Low Height Variability
The No Tall cases are considered as a reference state of RSL and ISL flow characteristics. Median vertical flow profiles of all No \(\hbox {Tall}_{\text {N,SE}}\) sites (Fig. 2b, e) are shown in Fig. 3 together with the BL–0 approach-flow conditions. For both model orientations, the variability in building heights for the No Tall cases is approximately 6 m (Table 3), with \(H_{\text {NoTall}} = 13.4\) m. Minor differences in morphometric parameters are due to buildings being removed between the two model orientations.
The profiles of the longitudinal velocity component (U; Fig. 3a) show logarithmic behaviour and relatively small spatial variations (narrow interquartile range) above a height of \(3 H_{\text {NoTall}}\) (40.2 m), which can be considered the upper limit of the RSL (i.e. the blending height) without tall buildings included. Expectedly, values of U in the RSL and UCL show large site-to-site variability. The logarithmic part of the upwind boundary layer (BL–0) occurs closer to the surface between 1 and \(4.5 H_{\text {NoTall}}\) (Sect. 3.3).
There is a distinct increase in turbulence levels in response to the roughness change between the flow-development section and the model. For the No Tall cases, the vertical turbulent momentum flux (\(-\overline{u'w'}\); Fig. 3b) and turbulence kinetic energy (TKE, \(k=\frac{1}{2}(\overline{u'^2}+\overline{v'^2}+\overline{w'^2})\); Fig. 3c) peak around a height of \(2H_{\text {NoTall}}\) (26.8 m full scale). Differences between the median No Tall profiles are linked to different local effects on individual profiles and different sample sizes. Profiles of the standard deviation of the horizontal wind direction (\(\sigma _{\theta }\); Fig. 3d) are shown above the level of maximum \(-\overline{u'w'}\). Below that, in the lower parts of the RSL and within the urban canopy, the horizontal flow may not have a single ‘preferred’ direction. The turbulence characteristics (Fig. 3b–d) converge back to the BL–0 state at around 6 to \(7H_{\text {NoTall}}\). Note that the tall building rooftops are located at heights of around \(6H_{\text {NoTall}}\) (building \(\hbox {T}_{81}\)) and \(10H_{\text {NoTall}}\) (building \(\hbox {T}_{134}\)).
Wake-Roughness Interaction
The momentum deficit in the wake of a building is traditionally assessed by the velocity difference (\(\Updelta U\)) to the upwind (or ambient) flow. We use velocity differences to study effects of, (i) tall buildings in an urban canopy (Core–No Tall cases), (ii) tall buildings in isolation (Tall–BL–0), (iii) an urban canopy surrounding tall buildings (Core–Tall), and (iv) increased building heights in the near-wake of a tall building (Increased–Tall).
Figures 4 and 5 show vertical profiles of U and differences \(\Updelta U\) between model configurations for sites on longitudinal transects through buildings \(\hbox {T}_{81}\) and \(\hbox {T}_{134}\) (site codes as in Fig. 2c, f). Results from the ADMS–Build wake model (Appendix 1) are shown for the Tall and Core configurations (Figs. 4a, b and 5a, b) at sites in the main wake (discussion in Sect. 4.2.2).
Flow in the Near-Wake
In all geometries including the tall buildings, sites N3 (\(\hbox {T}_{81}\) building, Fig. 4a, b) and S1–S3 (\(\hbox {T}_{134}\) building, Fig. 5a–c) are located in the near-wake region that is characterized by flow reversal (\(U<0\)) over at least parts of the velocity profile in the cavity region on the leeward side of the tall buildings. The along-wind extent of the near-wake (or cavity zone) observed in the wind tunnel, \(L^\text {WT}_{R}\) (Table 4), for building \(\hbox {T}_{81}\) is within the range \(0.1H_{81}< L^\text {WT}_{R} < 0.6H_{81}\) (i.e. between sites N3 and N4; Fig. 2c) and \(0.9H_{134}< L^\text {WT}_{R} < 1.9H_{134}\) (i.e. between S3 and S4; Fig. 2f) for building \(\hbox {T}_{134}\). Note that \(L^\text {WT}_{R}\) is measured from the downwind building face, not the centre.
In the ADMS–Build wake model the cavity length \(L_R\) is derived from the building geometry (Eq. 2 with \(L=L_f\), Table 1). When surrounded by the low-rise canopy we define the effective (reduced) height of the tall buildings in the Core cases as \(H_{\text {eff}} = H-(z_{0,K}+z_{d,K})\) to account for the vertical displacement of the flow profiles above the canopy and the roughness variability of the surroundings. This is consistent with the definition of the inflow profiles for the ADMS–Build model for the Core configurations (Appendix 1). Using the roughness length and displacement height of the No Tall cases (Table 3) this results in \(H_{81,\text {eff}} = 62.7\) m (\(\hbox {T}_{81}\); \(\hbox {Core}_{\text {N}}\)) and \(H_{134,\text {eff}} = 115.2\) m (\(\hbox {T}_{134}\); \(\hbox {Core}_{\text {SE}}\)). The calculated \(L_R\) values fall within the ranges determined in the experiment for building \(\hbox {T}_{134}\), and are only slightly larger for \(\hbox {T}_{81}\) (Table 4). As \(L_R/H \propto W_c/H\), the reduced near-wake extent for the \(\hbox {T}_{81}\) tower is related to the smaller building aspect ratio (\(W_c/H\)) compared to \(\hbox {T}_{134}\).
In the near-wake region of the isolated buildings (Tall configuration), U is almost uniform with height over large portions of the wake before increasing monotonically: for building \(\hbox {T}_{81}\) up to \(z/H_{81} \approx 0.8\) (site N3; Fig. 4b); for \(\hbox {T}_{134}\) up to \(z/H_{134} \approx 0.8\) (site S1) and 0.5 (sites S2/S3; Fig. 5b). When surrounded by the low-rise canopy the tall-building wakes show a reduction in the strength of flow reversal in the recirculation region above \(z_{0,K}+z_{d,K}\) (Figs. 4a, 5a). For building \(\hbox {T}_{134}\) this occurs up to \(0.5H_{134}\) in the Core case (Fig. 5e) and \(0.6H_{134}\) for the Increased geometry (Fig. 5f). In the lee of the \(\hbox {T}_{81}\) tower, flow reversal at site N3 is reduced over nearly the entire building height (Fig. 4d) with \(U>0\) between 0.3 and \(0.6H_{81}\) (Fig. 4a). The structure of the cavity zone is noticeably altered from the Tall to Core to Increased configurations in response to the presence of the urban canopy and interaction with RSL turbulence. Similar changes of the near-wake structure, notably a reduction in the cavity length with increasing turbulence intensity of the ambient flow, occur for isolated buildings (Ogawa et al. 1983).
Table 4 Effective building heights (\(H_{\text {eff}}\)) and cavity lengths based on the ADMS–Build model approach (\(L_R\); Eq. 2) and wind-tunnel measurements (\(L^{WT}_R\)) for the Tall and Core configurations The low-rise buildings modify the shape of the Core-case U profiles in two ways compared to the Tall cases: (i) the sheltering effect of the urban canopy reduces the magnitude of the longitudinal velocity below \(z_{0,K}+z_{d,K}\) (No Tall case), and (ii) larger vertical mean-flow gradients, \(\partial _z U\), occur throughout the wake and at roof-level of the towers (Figs. 4a, 5a, c). The low-level buildings reduce the effective vertical depth, \(z_R\), over which flow reversal occurs in the lee of the tall building above the canopy as the centre of the recirculation zone is displaced upwards. At site S2 (\(d_x/H_{134} = 0.55\)), for example, distinct peaks in the magnitude of backflow are evident at heights of \(z/H_{134} \approx 0.6\) (Core case) and \(z/H_{134} \approx 0.75\) (Increased case), at which flow speeds in the Tall case already start to increase. In the Tall set-up, the vertical extent of the flow recirculation region, \(z_R/H_{134}\), is approximately 0.82, 0.8 and 0.76 at sites S1, S2 and S3 (Fig. 5b), respectively. For the Core geometry the extent reduces to 0.63, 0.59, 0.56 (Fig. 5a) and for the Increased case to 0.62, 0.45, 0.5 (Fig. 5c) at the same locations.
For building \(\hbox {T}_{81}\), the large \(\partial _z U\) at rooftop for both the Tall and Core set-ups (site N3; Fig. 4a, b) suggests shear-layer separation at the trailing edge of the roof, i.e. re-attachment to the roof occurred after the initial separation at the leading edge. This is accompanied by a small momentum excess above roof-level (\(\approx 0.05U_{ref}\) at \(z/H_{81}=1.1\), Fig. 4c). This is in agreement with near-wake specifications in the ADMS–Build model, in which re-attachment is assumed to occur if \(L\ge \min (H,0.5W_c)\). However, re-attachment is not only controlled by the building’s geometry, but also by the nature of the ambient flow and the turbulence structure at roof-level (Fackrell 1984). Based on pressure measurements on the roof of an isolated cubic building (Castro and Robins 1977), permanent re-attachment occurs if the ratio of upwind boundary-layer depth to building height is \(>1.4\) (\(\hbox {Tall}_{\text {N}}\): \(\delta _{BL-0}/H_{81} = 1.7\), Sect. 3.3) and intermittent or absent re-attachment if it is \(<1.4\) (\(\hbox {Tall}_{\text {SE}}\): \(\delta _{BL-0}/H_{134} = 1\)). Furthermore, higher turbulence intensity in the ambient flow promotes re-attachment to the top and sides of the building (Castro and Robins 1977).
The orientation of the triangular tower \(\hbox {T}_{134}\) to the south-easterly approach flow creates a set of strong roof vortices for which re-attachment can be expected (Hunt 1971; Hunt et al. 1978). Although no measurements are available above roof-level to confirm this, the flow structure in the Tall case closest to the building (S1) suggests that re-attachment may be intermittent as the velocity deficit is still large at \(z/H_{134} = 1\) (Fig. 5b). In the Core and Increased configurations, however, \(\partial _z U\) near roof-level is larger (Fig. 5a, c), which implies a more stable re-attachment of the shear layer.
Flow in the Main Wake
In the main-wake region, flow reversal ceases and the wake is characterized by a momentum deficit. The impact of the tall building on the ambient flow decays with longitudinal distance (\(d_x/H\); Fig. 6). The velocity deficit (\(\Updelta U\)) for the Tall configurations (Fig. 6a, c) is assessed by the Tall–BL–0 difference (U(z) for BL–0 as in Fig. 13a) and for the Core and Increased cases as the difference to the No Tall reference state (Fig. 6b, d, e). Assuming the velocity difference decays as \((d_x/H)^{-p}\) (e.g. Hosker 1983), the fits in Fig. 6 indicate different flow-recovery behaviours in the different configurations (fit parameters for all curves are given in the Online Resource, Table ESM_1). For the Tall cases (Fig. 6a, c), for which the decay rates are quite homogeneous with height, \(p\approx 1.5\) on average for building \(\hbox {T}_{81}\) and \(\approx \)2.0 for \(\hbox {T}_{134}\). Hence \(\Updelta U\) in the wake of the higher and wider \(\hbox {T}_{134}\) building decays more rapidly with downwind distance, which could result from the stronger lateral fanning of the wake compared to the slender hexagonal \(\hbox {T}_{81}\).
The specifications in the ADMS–Build model define the decay of the velocity deficit \(\Updelta U\) with downwind distance at the building centreline (\(y=0\)) as
$$\begin{aligned} \Updelta U \propto \ell _y^{-1}\ell _z^{-3} \; z \exp \left( -z^2\ell _z^{-2}\right) \end{aligned}$$
(1)
following Eq. 3 in Appendix 1, where \(\xi = z/\ell _z\), and the length scales \(\ell _{y,z} \propto x^{1/2}\) (Eq. 6, setting \(x_0=0\)). Hence, \(\Updelta U \propto x^{-2} \exp {(-z^2x^{-1})}\). For small \(z^2x^{-1}\), \(\Updelta U \propto x^{-2}\) after which the decay rate along x decreases considerably with increasing height unlike in the experiment (Tall cases).
For both buildings, the wake structure and decay rates vary more strongly with height if the tall building is embedded in an urban canopy (Fig. 6b, d, e). For the Core cases, in the peak region of TKE and vertical turbulent momentum transport of the No Tall case RSL (Fig. 3b, c) the wake decay is rapid initially, but further downwind \(\Updelta U\) varies little with \(d_x\) (building \(\hbox {T}_{81}\) at \(z/H_{81}=0.33\), Fig. 6b; \(\hbox {T}_{134}\) at \(z/H_{134}=0.20\), Fig. 6d).
Compared to the Tall-case profiles, for building \(\hbox {T}_{134}\) velocities are further reduced in the main wake in the Core configuration at all heights, even well above the RSL (\(\hbox {Core--Tall}<0\); Fig. 5e). For building \(\hbox {T}_{81}\), however, the nature of the Core–Tall difference is more complex at sites N4 and N5 that are closest to the near-wake (Fig. 4d): the Core-case wake is weaker compared to Tall below \(z/H_{81} \approx 0.7\) and noticeably enhanced above, reflecting the differences in the height \(z_{\text {max}}\) associated with \(\text {min}(U)\) above the RSL (Fig. 4a, b). Although no flow reversal occurred at sites N4/N5, qualitatively this behaviour is very similar to that observed at the near-wake sites S1–S3 behind building \(\hbox {T}_{134}\) (Fig. 5e). Further downwind of building \(\hbox {T}_{81}\) (sites N6–N8), the wake in the Core set-up is amplified at all levels above the canopy, as found for building \(\hbox {T}_{134}\) at similar distances.
Interestingly, increasing the height of the canopy in the near-wake region of building \(\hbox {T}_{134}\) reduces the velocity deficit in the main wake. The Increased–Tall differences are small between \(0.5H_{134}< z\le 1\) (Fig. 5f) and the difference between the Core and Increased cases is negative throughout the main wake above \(z_{0,K}+z_{d,K}\) (see profiles in Fig. 5a, c). This is also apparent in the along-wind decay of \(\Updelta U\) (Fig. 6e), particularly close to roof-level, where \(\Updelta U \approx 0\) at \(z/H_{134} = 0.94\) (\(d_x/H_{134} = 4.45\)) as in the Tall case (Fig. 6c). This behaviour may be related to strong damping of flow reversal over larger parts of the near-wake compared to the Core set-up (sites S1–S3; Fig. 5c), which results in reduced initial velocity defects at the start of the main wake (Fig. 6d, e). In addition to that, sites S4–S7 are affected by secondary wake effects downwind of the increased buildings, leading to enhanced turbulent mixing that can contribute to a reduced velocity deficit, in agreement with theoretical and empirical considerations (Castro and Robins 1977). Furthermore, since tower \(\hbox {T}_{134}\) is located at the model edge, the displacement of the BL–0 approach flow locally leads to an increase in the vertical flow component. This is expected to be further enhanced in the Increased configuration and results may be different if building \(\hbox {T}_{134}\) were embedded further downwind in the model.
The ADMS–Build wake model shows remarkably good agreement with the measured Tall-case profiles for building \(\hbox {T}_{81}\) throughout the main wake (Fig. 4b). However, the observed upward shift in \(z_{\text {max}}\) for the Core case at sites N4/N5 is not represented (Fig. 4a). While accounting for the reduction of the effective building height in the Core case improves the results for building \(\hbox {T}_{81}\), this measure is not sufficient to represent the structural changes of the wake if the tower is embedded in an urban canopy. Overall larger differences between model and experiment are evident in the wake of the triangular building \(\hbox {T}_{134}\), even when considered in isolation, as the enhanced wake decay rate is not captured. Using \(H_{\text {eff}}\) for the Core-configuration modelling in this case did not result in an improved representation of the wake. Since the model was neither designed to represent the impact of an urban canopy surrounding the tall building nor the flow response to non-cuboid building shapes, the results are not surprising, but help to identify model development needs.
Vertical Mean Flow Characteristics
Figure 7 shows profiles of \(W/U_h\), where \(U_h = \sqrt{U^2+ V^2}\) is the horizontal wind speed, together with the flow angle in the vertical plane, \(\theta _z = \arctan (W/U_h)\), for the three sites closest to the tall buildings.
Qualitative and quantitative changes in the patterns of updrafts and downdrafts for the different test geometries are evident. For building \(\hbox {T}_{81}\) there is a large amplification of the characteristic updrafts on the leeward building side at site N3 in the Core case (\(\text {max}(W/U_h)\approx 10\); Fig. 7a). The much stronger upward flow deflection (\(50^{\circ }< \theta _z < 90^{\circ }\) for \(0.3< z/H_{81} < 1\)) is linked to the initial confinement of the horizontal flow in the street canyon between building \(\hbox {T}_{81}\) and the downwind 24-m tall neighbouring building (Fig. 2a). Once the updraft clears the height of the downstream neighbour most of the air initially escapes in the longitudinal direction. This is consistent with the local increase of U to positive values above the low-level canopy at site N3 (Fig. 4a) and S1 (Fig. 5a, c), before backflow in the displaced recirculation zone of the tall building becomes dominant. Drastic effects of the underlying buildings are also evident at main-wake sites N4 and N5 (Fig. 7b, c). While for the Core geometry W remains positive between \(0.4\le z/H_{81} \le 0.8\) and negative at the top of the low-level canopy, the Tall-case profiles have upward then downward flow.
For building \(\hbox {T}_{134}\), qualitative differences mainly occur at S1, closest to the building (\(d_x/H_{134} = 0.27\); Fig. 7d). While the Tall case has strong upward flow at all levels, this is only the case above \(z/H_{134} \approx 0.6\) for the Core and Increased cases.
Wake Turbulence
Figure 8 shows profiles of TKE (k), vertical turbulent momentum transport (\(-\overline{u'w'}\)) and integral turbulence time scale (\(\tau _u\)) of the u-component for building \(\hbox {T}_{81}\) (Tall and Core cases) for the same sites as in Fig. 4. \(\tau _u\) is determined by integrating over the 1D temporal autocorrelation of \(u'\) down to a cut-off point of 0.25. An empirically determined correction factor of 1.336 is then applied to compensate for not integrating down to zero.
Turbulence characteristics are qualitatively similar for building \(\hbox {T}_{134}\) (Online Resource: Figs. ESM_2, ESM_3). Compared to the N1/N2 locations upwind of building \(\hbox {T}_{81}\), at the downwind sites k is enhanced by up to a factor of 10 (e.g. site N4 in the Tall case at \(z/H_{81}=0.7\)). In both geometries, at site N3 the peak of k at \(z/H_{81}=1\) is caused by strong contributions of \(\overline{u'^2}\) in the shear layer (\(\overline{u'^2}:\overline{v'^2}:\overline{w'^2}\) as 1 : 0.5 : 0.5 at \(z/H_{81}=1\); Online Resource: Fig. ESM_4). While above building \(\hbox {T}_{81}\)’s roof k in the Tall case rapidly converges back to the upwind flow conditions at any longitudinal distance in the wake, in the Core geometry it remains enhanced slightly longer. The larger peak of k closest to the building and the larger amount of shear developed in the Core case could indicate structural differences of the roof vortex compared to the Tall set-up and reflects the fact that the region of maximum velocity deficit in the Core geometry lies closer to the roof of the tower. Likewise, the different heights of \(\text {max}(k)\) in the main wake (sites N4–N8, Tall case: \(z/H_{81} \approx 0.7\); Core case: 0.9) can be attributed to the displacement of the Core-case profiles above the canopy (\((z_{0,K}+z_{d,K})/H_{81} \approx 0.25\)). Greater TKE values at sites N4/N5 (upwind part of the main-wake) for the Tall case throughout the vertical extent of the wake are associated with large variances of the lateral velocity component (\(\overline{v'^2}\)), with \(\text {max}(\overline{v'^2})\) being larger by a factor of \(\approx \)1.5 at both sites compared to the Core geometry (Online Resource: Fig. ESM_4).
In both configurations, \(-\overline{u'w'}\) changes sign in response to the sign change of \(\partial _z U\) between \(0.4< z/H_{81} < 1\) (sites N1–N3; Fig. 4a, b). In the Core set-up at sites N4/N5 there are notable peaks of \(-\overline{u'w'} > 0\) (downward momentum transfer) at the top of the low-level canopy (Fig. 8e), while in the Tall configuration in that region the transfer is oriented upwards (\(-\overline{u'w'} < 0\); Fig. 8b). Momentum exchange in the Core configuration is also enhanced at the roof-level of building \(\hbox {T}_{81}\), where fluxes at sites N3–N5 exceed the Tall-case values by factors of 1.5–2. At roof-level of building \(\hbox {T}_{134}\), fluxes are enhanced even more strongly at site S1 by factors of 2.5 for the Core case and 3 for Increased (Online Resource: Fig. ESM_3). The large momentum exchange at roof-level compared to the isolated building case is associated with larger \(\partial _z U\), \(\overline{u'^2}\) and \(\overline{w'^2}\), contributing to the reduction of the recirculation intensity. This has also been observed for isolated buildings in highly turbulent boundary layers (e.g. Becker et al. 2002).
Upwind of building \(\hbox {T}_{81}\), k and \(-\overline{u'w'}\) (sites N1/N2; Fig. 8d, e) are locally enhanced in the Core case due to the presence of some taller buildings with heights between 24 and 28 m (Fig. 2a), while downwind of location N3 the surrounding structures are notably lower (\(H<12\) m). Changes of wake turbulence in the Core geometry are accompanied by a reduction of \(\tau _u\) below \(z/H_{81} = 0.9\) in the main wake (Fig. 8c, f), reflecting the reduction of length scales of the energy-containing eddies generated in the RSL and UCL compared to the conditions in BL–0 approaching the isolated tall building.
Instantaneous Flow Structure
To understand better the observed response of mean flow and turbulence to changes in geometry, the flow structure is evaluated in terms of frequency distributions of the instantaneous vertical velocity component (w) and horizontal wind direction (\(\theta = \arctan (v/u)\)).
In the Tall case for building \(\hbox {T}_{81}\) (Fig. 9, near-wake) the recirculation pattern is quite symmetric at site N3 (\(\theta \) peaks at \(\pm 180^{\circ }\)), while it is absent in the Core case below \(z/H_{81} = 0.5\), where the flow initially has a preferred channelling direction. Only at higher elevations do the histograms start to converge. While for the Core configuration at site N3 the instantaneous vertical velocity remains mostly positive up to \(z/H_{81} \approx 0.7\), for the Tall set-up there are notable fractions of downdrafts at lower elevations that contribute to the overall low mean value, W (Fig. 7a). This pattern is perhaps associated with vortex shedding from the roof of building \(\hbox {T}_{81}\), which affects the near-wake more strongly if the incident flow has lower turbulence intensity (Becker et al. 2002).
In the main wake of \(\hbox {T}_{81}\) (site N4), the occurrence frequency \(P_{\theta }\) exhibits a distinct double peak in the Tall geometry. This pattern also occurs at site N5 (not shown) and may be linked to large vortices generated at the building sides, explaining the large amplitudes of \(\overline{v'^2}\) and hence k (Fig. 8a). Huber (1988) used wind-tunnel flow experiments for isolated buildings to show that the length scales of such vortices in the wake centre are of the order of 1 to 2 times the building height. For the Core case, bimodal patterns of \(P_{\theta }\) are absent; instead the histograms show mirrored tails between \(z/H_{81} = 0.45\) and 0.68. Again this change in the wake structure can in part be related to the impact of smaller scale, less organized eddies created by the low-level canopy. The effect is to cascade the energy of large (‘coherent’) vortices down to smaller eddies that dissipate more quickly, which affects the intensity of vortex shedding (Khanduri et al. 1998).
Similar conclusions can be drawn for building \(\hbox {T}_{134}\) (Online Resource: Fig. ESM_5). Although the shapes of the two tall buildings are rather different, the flow response is very similar in terms of changes in flow recirculation and the bimodality of \(P_{\theta }\), affecting the magnitude of \(\overline{v'^2}\).
Lateral Wake Characteristics
The lateral structure of building \(\hbox {T}_{134}\)’s wake is investigated on three cross-wind transects (L1–L3) in the Core, Tall and No Tall configurations (Fig. 2d, e, f). Figure 10 shows the evolution of the velocity difference \(\Updelta U\) with lateral distance (\(d_y/H_{134}\)) from the building centreline for Core–No Tall and Tall–BL–0. For the same sites, Fig. 11 shows lateral changes in the mean vertical velocity, W, in the Core and Tall geometries. The x locations of transects L1 and L2 match those of the vertical profile sites S3 and S4, located in the near-wake and main wake. At transect L3, the near-wake of building \(\hbox {T}_{81}\) is overlapping with the main wake of \(\hbox {T}_{134}\). ADMS–Build model results are shown for the main-wake transect L2.
In both configurations the maximum velocity deficit at L1 is slightly offset from the building centreline at all heights as a result of the angle between the triangular tower \(\hbox {T}_{134}\) and the oncoming flow (Fig. 10a, b). At the downwind edge of the near-wake (transect L1), the variability of \(\Updelta U\) near the rooftop (\(z/H_{134}=0.94\) and 1) confirms the large gradients in that flow region. At this height, \(\Updelta U\) in the Core and Tall cases shows distinct minima near the edges of the tower and rises towards the centre of the wake. This is accompanied by peaks of the velocity variances (Online Resource: Figs. ESM_6–8) and probably indicates the existence of counter-rotating vortices curling up from the building sides. The low spatial resolution of the L3 transect relative to the building width of building \(\hbox {T}_{81}\) does not permit to assess the existence of similar patterns for this case. Strong downdrafts near roof-level of building \(\hbox {T}_{134}\) (Fig. 11a, b) exist in both configurations, but in the near-wake of the Core set-up (L1 transect) downward flow is confined to the upper levels of the wake (\(z/H_{134} > 0.6\)), while in the lower half strong updrafts up to 0.4\(U_{ref}\) exist. Updrafts are also enhanced in the near-wake of building \(\hbox {T}_{81}\) (Core case; Fig. 11e) by up to a factor of 4 compared the values in the Tall case (Fig. 11f) at \(z/H_{81}=0.33\) and 0.8.
It is noticeable that the W values at roof-level of building \(\hbox {T}_{134}\) do not converge back to the ambient \(W \approx 0\), but remain negative on the \(d_y>0\) side of the wake (Fig. 11). In the Core configuration this is also occurring at \(z/H_{134}=0.48\). This asymmetry is likely a response to blockage effects and the corresponding pressure distribution around building \(\hbox {T}_{134}\), which is not aligned with the tunnel centreline (Fig 1d).
Close to the low-level canopy (\(z/H_{134} = 0.2\)), the Core-case transects show a superposition of wake characteristics of building \(\hbox {T}_{134}\) and local features of the RSL. On the L1 transect, for instance, the wake of a 30-m tall building located upwind (Fig. 2d) is captured at \(d_y/H_{134}=-1\). The negative \(\Updelta U\) (Fig. 10a) indicates that the wake of this lower building is amplified by the presence of the tall building \(\hbox {T}_{134}\) compared to the No Tall reference state. Near the corners of \(\hbox {T}_{134}\) (Fig. 10b) and \(\hbox {T}_{81}\) (Fig. 10f) in the Tall set-up there is a speed-up of U compared to the background state as the flow is deflected around the buildings. The presence of the urban canopy can locally enhance or reverse this feature, as seen on transect L1 on either side of building \(\hbox {T}_{134}\) (Fig. 10a; \(z/H_{134}=0.2\)) or on transect L3 near building \(\hbox {T}_{81}\) (Fig. 10e; \(z/H_{81}=0.33\)).
In the main wake of building \(\hbox {T}_{134}\) (transects L2/L3), the \(\Updelta U\) profiles in the Core and Tall configurations show the expected bell shape (e.g. Castro and Robins 1977) at sufficient distance from the low-level canopy. As in classic wake theory this is associated with a fast decay of the velocity deficit with \(d_y\), accompanied by \(W<0\). The magnitude of change of \(\Updelta U\) with \(d_y\) decreases with height and with downwind distance (\(d_x\)) from the tall building. The wake width, here defined as the extent of the region where the magnitude of \(\Updelta U\) is larger than 10% of \(U_{ref}\), for the Core/Tall geometries is 0.98/1.1\(H_{134}\) (L1 transect), 1.1/1.27\(H_{134}\) (L2) and 1.27\(H_{134}\) (L3; Core case only). While the lateral growth of the wake is slightly greater in the Tall configuration, the magnitude of \(\Updelta U\) is enhanced in the Core case. When assessed through the disturbance of the velocity variances, the wake is noticeably wider below the rooftop of building \(\hbox {T}_{134}\) (up to a factor of 2 at \(z/H_{134}=0.48\) in both configurations) compared to the mean-flow wake (Online Resource: Figs. ESM_6–8). Differences between the two geometries are more strongly reflected in the variances. The roof-level turbulence for tower \(\hbox {T}_{134}\) is enhanced over a wider lateral extent in the Core set-up, whereas below rooftop the variances show larger magnitudes in the isolated building case.
In the ADMS–Build wake model, similar to Eq. 1 but now at constant z, \(\Updelta U \propto e^{-y^2/x}\) (Eqs. 3, 7). Hence, \(\Updelta U \propto 1-y^2/x\) for \(y^2/x \ll 1\), whereas for large \(y^2/x\) the change in \(\Updelta U\) becomes slower and the profiles gradually converge back to the ambient flow. In between these limits, the lateral flow profiles exhibit a nearly linear portion (\(\Updelta U \propto y/x\)). Experimental and model results show very good agreement for the isolated building case (Fig. 10d) with respect to the overall magnitude of \(\Updelta U\) and the profile shape. Considering that the model does not reproduce the asymmetry of the wake caused by the oblique flow angle, the agreement between the wake widths is very good. While not capturing the magnitudes of W well for this configuration, the model shows the same small vertical gradients in the Tall case as in the experiment (Fig. 11d). In agreement with the vertical flow structure in the Core set-up (Fig. 5a), U is significantly overestimated at \(z/H_{134} = 0.48\), leading to a much smaller velocity deficit (Fig. 10c), while better predicted at roof-level. Similar conclusions can be drawn from the comparison of W (Fig. 11c), where the model underestimates the increase of downdrafts with increasing height, resulting in larger differences at \(z/H_{134}=1\) compared to 0.48.