The relation between turbulence and chemistry in a convective boundary layer is investigated in this work by means of direct numerical simulation. There are two common approaches to numerically simulate turbulent flows, namely large-eddy simulation (LES) and direct numerical simulation (DNS). The former applies a low-pass filter and models the subgrid-scale effect on the filtered variables. The later solves the original Navier–Stokes equations but often with a molecular viscosity that is larger than the value in the real application represented . Hence, both approaches are restricted to low-to-moderate Reynolds numbers. The Reynolds number is defined in terms of the subgrid-scale viscosity and numerical diffusivity in LES and in terms of the molecular viscosity in DNS. It can be interpreted as the scale separation between the largest and the smallest resolved scales (i.e. the Kolmogorov and Batchelor scales in DNS), which is in turn related to the number of grid points in the simulation and hence the computational resources needed for the simulation. Current computational resources allow the Reynolds numbers in simulations to reach the order of 103–104 (the range within which the Reynolds number of our simulations lies; see Appendix ), which are substantially smaller than the typical atmospheric values of 108. Fortunately, relevant turbulence statistics such as variances, covariances and entrainment rates tend towards Reynolds-number independence once the Reynolds number increases beyond 103–104 . When studying the properties of the smallest resolved scales and their substantial effect on large-scale dynamics, DNS eliminates the uncertainty introduced by subgrid-scale models and numerical artefacts, which complicates the interpretation and the comparison of results from different LES models . DNS provides results that depend only on the achievable Reynolds number in the simulation, and one can perform sensitivity analyses to estimate such dependence. The disadvantage of DNS is the higher computational cost, since DNS typically utilises higher-order numerical schemes and higher resolutions. Nonetheless, DNS is gaining traction as it approaches a degree of Reynolds number similarity that allows for certain extrapolation to atmospheric conditions .

In this work, we opt for DNS because we are studying the variance and covariances of various fields in which entrainment may play an important role. It is known that the smallest resolved scales might become important for these variables in typical resolutions . In addition, with strong emission fluxes, subgrid turbulent parameterisation in LES simulations may induce significant errors near the surface where the tracer is emitted . Therefore, here DNS provides an alternative for studying the topic and also a tool for an intercomparison study of the LES results. In Sect.  and , we will intercompare the results from our DNS model with the LES results by adopting the same initial conditions as in for some of our simulations.

We employed the direct numerical simulation tool Turbulence Laboratory (TLab) to perform our computational experiments of turbulent mixing of reactive species in the convective boundary layer. Source files with the implementation of TLab and further documentation can be found at https://github.com/turbulencia/tlab (last access: 13 January 2021). The dynamical part of the simulations performed in this work follows similar settings as in and . In the model, the Navier–Stokes equations of incompressible fluids in the Boussinesq approximation are solved to calculate the buoyancy and the velocity fields: ∇⋅u=0,∂u∂t+∇⋅(u⊗u)=-∇p+ν∇2u+bk,∂b∂t+∇⋅(ub)=κ∇2b, where u(x,t) is the velocity vector with components (u,v,w) in the directions x=(x,y,z) at time t, respectively. p is the modified pressure divided by the constant reference density, and b(x,t) is the buoyancy, expressed as b=g(θv-θv,0)/θv. The background buoyancy profile is set as b0(z)=N2z, where N2 is the Brunt–Väisälä frequency. The surface buoyancy flux is set to be Fb (see Appendix ). The parameters ν and κ are the kinematic viscosity and the molecular diffusivity, respectively. k is the unit vector in the z direction. The system is statistically homogeneous in the horizontal direction, such that its statistics depend on z and t only.

A no-penetration, no-slip boundary condition is imposed at the surface, and a no-penetration, free-slip boundary condition is imposed at the top boundary. Neumann boundary conditions are imposed for the buoyancy and velocity fields at both the top and the surface to maintain constant fluxes. The velocity and buoyancy fields are relaxed towards zero and N2z, respectively, at the top of the computational domain. The height of the top boundary is adjusted so that the turbulent region is far enough from the top to avoid significant interaction. Periodic boundary conditions are implemented in lateral directions.

The size of the computational grid is 720×720×512 for all simulations (the number of vertical layers is 512). Stretching is applied vertically to increase the resolution near the surface in order to resolve the surface layer and to stretch the grid size in the upper portion of the domain end to further separate the top boundary from the turbulent region. The total simulation domain size is 120L0×120L0×34.4L0, where L0 is the reference length scale. Together with the reference time and velocity timescales T0 and U0, L0 is used to non-dimensionalise the Navier–Stokes equations (see Appendix ). With typical atmospheric parameters of L0∼100 m and U0∼1 ms-1, the horizontal resolution of the model in use is equivalent to 15m×15m with a total domain size of 12km×12km. The resolution is considerably higher than those adopted in the previous LES studies, and it is fine enough to resolve convective turbulent motion in the convective boundary layer. In the vertical direction, the grid spacing increases from Δz=6.72m at the surface to Δz=266.28m at the top of the domain at 16 km. The vertical grid spacing vs. height in the first 5 km is shown in Fig.  (black line).

We use a sixth-order compact scheme to calculate the spatial derivatives and a fourth-order Runge–Kutta scheme to advance the equations in time. The pressure Poisson equation is solved by applying a Fourier decomposition along the horizontal directions and solving the resultant set of finite-difference equations in the vertical direction to machine accuracy . The sensitivity to grid resolution has been tested up to the triple-velocity correlation in the transport term of the evolution equation for the turbulence kinetic energy, observing an error of less than 5 % at the surface when doubling the spatial resolution. Further details of the numerical algorithm and the grid-sensitivity studies can be found in , , and .

The simulations are terminated after a total simulation time equivalent to 4.5 h, during which the boundary layer grows convectively. The simulation time represents the hours from sunrise to midday, when the boundary layer is well developed and statistical equilibrium is attained. The boundary layer height zi is identified as the height where the buoyancy variance [b′b′] is maximum away from the surface layer . At the end of our simulations, the boundary layer height is around 2.2 km. As the boundary layer grows in depth, the corresponding convective velocity and timescales evolve in time. In this study, the convective timescale is adopted as the turbulent timescale tturb, which is related to the convective velocity wc by 1tturb=ziwc=zi23Fb . This turbulent timescale will be used to calculate the Damköhler number Da in later sections.

Two numbers are mainly employed to quantify the effect of turbulent mixing on chemical reaction, namely the Damköhler number Da and the effective chemical reaction rate keff. The first number, the Damköhler number (Da), is defined as the ratio between the turbulent timescale (tturb) and the chemical timescales (tchem) . For a second-order chemical reaction A+B→C, the Damköhler number of tracer A is given by 3DaA=tturbtchem,A=zi/wc1/k〈B〉=k〈B〉zi2Fb13. Similarly the Damköhler number of tracer B can be written as 4DaB=k〈A〉zi2Fb13. The Damköhler numbers of tracers A and B at the start (DaA,i and DaB,i) and at the end (DaA,f and DaB,f) of each of our simulations are listed in Table . For a slow chemical reaction of two initially segregated reactants with the respective Da≪1, the chemical lifetime of the reactants is long enough for turbulence to mix them in the boundary layer at a rate fast enough that they are homogeneously distributed in a confined volume (e.g. a model grid) in a short time compared to the chemical lifetime. In that case chemical reaction can occur everywhere in that confined volume and the corresponding volumetric-mean production rate of tracer C can be approximated as the product of k and the volumetric means of the reactants (k〈A〉〈B〉). On the other hand, for fast reactions with the respective Da>1, the reactants are not well mixed by turbulence during the theoretical chemical lifetime of the reactants, such that they can react only in a fraction of the confined volume where turbulent motion brings the two species together. In that case the volumetric-mean of the production rate of tracer C also depends on the turbulent timescale and would be overestimated by k〈A〉〈B〉. Hence, the Damköhler number can indicate whether the effect of turbulent mixing on a chemical reaction is significant in the flow. For instance, the eddy turnover timescale for large-scale eddies in a CBL is typically 102–103 s, to which the chemical lifetime of NOX and O3 in the boundary layer is comparable (102–105). Therefore, the turbulent motions in the CBL potentially affect any chemical reaction occurring at a rate higher than that between NO and O3.

To quantify the chemistry–turbulence interaction at the molecular diffusion spatio-temporal scale, the Kolmogorov Damköhler numbers are also calculated in some of simulations. The definition of Kolmogorov Damköhler number is adopted from , i.e. Dak,A=tktchem,A for tracer A and similarly for tracer B (Dak,B) by replacing the denominator with tchem,B. The Kolmogorov timescale tk is around 10 s for all the simulations .

The second number, the effective chemical reaction rate (keff), can quantitatively measure the actual chemical reaction rate averaged in a confined volume under the consideration of chemical segregation due to inefficient turbulent mixing , and it can be written as 5keff=1+〈A′B′〉〈A〉〈B〉k, where the angle-bracketed and primed terms are the means and the deviations from the means, respectively, of the Reynolds-decomposed concentrations.

The error induced by neglecting such chemical segregation in a complete-mixing model, in which both tracers A and B are assumed to be evenly distributed throughout the boundary layer, can be written as 6E=1-keffk=-IS, where the segregation coefficient 7IS=〈A′B′〉〈A〉〈B〉 represents the state of mixing of tracers A and B in the boundary layer (e.g. ). If tracers A and B are completely mixed, then IS=0. If tracers A and B are completely segregated, then IS=-1. If tracers A and B are emitted simultaneously and at the same location so that their concentrations are correlated, then IS>1. With the DNS model fully resolving the chemical segregation in the boundary layer, the error from a complete-mixing or coarse-grid model can be calculated by 8E=keff, cm-keff, DNS, where keff, cm is the calculated boundary-layer-averaged effective chemical reaction rate in a complete-mixing or coarse-grid model, and keff, DNS is the calculated value in the corresponding DNS model.

When one considers a confined volume within a horizontal layer at a specific height z, the corresponding effective chemical reaction rate also varies with height. The height-dependent effective chemical reaction rate can be written as a function of z: 9keff(z)=1+A′B′ABk=(1+IS(z))k. The square-bracketed terms denote the horizontal means of the quantities. The corresponding height-dependent error induced by neglecting chemical segregation by a model that assumes tracers A and B are well-mixed horizontally within a horizontal layer at z is then 10[E](z)=1-keff(z)k=-IS(z), where the height-dependent segregation coefficient is 11IS(z)=A′B′AB.

With the emissions of tracers A and B heterogeneously distributed on the surface, the segregation is maximum at the surface with its magnitude decreasing with increasing altitude, as seen from the vertical profiles of the horizontally averaged segregation coefficient ([IS](z)) in Fig. . It is because under this setting mixing is most difficult near the surface where the tracers are emitted separately. This description of the profiles agrees with the results of the simulations with heterogeneous emissions presented in and , despite that they implemented a different emission configuration with a Gaussian function imposed on the surface emission flux. To examine how the segregation between tracers A and B changes with the emission flux and the imposed chemical reaction rate, the results of the set of simulations with the length of heterogeneity (dx) of 2 km (all plotted in red) are first compared. In the slow-2 km-VV05 run (dashed red line), the magnitude of [IS] decreases with increasing altitude in the boundary layer, so at a height above 0.8zi, [IS] becomes larger than zero, meaning that tracers A and B are not only well mixed but also that their flows are correlated. This results in [keff]>k, where the assumption of complete mixing in the model grid will underestimate the reaction rate. This phenomenon is also reported in , showing [IS]>0 at higher altitudes in their LES simulations with heterogeneous isoprene emission fluxes. On the other hand, as the surface emission flux increases to 0.5 ppbms-1 in the slow-2 km-sflux run (red solid line), [IS]>0 only at the height above 0.98zi.

When shifting from slow to fast chemistry (dotted red line), the magnitude of the segregation further increases, resulting in a boundary-layer-averaged value of -0.95. The segregation at the top of the boundary layer remains high, with [IS]=-0.8. Sometimes the segregation caused by an increase in imposed reaction rate k can reduce keff so much that merely increasing k can no longer increase the production of tracer C. This happens between the two 6 km-sflux runs (check Table  for their resultant keff). When shifting from slow chemistry to fast chemistry, keff drops 9.18 times, such that it in turn cancels the effect of the 10 times increase in k. This results in similar amounts of tracer C produced in the two 6 km-sflux runs, with the mixing ratio of tracer C equal to 1.58 and 1.60 ppm at the end of the simulations for the slow- and fast-chemistry cases, respectively.

To discuss the effect of the length of heterogeneity (dx) on segregation, the three solid lines in the left panel of Fig. , which indicate the slow-sflux runs at different dx (dx=1 km plotted in blue, dx=2 km in red and dx=6 km in green), are compared. In general, the segregation increases with increasing dx. This agrees with the conclusion from . For the cases with dx=1 km and dx=2 km, one can still observe a decrease in the magnitude of the segregation with increasing altitude, with the corresponding boundary-layer-averaged IS equal to -0.49 and -0.69, respectively. However, for dx=6 km, the segregation remains almost constant throughout the mixed layer and starts to decrease only below the top of the boundary layer. This also results in a very large segregation throughout the boundary layer, with the boundary-layer-averaged IS equal to -0.97. This shows a similar phenomenon, as described in , that as the length of heterogeneity exceeds a few boundary layer heights,

Converting the conclusions of to our denotation, the separation of the boundary layer above the different emission patches occurs when dx>8zi.

Similar to the cases with homogeneous emissions, the increased segregation with increasing surface emission flux and imposed chemical reaction rate can be indicated by the relatively large values of the final Damköhler numbers. Since the boundary-layer-averaged Damköhler numbers of tracers A and B are statistically the same in the simulations with heterogeneous emissions, here we take the mean of the two numbers to get the averaged final Damköhler number Daf (equal to 1/2(DaA,f+DaB,f)). We then fit Daf with the normalised boundary-layer-averaged keff/k for the simulations with each dx (check Table  for the values). The results are plotted in Fig. . In general, log⁡(keff/k) follows a square law with log⁡(Daf), i.e. log⁡(keff/k)=-afit(log⁡Daf+1)2, where afit is the fitting coefficient varying with dx. Or in another way, keff/k follows a Gaussian function of Daf, i.e. keff/k=exp⁡(-afit(log⁡Daf+1)2). The x intercept is chosen to be -1 because keff≈k when Daf≲0.1 (or log⁡Daf∼-1). As dx increases, afit also increases (see the values in Fig. ). However, their relation is unlikely to be linear.

We take a closer look at the results of the simulations with homogeneous emissions as described in Sect. . Figure  shows the model errors from the complete-mixing model (black circles) and the four coarse-grid models (+ and × marks) against the corresponding final Damköhler number of the limiting reactant (Dalim; see the values in Table ). One can see that in all runs the errors from all coarse-grid models are reduced in comparison to the complete-mixing model. The model errors from the coarse-grid models are largely reduced when Dalim>10, which corresponds to the simulations with urban surface emission fluxes (mflux, sflux and ssflux). In those runs, the model errors drop from 77 %–98 % in the complete-mixing model to 36 %–69 % in the 32-level models and further to 15 %–51 % in the 64-level models. However, this also means that even with the highest resolution the model errors are still noticeably significant. Also, for five out of seven runs (the slow-VV05 run is excluded here due to the insignificant errors), a larger reduction of the model error is observed with an increased vertical resolution (from blue + to blue ×) than with an increased horizontal resolution (from blue + to red +). The reason behind this is that tracers A and B are segregated along the vertical direction.

Figure  shows the vertical profiles of the horizontally averaged error ([E](z); see Eq. ) of the four coarse-grid models for the slow-mflux and slow-sflux runs. All coarse-grid models fail to show the local minimum at the top of the surface layer, as the surface layer is too thin for these models to resolve. They also show a less prominent minimum at the top of the boundary layer. The distinct underestimation of [E] in the surface layer and entrainment zone indicates that high vertical resolution is especially important to resolve the chemical segregation around these two zones.

The errors from the four coarse-grid models (E) in the simulations with heterogeneous emissions are then plotted against the errors from the corresponding complete-mixing model (Ecm) in Fig. . These data points are categorised with different lengths of heterogeneity (dx) implemented in the corresponding simulations. The dashed line indicates the value where E=Ecm. The points below the dashed line show the cases for which the corresponding coarse-grid model improves from the complete-mixing model, while those above the dashed line show a deterioration. Contrary to the simulations with homogeneous emissions the coarse-grid models do not always perform better than the complete-mixing model, especially when the horizontal model grid size is larger than the length of heterogeneity. It is because under this condition, the model grid fails to resolve the heterogeneity of the emission sources. This also applies to the simulations with dx=1 km in the 1 km resolution coarse-grid models, as the model grids are slightly offset from the emission patches. In these runs, the coarse-grid models mix the originally segregated tracers in the lower layers at a higher concentration than the complete-mixing model, in which the latter artificially mixes the tracers all over the whole boundary layer and dilutes the tracer concentrations. That is why the coarse-grid models give larger overestimations. The model with the higher vertical resolution overestimates the reaction rate even more, as its first layers are thinner and hence contain even higher concentrations of the artificially mixed tracers in the lower-level grids.

For the simulations with dx=6 km, the coarse-grid models always perform better than the complete-mixing model. In these simulations, the horizontal grids in the coarse-grid models can always resolve the emission heterogeneity. Note that the reduction of the errors from the coarse-grid models is larger for the increased horizontal than vertical resolution, as tracers A and B are now segregated in the horizontal direction.

Although the DNS runs in this work are only conducted in idealised conditions, they can provide insights into and estimations of the errors induced by neglecting the subgrid chemical segregation due to inefficient turbulent mixing in larger-scale models. The simulations with homogeneous emissions (Sect. ) show significant errors in the low-resolution model under strong emission flux conditions, which are indicated by a large (>1) Damköhler number of the limiting reactant (Dalim). This suggests that Dalim>1 can be taken as a condition in the model under which the chemical calculation should be corrected by taking the subgrid chemical segregation into account. One way to implement such correction is to substitute the imposed chemical reaction rate k by the effective rate keff which, as shown in Fig. , can be expressed as a function of Dalim. The results from the simulations with heterogeneous emissions (Fig. ) suggest that keff additionally depends on the length of heterogeneity (dx). When considering increasing model resolution to reduce the errors induced by neglecting subgrid chemical segregation, we learn from Sect.  that whether it is more effective to increase the horizontal or vertical resolution depends on the direction of the initial segregation of the reactant sources. High resolution is in particular necessary around the surface layer and entrainment zone. When the reactant sources are horizontally segregated, it is essential that the horizontal resolution of the model is fine enough to resolve the emission heterogeneity. Otherwise, increasing the vertical resolution can induce even larger model errors.

There are additional points to note in our estimations. When arriving at our conclusion of the dependency of keff on Dalim, we increase Dalim by shortening the corresponding chemical timescale with increased imposed k and emission fluxes. One should not neglect the dependency of Dalim on the buoyancy fluxes, which determine the turbulent timescale. However, we expect to see a similar keff dependency on Dalim when one repeats the simulations with increasing buoyancy fluxes instead.

By increasing the emission fluxes to urban values in Sect. , it is shown that the effective chemical reaction rate can be much smaller than the values reported in previous studies under rural conditions (e.g. ). However, it should be also noted that the chemical segregation is particularly large in these simulations, because one of the reactants (in this case tracer B) is depleting. Despite the large deviation of keff from k, the production term kAB is anyway small due to the low concentration of tracer B. Therefore, the actual effect on the calculated concentration of tracer B may not be as large as one may expect from the overestimation of keff. A similar reasoning also applies to tracer A. When the emission flux of tracer A is large, the main process affecting the concentration of tracer A is emission instead of chemistry. However, the effect of chemical segregation on the concentrations of the product tracer C is still worth noticing.

Unlike other studies (e.g. ) in which multiple-reaction chemical systems are employed, our work mostly focuses on an idealised second-order chemical reaction of two non-specific reactive species. This approach allows us to interpret our work for any second-order chemical reactions. For a chemical species involved in a multiple-reaction chemical system, like O3, one can still calculate the net impact of chemical segregation by considering the errors of all reactions in which the species is involved. However, it is also important to notice that the net impact of chemical segregation on such a species would in general be reduced with the increasing complexity of the chemical system, because cycling reactions tend to lengthen the chemical timescale and reduce the corresponding Damköhler number and hence reduce the chemical segregation. For example, with emission fluxes of NOX comparable to our sflux and ssflux cases, the segregation coefficient between isoprene and OH is only -0.05 and -0.17 in the high-NOX and very-high-NOX cases of , respectively. also performed simulations similar to this study with the NO-NO2-O3 triad, and they found less significant errors than with the A–B–C chemical system. Also, this error does not increase with Dalim when Dalim reached the order of 10, contrary to the increasing trend observed in the A–B–C chemical system. Therefore, we expect the magnitude of chemical segregation to be smaller than the values reported in this study when a multiple-reaction chemical system is included. Future studies can also consider implementing a backward reaction in addition to the idealised second-order chemical reaction to approximate the effect of a multiple-reaction chemical system.

The work in Sect.  gives an estimation of the error in a regional chemical-transport model when neglecting subgrid chemical segregation, where the model possesses relatively high horizontal and vertical resolution. The method we employed is to average the concentration fields within the volume of each model grid. Current regional chemical-transport models often include additional measures to prevent accumulation of reactants close to the emission sources, such as distributing the emitted species in the first few vertical layers (e.g. ) and employing boundary layer schemes to parameterise eddy transport in the lower troposphere (e.g. ). These measures may diminish the excessive overestimation in the coarse-grid models reported in Sect.  in cases in which the model fails to resolve emission heterogeneity. However, these measures may introduce additional artificial mixing in other cases. Also, there is an inherited difference in modelling framework that makes the comparison between regional chemical-transport models and turbulence-resolving models like DNS and LES difficult. The deficiency of regional models to only parameterise the vertical mixing in the boundary layer causes its inaccuracy in representing the boundary layer dynamics. For instance, by comparing the model results from WRF-Chem and from the NCAR LES model, reported a weaker vertical mixing in the WRF-Chem simulations than in the LES simulations, causing the upward transports of surface-emitted chemicals and hence the chemical production of OH and O3 to be undermined aloft in the mixed layer. Our averaging method employed in the coarse-grid models may not be able to account for these undermined upward transports in regional chemical-transport models. Nevertheless, our estimation shows that the model resolution clearly plays an important role in resolving chemical segregation and providing accurate chemical calculations in the models.

One important aim of the study of chemistry–turbulence interaction is to provide a correction to the error in large-scale models induced by neglecting subgrid chemical segregation. While our work suggests a correction of keff with dependencies on Dalim and dx, other works suggest that such correction should also include other variables such as updraught and/or downdraught fluxes , variance of the reacting species, entrainment and/or emission fluxes , turbulent fluxes , variance of the emission , magnitude and direction of mean horizontal wind , and distance from the sources . The correction to the vertical exchange coefficient (i.e. the ratio between the turbulent flux and the mean gradient) can also serve as an alternative way to address the change in the transport terms from the effect of chemical reactions . There have been attempts to implement a parameterisation of subgrid chemistry–turbulence interaction to large-scale models. For example, suggested the use of lookup tables to indicate how chemical reaction rates should be corrected under different physical or chemical scenarios. developed a one-dimensional second-order closure model to account for the vertical turbulent mixing of chemical species ready to be incorporated into large-scale models. Given that the effect of subgrid chemical segregation is non-negligible under urban conditions, modellers should consider applying similar parameterisations in areas with intense emission and large source heterogeneity.

Due to computational limitations of the DNS runs, some other conditions that may be important for turbulent mixing in the urban boundary layer were neglected in our work. First of all, the growth of the boundary layer is driven by a constant buoyancy flux, so the boundary layer height gradually increases. Hence, the simulation can only approximate the time when the boundary layer grows from sunrise to mid-afternoon. This also raises the issue of the time required for statistical equilibrium to be attained. In some cases, this time may be longer than the duration of daylight, after which the atmosphere is no longer convective. This poses a greater problem to cases with strong emission fluxes, as the time required to attain statistical equilibrium is even longer. It may not be practical to run longer than the duration of daylight even though statistical equilibrium is not reached. Second, our simulations only address a convective boundary layer under clear-sky conditions. We do not take other scenarios with different weather conditions (such as cloud-top boundary layer, e.g. ) or when the atmosphere is stably stratified (typical for nighttime, e.g. ) into account. For instance, the perturbation in radiation with the existence of clouds closely couples to the turbulent effect and also modifies chemical reactions . Third, it may be useful to consider other boundary conditions of the entrained tracers, such as varied entrainment fluxes (e.g. ) and varied concentrations in the free troposphere due to long-range transport (e.g. ). Fourth, our simulations also do not include any mean horizontal winds (e.g. ) or forcings from the surface other than the constant buoyancy flux, such as varied surface heat fluxes (e.g. ) and surface roughness.

An important source of surface forcings in an urban boundary layer is undoubtedly from the urban structures (buildings and streets in the urban canopy). The structure of turbulent flow can be significantly altered in the street canyons due to the perturbation in radiation and the exchange of heat and momentum with the urban structures (e.g. ). These urban canopy meteorological forcings also affect vertical turbulent transport and hence the vertical distribution of chemical species . Therefore, our DNS runs are more suitable for addressing the vertical mixing caused by the turbulent motions in the mixed layer relatively far away from the surface features that may induce other additional forcings. But in the mixed layer, the urban canopy still potentially affects the chemistry and dynamics in the boundary layer by means of surface roughness and emission heterogeneity. While in this work we have addressed the effect of emission heterogeneity, the effect of surface roughness and other configurations of emission patterns (e.g. ) can be further studied in the future. Previous work on natural canopies can also be combined into further studies with urban canopies, as the vegetation is mixed within the urban canopies in many cities.