31

*T*resulting in converged results. This duration corresponds to approximately 125 uncorrelated samples in the experiment. The simulations were well-resolved, such that the average subgrid stress \(\overline{-2\nu _\mathrm{sgs}S_{13}}\) did not exceed 6% of the total Reynolds stress, as shown in Tomas et al. (2016). Therefore, only the resolved statistics are shown in the subsequent sections.

Summary of the properties of the approaching boundary layer; \(\delta ^*\) is the displacement thickness, \(\theta \) is the momentum thickness, and *H* is the shape factor

\(\dfrac{\delta _{99}}{h}\) | \(\dfrac{\theta }{h}\) | \(\dfrac{\delta ^*}{h}\) |
| \(\dfrac{U_{\infty }}{U_h}\) | \(\dfrac{u_{\tau }}{U_h}\) | \(Re_{\tau }\)\(\left( \frac{u_\tau \delta _{99}}{\nu }\right) \) | \(h^+\)\(\left( \frac{u_\tau h}{\nu }\right) \) |
| |
---|---|---|---|---|---|---|---|---|---|

Exp. | 9.6 | 0.95 | 1.46 | 1.56 | 1.41 | 0.060 | \(2.0\times 10^3\) | 213 | \(5.4\times 10^3\) |

LES | 10.3 | 1.28 | 1.78 | 1.39 | 1.56 | 0.059 | \(2.0\times 10^3\) | 194 | \(5.0\times 10^3\) |

## 3 Results: Flow Statistics

### 3.1 Approaching Flow Conditions

The characteristics of the approaching flow boundary layer have an influence on the flow development over obstacles (Castro 1979; Blackman et al. 2015). Therefore, here a comparison is given of the approaching flow boundary layer in the experiments and in the simulations. A summary of the relevant boundary-layer properties for both the experiments and the simulations can be found in Table 1. All profiles are normalized with the velocity at obstacle height at the start of the measurement/simulation domain (in absence of the urban array), \(U_h\equiv \overline{u}|_{z=h}\), which proved to be the best scaling for the rural-to-urban flows discussed in the subsequent sections. However, it should be kept in mind that *h* and \(U_h\) are not the length scale and velocity scale for smooth-wall turbulent boundary layers, since normally \(\delta \) and \(U_\infty \) are used. Therefore minor discrepancies are found when comparing the two methods.

Figure 3 depicts the velocity profile, the profiles of the root-mean-square (r.m.s.) of the velocity fluctuations, and the mean Reynolds stress distribution in the vertical direction for the experiments and the LES. Despite the different ways of generating the approaching boundary layer there is a satisfactory agreement between the results of the two methods; a good match is found for the mean velocity profile in the range \(0\le z/h\le 3\) (Fig. 3a). In the LES a zero pressure-gradient boundary layer was generated, while in the experiment a slightly favourable pressure gradient was present due to the boundary-layer growth and the constant cross-sectional area of the tunnel. With the normalization with \(U_h\) this difference adds to a lower streamwise velocity component in the outer region (above \(z/h=3\)) of the experimental boundary layer. As observed in Fig. 3b the profiles of \(u_\text {rms}\) and \(w_\text {rms}\) are similar in shape when comparing the experimental data with the LES simulations. The main differences are attributed to the difference in predicted and measured \(U_h\) (see Table 1), i.e. the lower \(U_h\) in the LES causes the scaled velocity fluctuations to be larger than in the experiments. In addition, the small favourable pressure gradient in the experiments reduces the velocity fluctuations in the experimental boundary layer (Joshi et al. 2014). Furthermore, a reduction is observed in the mean Reynolds stress in the experiments in the region \(2\le z/h \le 5\), see Fig. 3c. This is most likely attributed to the design and the arrangement of the spires. Nevertheless, as will be shown in the subsequent sections, the differences in characteristics of the approaching flow did not cause significant discrepancies in the development of the flow over the urban canopy.

*Re*), based on \(U_\infty \) and

*h*, was approximately \(5.0\times 10^3\) for both the numerical simulations and the experiments, which is in the regime where Reynolds number effects are small when flow over sharp-edged obstacles is considered (Cheng and Castro 2002b). In addition, the wall-friction Reynolds number (\(h^+\)), based on \(u_{\tau }\) and

*h*, was around 200 in both cases, which is slightly above the lower limit of \(h^+\approx 100\) for dynamically fully rough flow (Raupach et al. 1991).

### 3.2 The Flow Over the Urban Canopy

Figure 6 shows the mean Reynolds stresses \(\overline{u'u'}\) and \(-\overline{u'w'}\) for the same case. The strong shear layer emanating from the upstream corner of the first obstacle generates large turbulent fluctuations resulting in a peak in \(\overline{u'u'}\) above the first obstacle and a peak in \(-\overline{u'w'}\) above the first street canyon. The flow appears to be also strongly affected by the presence of the second obstacle, above which another peak in \(\overline{u'u'}\) is present, while a peak in \(-\overline{u'w'}\) is located above the second street canyon. The intensity of the turbulent plume decreases in downstream direction, while weaker plumes of \(-\overline{u'w'}\) are produced by the shear layers above the street canyons. Just as for \(\overline{u}\) and \(\overline{w}\) there are some discrepancies between the experiments and the simulations above the first three obstacle rows due to the aforementioned reasons. The contour plots in Figs. 5 and 6 give an overall view of the flow and can be used for a qualitative comparison of the two methods. Figure 7 allows for a quantitative comparison of cases AR1, AR2, AR5, AR8, and 2D, by showing the vertical profiles of the mean streamwise velocity component 0.5*h* in front of the first obstacle row and in the middle of each subsequent street canyon. The LES data are shown by continuous lines, while, if available, the experimental data are shown by dashed lines. In all cases backflow occurred inside the canopy, while above the canopy an internal boundary layer developed, which is defined and discussed in Sect. 3.3 and shown in Fig. 7 by open symbols for the experiment and by solid symbols for the LES. In all cases the flow profiles in the street canyon changes significantly over the first three to four rows of obstacles while only minor changes are observed from street canyon 4 onwards. For case AR1, and especially case AR2, \(\overline{u}\) is mostly negative at this location in the street canyon, while for cases AR5, AR8, and 2D a ‘canyon vortex’ arises that is most apparent in case 2D.

*u*to decrease to 0.5. Above the first street canyon in case AR8 (Fig. 8d) \(\varLambda \) is 0.3

*h*, resulting in approximately 83% of the Reynolds stress being resolved at that location.

With increasing aspect ratio *l* / *h* the blockage of the incoming flow increases, which results in an increase of the peak in \(-\overline{u'w'}\) behind the first row of obstacles. Further downstream this peak diffuses, and eventually the largest value of \(-\overline{u'w'}\) occurs near the top of the canopy, where the rooftop shear layers are the largest sources of turbulence production. In view of blockage of the flow case AR8 approximates the 2D case, which is reflected in a similar peak in \(-\overline{u'w'}\) behind the first row. However, in the eighth street canyon the depth of the region with increased Reynolds stress is larger for case AR8 than case 2D. This is because the three-dimensional roughness arrays (all cases other than 2D) induce a secondary flow that causes the internal boundary layer to grow more rapidly in case AR8 than in case 2D. This is further discussed in Sect. 3.3.

### 3.3 Surface Forces and Internal Boundary-Layer Growth

*h*and a width equal to the domain size. The total drag force consists of skin frictional drag, \(F_\tau \), and form drag, \(F_p\);

*d*, which is the height at which the total drag force acts (Jackson 1981). It is computed by dividing the total moment of the drag forces by the total drag force. After approximately nine streets

*d*has reached a constant value, where the cases with highest blockage need longest distance to adapt. Moreover, it can be seen that with increasing

*l*/

*h*,

*d*increases to the maximum of nearly

*h*for case 2D.

*d*; both \(d^*\) and \(z_0\) are found by fitting the velocity profile from the LES to Eq. (6), while

*d*follows directly from the force balance. In Fig. 9c both

*d*and \(d^*\) are plotted for the 23rd street for all cases, showing a discrepancy that has also been reported by Cheng and Castro (2002b) and Cheng et al. (2007). They suggest that this difference arises from either a different value for the von Kármán constant or significant dispersive stresses within the canopy. The latter is confirmed by a DNS investigation by Coceal et al. (2006). Figure 9d shows \(z_0\) for all cases at the same location from which it can be concluded that, except for case AR2, \(z_0\) decreases with increasing aspect ratio, which is in agreement with earlier studies that show that for cubical roughness \(z_0\) decreases for \(\lambda \gtrsim 0.2\) (Macdonald et al. 1998). Nevertheless, from Fig. 9a, c, d it is clear that case AR2 induces the largest drag force and that, unlike the other cases, this drag force has not yet fully developed. In addition, at the end of the domain the velocity profile for case AR2 showed only a small logarithmic region, most likely because it was still developing.

*l*/

*h*ratio. For all cases the contours show spanwise variations that correspond with the size of the repeating element. Local upwash and downwash regions can be identified. These are of largest magnitude in case AR2, resulting in two counter-rotating streamwise vortices that reach up to 2

*h*above the canopy. We hypothesize that the strength of the secondary flow, and thus the increase in drag, is largest when the spanwise spacing of the roughness elements is roughly proportional to \(\delta _i - h\). This is analogous to the conclusion by Vanderwel and Ganapathisubramani (2015), who experimentally measured a fully-developed boundary layer with a depth of 11.3

*h*and found that large-scale secondary flows are accentuated when the spanwise spacing of roughness elements is roughly proportional to the boundary-layer depth. Finally, it must be noted that the presence of large-scale secondary flows requires spatial averaging of \(-\overline{u'w'}\) over regions of at least the size of the repeating element in order to derive an accurate estimate of \(u_\tau \). The experimental results in Fig. 9a are based on a spatial average in the midplane only. Fortunately, as shown in Fig. 10, the spanwise variation of \(-\overline{u'w'}\) is relatively small for these cases (AR1, AR5, and AR8).

## 4 Results: Pollutant Dispersion

*h*upstream of the urban canopy. The concentrations \(c^*\), retrieved both from measurements and from simulations, are non-dimensionalized using the reference velocity \(U_h\), obstacle height

*h*, source width \(L_y\), source concentration \(c_\text {s}\), and source volume flow rate \(\phi _\text {s}\) (see Sect. 2.2.3),

*c*for case AR5 corresponding to the instantaneous velocity field shown in Fig. 4. The experimental results exhibit more distinctive layers than the simulations due to the larger Schmidt number (

*Sc*). Nevertheless, there is a high degree of similarity when the larger structures are considered. This is reflected in a turbulent Schmidt number of 1.21 in the experiments and 0.77 in the LES, which was estimated by deriving the turbulent viscosity and the turbulent diffusivity using the ‘Boussinesq approximation’.

### 4.1 Mean Concentration Fields

*h*upstream of the first row of obstacles and in the middle of each subsequent street canyon for cases AR1, AR5, AR8, and 2D. The LES data are shown by continuous lines, while, if available, the experimental results are shown by the dashed lines. The internal boundary-layer depth \(\delta _i\) is plotted by solid markers for the LES and by open markers for the experiment. Clearly, the vertical profiles for \(\overline{c}\) are largely controlled by \(\delta _i\) as high concentrations remain inside the internal boundary layer. The most pronounced differences between the numerical and experimental results are observed inside and just above the street canyons (i.e. \(z/h<1.5\)), where the experiments indicate a significantly higher concentration. Additional tests revealed that the line source was slightly non-uniform in spanwise direction with a higher than average flow rate at the location of the measurement plane. Nevertheless, the average flow rate through the line source was kept constant in time. The influence of the spanwise non-uniformity decreases in downstream direction as turbulence decreases this lateral inhomogeneity, leading to a closer match between the two methods further downstream. This behaviour is also reflected in Fig. 12e, where the average street-canyon concentration is shown. Since the street canyon is not completely visible in the experimental results, the average street-canyon concentration is determined only in the upper part of the street canyon. From the LES results it is concluded that this is a good approximation, as the street-canyon concentration is quite uniform (especially in the more downstream street canyons). Considering the different aspect ratios it is clear that cases AR5, AR8, and 2D predict qualitatively similar behaviour: the maximum average concentration occurs in the first street and the average concentration decreases slowly in subsequent streets. Different behaviour is found in the AR1 case, where the street-canyon concentration is lower in the first street and subsequently reaches its maximum in the third street canyon. This is because for case AR1 a large part of the concentration is advected with high velocity through the streamwise streets, thereby passing the first two street canyons. As the flow velocity has decreased after two streets, the concentration in the wakes of the cubes increases.

### 4.2 Pollutant Dispersion Mechanisms

To investigate under which conditions pollutants are ventilated from street canyons, the joint probability density function (p.d.f.) of streamwise velocity fluctuation \(u'\) and instantaneous vertical pollutant flux *wc* was computed in each street in the region \(\left( 0.05<\right. \)\(x'/h\)\(< 0.95\), \(0.95<\)\(z/h<\)\(\left. 1.05\right) \), where \(x' = 0\) represents the location of the upstream wall of the street canyon. The shape of the joint p.d.f. does not vary significantly inside this region. Therefore, the joint p.d.f. is averaged over this region and shown for street 6 for cases AR1, AR5, AR8, and 2D in Fig. 14, where the joint p.d.f. has been multiplied with the associated value of *wc* to visualize the contribution to the total average pollutant flux \(\overline{wc}\). For all cases the pollutant flux *wc* is mainly negative when \(u'>0\) , i.e. pollutants enter the street canyon from above, while for \(u'<0\) the pollutant flux *wc* can be either positive or negative. It is found that after three streets the joint p.d.f.s have the same shape as shown in Fig. 14, which suggests the dominating mechanism responsible for pollutant removal has developed after three streets. Accordingly, in (periodic) simulations of fully-developed flow over street canyons qualitatively similar joint p.d.f.s are found (Michioka et al. 2014). From the results presented here it can be concluded that ventilation of street canyons is associated with low momentum regions passing the street canyons.

#### 4.2.1 The Mean Fluctuating Velocity Field for Street-Canyon Ventilation

*u*. However, the direct correlation between street-canyon ventilation and the flow was not made. Here, use is made of linear stochastic estimation (Adrian 1988) to approximate the conditional mean velocity fluctuation for the event of a pollutant flux \(\langle wc \rangle _\text {e}\) out of the street canyon: \(\overline{u'_i(\varvec{x})|\langle wc\rangle _\text {e}}\), where \(\varvec{x}=(x,y,z)\) and \(\langle ..\rangle \) represents the spatial average over the region \(\left( 0.05<\right. \)\(x'/h\)\(< 0.95\), \(0.95<\)\(z/h<\)\(\left. 1.05\right) \) in the midplane of the obstacles. Analogously to Christensen and Adrian (2001) this conditional mean is approximated by

## 5 Conclusions

Large-eddy simulations as well as simultaneous PIV and LIF measurements were employed to investigate flow and pollutant dispersion behaviour in regions where the surface changes from rural to urban type roughness. The influence of the aspect ratio of the obstacles, which make up the urban canopy, was investigated for the case of approaching flow over a smooth wall at a roughness Reynolds number, \(h^+\), of 194 for the simulations and 213 for the experiments. The results show that the two methods independently predict practically the same velocity statistics. Furthermore, minor differences in the region of the first row of obstacles can be attributed to the accuracy of both methods and slight differences in the generated smooth-wall boundary layers. The concentration statistics show some differences at the start of the canopy due to a slight non-uniformity in the emission source in the experiment. Nevertheless, qualitatively there is a good agreement between the methods, and the same dispersion mechanisms are identified.

The force balance from the simulations shows that for all cases, except one, after approximately eight streets the surface forces have adapted to the surface roughness. However, for \(l/h=2\) the surface forces are still developing at \(x=46h\) (which is the end of the considered numerical domain) due to the occurrence of large-scale secondary flow. As a consequence, the roughness length \(z_0\) and the displacement height \(d^*\), as used in the standard logarithmic law, are discontinuous when plotted against *l* / *h*. It is hypothesized that this phenomenon occurs because for \(l/h=2\) the spacing of the roughness elements is proportional to \(\delta _i-h\), analogous to conlusions by Vanderwel and Ganapathisubramani (2015). As to whether or not this large-scale secondary flow eventually disappears, as the internal boundary layer grows, remains an open question. Nonetheless, it is concluded that estimating \(u_\tau \) by using \(\overline{u'w'}\) from single plane measurements only, can be inaccurate due to the spanwise variation caused by this secondary flow. In addition, it is found that with \(l/h>2\) the surface drag decreases as the flow is characterized to a larger extent by the skimming flow regime.

The effect of the roughness transition on pollutant dispersion is that the mean vertical pollutant flux at the top of the street canyons is dominated by the advective pollutant flux \(\overline{w}\,\overline{c}\) in the first three streets, after which the profiles of \(\overline{w}\,\overline{c}\) and \(\overline{w'c'}\) along the streamwise extent of the street canyons become similar to those for the fully-developed cases described by Michioka et al. (2014). Likewise, the joint p.d.f.s of the streamwise velocity fluctuation \(u'\) and the instantaneous vertical pollutant flux *wc* have a comparable shape from the fourth street onwards. In addition, it is found that, in agreement with Michioka et al. (2014), the joint p.d.f.s are qualitatively similar for all considered *l* / *h*, showing that street canyon ventilation of pollutant is mostly associated with \(u'<0\).

Subsequently, the flow structure that is responsible for street-canyon ventilation was identified by means of linear stochastic estimation. It is found that for larger *l* / *h* street-canyon ventilation is associated with larger regions of \(u'<0\), and that their vertical length scale increases linearly with increasing *l* / *h*. However, the result for the 2D case does not result in the largest structure. In addition, during such a ventilation event the flow structure inside the urban canopy shows more variation in the horizontal plane for \(l/h=1\) and \(l/h=2\) than for larger aspect ratios, for which the variation is confined mostly to the considered street canyon.

## Notes

### Acknowledgements

This study was done within the STW project DisTUrbE (Project No. 11989) using the computational resources of SURFsara with the funding of the Netherlands Organization for Scientific Research (NWO).

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