Lagrangian dynamics of contaminant particles released from a point source in New York City

Abstract

In this study, we investigated the transport of contaminants in the southern tip of Manhattan, New York City, under prevailing wind conditions. We considered a hypothetical contaminant particle release on the East side of the New York Stock Exchange at 50 m above the ground level. The transport of individual particles due to the wind flow in the city was simulated by coupling large-eddy simulations (Eulerian) with a Lagrangian model. The simulation results of our coupled Eulerian and Lagrangian approach showed that immediately after the contaminant particles are released, they propagate downwind and expand in the spanwise direction by ∼0.5 km. Specifically, approximately 15 min after the release, the contaminant particles reach the end of the 2.5-km-long study area with a mean velocity of 1.8 m/s, which is approximately 50% of the dominant wind velocity. With the cessation of the particle release, the contaminant particles start to recede from the urban area, mainly owing to their outflux from the study area and the settling of some particles on solid surfaces in the metropolitan area. More specifically, the study area becomes clear of particles in approximately 48.5 min. It was observed that some particles propagate with a mean velocity of 0.6 m/s, i.e., ∼17% of the dominant wind velocity. We also conducted a detailed investigation of the nature of particle transport patterns using finite-time Lyapunov exponents, which showed that dynamically rich Lagrangian coherent structures are formed around the buildings and off the tops of the skyscrapers.

I. INTRODUCTION

On January 6, 2005, at 2:30 am, a train was delivering 90 tons of liquified chlorine gas to Avondale Mill in Graniteville, South Carolina. A switch connecting the spur of the train to the main rail line had mistakenly remained connected when another train traveling at 47 mph was diverted onto it. The resulting collision ruptured the tank car, causing a spill of 60 tons of chlorine, which rapidly vaporized. Chlorine, which is denser than air, formed a cloud that spread West and Southwest, filling shallow valleys, and was finally transported out of the area by a prevailing South–Southwest wind after more than 3 h. A total of nine human fatalities, 71 hospitalizations, and several hundreds of animal and fish deaths were reported.^1,2 Such events (also see Refs. 3–6) show that biological, radioactive, and poisonous chemical contaminants are dangerous when released in urban areas. The prediction of airborne contaminant transport and its effects on public safety and welfare downstream of the release could help agencies plan emergency responses.

Computational fluid dynamics has been extensively used to predict containment trajectories and concentrations over wide areas and under various wind conditions. For example, Oaks et al.⁷ employed an Eulerian–Eulerian (EE) numerical approach to study contaminant transport in New York City (NYC). Huang et al.⁸ used an Eulerian–Lagrangian (EL) atmospheric dispersion model with Reynold's averaged Navier–Stokes turbulence model to investigate contaminant transport around a laboratory-scale model of a single building. Haghighifard⁹ employed a similar numerical model to study the dispersion and deposition of spherical dust particles on the ground around two small-scale inline buildings. The main results showed that the front of the foremost windward building had a much higher particle deposition than the second building.⁹ Chang et al.¹⁰ used a building layout of approximately 20 buildings with square box shapes in open and staggered arrangements. Accordingly, they studied the transport of PM₁₀, PM_2.5, and PM₁ particles (n in PM_n is the average particle size in micrometers) to investigate different transport mechanisms. On a relatively larger scale, Hassan et al.¹¹ used an EL-based approach to conduct a numerical experiment to determine favorable air pollution concentrations in a city block of buildings by changing its morphology. Using several different wind velocities, directions, and morphologies, they showed that the morphology significantly affects pollutant concentrations; thus, the morphology can be designed such that contaminant concentrations are reduced.¹¹

A similar study using a Lagrangian approach showed that building morphology can strongly affect pollutant transport.¹² In a seminal study, Hanna et al.¹³ studied the wind flow in central Manhattan by combining experimental observations and five computer simulations and evaluated the performances of computation dynamics software at that time. Although the main emphasis of the study was not particle tracking, the authors obtained some tracer results, which agreed with the data measured within a couple of blocks of the containment release.¹³ Studies on source inversion particle tracking frequently utilize a numerical method to find the release points of contaminants from downwind concentration measurements.^14,15 Inverse tracking starts at the concentration measurement time and calculates the tracks of particles back to the source in reverse time. It requires information on the flow field from the particle source release time until the concentration measurement time and the locations of the measured particles. Chow et al.¹⁴ used Bayesian inference combined with the Markov chain Monte Carlo sampling procedure and the source inversion method. A statistical approach can be used in the case of uncertainty in the observed data and/or insufficient data quantity or quality. Using this procedure, they estimated the source location within 70 m.¹⁵ Sargent et al.¹⁶ conducted a mesoscale study in Boston and measured the CO₂ levels in the city to determine the sources of CO₂ release and reduce emissions. The study relied on observational data with uncertainty in the wind flow; thus, finding trends of source locations was difficult. However, the authors argued that the use of measurements over long time scales and accurate atmospheric transport models could help achieve quantifiably consistent results.¹⁶

In this paper, we investigated the dispersion of contaminant particles in lower Manhattan, NYC, using a coupled EL model under the local prevailing wind conditions. The mean flow velocity (3.58 m/s) and its direction were selected by analyzing the recorded wind rose of NYC.⁷ The background turbulent wind flow was obtained using the Eulerian large-eddy simulation (LES) method,⁷ whereas the released contaminant particles were tracked using a Lagrangian module that solves the momentum equation of individual particles.¹⁷ The study area in NYC was densely populated with buildings of various heights, including skyscrapers, which have a significant effect on the velocity fields and the transport processes. The study area, located in lower Manhattan, was 2.5 km long (from North to South), 1.8 km wide (from East to West), and 600 m high. The buildings and the ground were modeled using the sharp-interface immersed boundary (IB) method⁷ and discretized using an unstructured triangular grid. The background computational grid system on which the wind flow was resolved consisted of over 76.5 × 10⁶ grid nodes. The mean flow velocity (3.58 m/s) and its direction were selected by analyzing the recorded wind rose of NYC.⁷ Particles were released at random locations within a 24-m sphere 50 m above the ground, and they eventually resembled a biochemical cloud located on the East side of the New York Stock Exchange. The objective of the study was to gain insights into the mechanisms contributing to the dispersion of contaminant particles in NYC under prevailing wind conditions. The simulation results allowed (1) quantifying the time required by the contaminants to reach the end of the study area and the mean propagation speed of the contaminants through the highly populated urban area, (2) determining the shape and geometry of the contaminant plume dispersing through the study area, (3) detecting areas of high contaminant concentrations within the urban area, and (4) quantifying the resident time of the contaminant particles after their release was stopped and as they gradually advected out of the study area.

Additionally, to understand the complex turbulence patterns generated by the wind flow in NYC, Lagrangian coherent structures (LCSs) raised in the urban area were calculated using finite-time Lyapunov exponents (FTLEs). The FTLE analysis was conducted to characterize the turbulence using calculated particle trajectories and to find the LCSs that form in building wakes, street-canyon channels, and vertical advection along building surfaces. An LCS describes the turbulence in attacking and repelling manifolds and provides insight into turbulent properties.^18–26 Similar LCS diagnostics using the FTLE field have been conducted to gain insight into complex fluid motions and material transport in various geophysical^27–29 and aerospace flows.¹⁹ However, to the best of our knowledge, this study is the first to apply such LCS diagnostics to turbulence within large, high-density city areas with buildings of various heights, including skyscrapers. Plots of FTLE scalar contours over two-dimensional (2D) planes within the study area revealed intricate attracting ridges that mark LCSs and material boundaries close to the skyscrapers. Overall, the innovation of this study was the use of coupled EL and FTLEs to study contaminant transport and turbulence of the wind flow field in a microscale model of a highly populated urban environment.

The remainder of this paper is organized as follows. Section II presents the governing equations of the numerical models, and Sec. III presents a model validation study. In Sec. IV, computational details of the simulations are discussed. Subsequently, the simulation results are presented in Sec. V. Finally, we conclude the findings of this study in Sec. VI.

II. GOVERNING EQUATIONS

A. Equations of fluid motion

We solved spatially filtered incompressible forms of the continuity and Navier–Stokes equations in a nonorthogonal, generalized, curvilinear coordinate form over a structured grid system, referred to as the background mesh, to obtain the wind flow field. Using generalized curvilinear coordinates { ${\xi }^j$} and a compact tensor notation, we can rewrite these equations as follows:⁴¹

$$J\frac{\partial U^j}{\partial {\xi }^j}=0,$$ (1)

$$\frac{1}{J}\frac{\partial U^i}{\partial t}=\frac{{\xi }_l^i}{J}\left[-\frac{\partial \left(U^j{u}_l\right)}{\partial {\xi }^j}+\frac{1}{\rho }\frac{\partial }{\partial {\xi }^j}\left(\mu \frac{g^{jk}}{J}\frac{\partial u_l}{\partial {\xi }^k}\right)-\frac{1}{\rho }\frac{\partial }{\partial {\xi }^j}\left(\frac{{\xi }_l^{j}p}{J}\right)-\frac{1}{\rho }\frac{\partial {\tau }_{lj}}{\partial {\xi }^j}\right],$$ (2)

where repeated free and dummy indices take the values from 1 to 3, $u_i$ is the filtered ith Cartesian velocity component, $U^i=\left({\xi }_m^i/J\right)u_m$ is the filtered contravariant volume flux, J is the Jacobian of the geometric transformation $[J=|\partial \left({\xi }^1,{\xi }^2,{\xi }^3\right)/\partial \left(x_1,x_2,x_3\right)\left|\right]$, $\rho$ is the air density, $\mu$ is the dynamic viscosity of the fluid, ${\xi }_l^i$ represents the transformation metrics, $g^{jk}={\xi }_l^j{\xi }_l^k$ is the contravariant metric tensor, $p$ is the pressure, and ${\tau }_{lj}$ is the subgrid stress tensor from the LES model.³⁰ The unresolved turbulence was modeled with the dynamic Smagorinsky subgrid-scale model as follows:³¹

$${\tau }_{ij}-\frac{1}{3}{\tau }_{kk}{\delta }_{ij}=-2{\mu }_t\overline{S_{ij}},$$ (3)

where ${\delta }_{ij}$ is the Kronecker delta, ${\mu }_t=C_s{\Delta }^2\left|\overline{S}\right|$ is the dynamic eddy viscosity, $\overline{S_{ij}}=1/2\left(\partial u_i/\partial x_j+\partial u_j/\partial x_i\right)$ is the filtered strain rate tensor, $C_s$ is the Smagorinsky constant, $\Delta =J^{-1/3}$ is the box filter size, and $|\overline{S}|={\left(2\overline{S_{ij}}\overline{S_{ij}}\right)}^{1/2}$.³⁰

The continuity and momentum equations were solved on the structured background mesh on which the governing equations were discretized in space. A hybrid staggered/nonstaggered arrangement was used in which variables were stored in the cell center, whereas mass fluxes were stored on the faces.^32,33 A second-order accurate central differencing scheme was used to discretize the convective terms. In contrast, the divergence, pressure gradient, and viscous-like terms were discretized using a second-order accurate, three-point central differencing.³² Additionally, a second-order backward-differencing scheme was used to discretize the time derivatives.³⁴ A second-order accurate fraction-step method was used to incorporate a pressure solution into the procedure for solving the momentum equations. The Jacobian-free Newton–Krylov solver was employed to solve the momentum equations. The generalized minimal residual solver was used to solve the Poisson pressure equation using a multigrid method as a preconditioner.

It should be noted that the geometries of the buildings and other cityscape features were dealt with using the IB method. The geometries were discretized using unstructured triangulated surfaces in space and immersed within the structured background mesh. The governing equations were solved on the background mesh, whereas the velocity fields at the nodes adjacent to the solid surfaces of the immersed bodies were reconstructed using a wall model.^35,36 The computational nodes of the background mesh located inside the immersed bodies of the buildings and other solid objects were blanked out of the computations.

B. Lagrangian particle tracking equations

We coupled a particle tracking framework to the Eulerian LES model to calculate the transport of individual contaminant particles within the Eulerian velocity field.¹⁷ The particle tracking module calculates the trajectories of the contaminant particles by solving the following equations for each particle:^36–38

$$\frac{d{\mathit{x}}_{\mathit{p}}}{dt}={\mathit{u}}_{\mathit{p}},$$ (4)

$$m_p\frac{d{\mathit{u}}_{\mathit{p}}}{dt}={\mathit{f}}_{\mathit{g}}+{\mathit{f}}_{\mathit{D}}+{{\mathit{f}}_{\mathit{L}}+\mathit{f}}_{\mathit{AM}}+{\mathit{f}}_{\mathit{S}}{+\mathit{f}}_{\mathit{P}},$$ (5)

where ${\mathit{x}}_{\mathit{p}}$ and ${\mathit{u}}_{\mathit{p}}$ are the position and velocity of a particle, respectively, $m_p$ is the mass of the particle, ${\mathit{f}}_{\mathit{g}}$ is the gravitation force, ${\mathit{f}}_{\mathit{D}}$ is the drag force, ${\mathit{f}}_{\mathit{L}}$ is the lift force, ${\hspace{0.17em}\mathit{f}}_{\mathit{AM}}$ is the added mass, ${\mathit{f}}_{\mathit{S}}$ is the collision forces from solid boundaries on the particle, and ${\mathit{f}}_{\mathit{P}}$ is the force due to fluid stresses. The forces are computed as follows:³⁸

$${\mathit{f}}_{\mathit{g}}=\left(\hspace{0.17em}\frac{{\rho }_p-{\rho }_0}{{\rho }_p}\right)m_p\mathit{g},$$ (6)

$${\mathit{f}}_{\mathit{D}}=-\frac{1}{2}{\rho }_0{C}_d\frac{\pi D_p^2}{4}‖{\mathit{u}}_{\mathit{pf}}‖{\mathit{u}}_{\mathit{pf}},$$ (7)

$${\mathit{f}}_{\mathit{L}}={\rho }_0{C}_l\frac{\pi D_p^3}{6}\left({\mathit{u}}_{\mathit{pf}}\times \mathit{\omega }\right),$$ (8)

$${\mathit{f}}_{\mathit{AM}}={\rho }_0{C}_{AM}\frac{\pi D_p^3}{6}\left(\frac{D{\mathit{u}}_{\mathit{f}}}{Dt}-\frac{d{\mathit{u}}_{\mathit{p}}}{dt}\right),$$ (9)

$${{\mathit{f}}_{\mathit{P}}=\rho }_0\frac{\pi D_p^3}{6}\left(\nabla p+\mu {\nabla }^2{\mathit{u}}_{\mathit{f}}\right),$$ (10)

where ${\mathit{\rho }}_0$ is the air density, ${\mathit{\rho }}_{\mathit{p}}$ is the particle density, ${\mathit{m}}_{\mathit{p}}$ is the particle mass, $\mathit{g}$ is the acceleration of gravity, ${\mathit{C}}_{\mathit{d}}$ is the drag coefficient, ${\mathit{D}}_{\mathit{p}}$ is the particle diameter, ${\mathit{u}}_{\mathit{f}}$ is the fluid velocity, ${\mathit{u}}_{\mathit{p}}$ is the particle velocity, ${\mathit{u}}_{\mathit{pf}}$ is the particle velocity relative to the fluid velocity ( ${\mathit{u}}_{\mathit{f}}-{\mathit{u}}_{\mathit{p}})$, ${\mathit{C}}_{\mathit{l}}$ is the empirically obtained lift coefficient, $\times$ is the cross product, $\mathit{\omega }$ is the vorticity vector ( $\mathbf{\nabla }\times {\mathit{u}}_{\mathit{f}}$), ${\mathit{C}}_{\mathit{AM}}$ is the coefficient of the added mass, $\mathit{D}/\mathit{Dt}$ is the total time derivative, $\mathit{p}$ is the fluid pressure, and $\mathit{\mu }$ is the dynamic viscosity of the fluid. Given the number of particles released, particle–particle and particle–solid interactions are unlikely to occur in large numbers; thus, they were not addressed. The lift force was also omitted because the particle size [O(10⁻⁵)] is much smaller than the grid resolution [O(10°)]. Additionally, because of the small size of the contaminant particles, the drag coefficient was inversely proportional to the Reynolds number, and the added mass and the fluid stress-induced forces could be safely neglected as they were insignificant.⁵¹ Thus, in this study, we considered a simplified version of Eq. (5) that includes only the dominant forces of drag and gravity, i.e., the first two terms on the right-hand side of this equation.

C. Finite-time Lyapunov exponents

The use of LCS diagnostics obtained from the FTLE field for detecting regions of flow with similar properties was introduced by Pierrehumbert and Yang.^39–42 The calculation of FTLEs and the supporting mathematical theory were established by Haller,^{18,24,43–45} with significant contributions from Shadden et al.²² and Haller⁴⁵ showed that LCSs can be determined from approximate velocity data. The author proved that FTLE reliably predict LCSs, even when using velocity fields with large errors.⁴⁵ LCS diagnostics can detect dynamically rich Lagrangian structures of turbulent flows,^18–20 elucidate transport mechanisms,^21,46 and categorize flow fields into regions with different dispersion rates.²² It is generally seen as superior to Eulerian turbulence measures such as the Q-, Δ-, and ${\hspace{0.17em}\lambda }_2$-criteria because they only use the information from one time step and are not objective,⁴⁶ i.e., the material response is dependent on the observer.²³ Furthermore, Eulerian turbulence measures are substantially different from LCSs in unsteady flows.²⁷ Lyapunov exponent-based methods, in which small tracer parcels are tracked over space and multiple timesteps, provide a measure of the rate of stretching of fluid parcels, i.e., the increased or decreased distance between neighboring fluid particles within the time-varying Eulerian velocity field.^22,24–26 Attracting and repelling hyperbolic LCSs are found by calculating the maximum stretching of the particle trajectories over a given time interval.^22,24–26 When the particle trajectories are calculated in forward time, they diverge from the LCSs, which results in a repelling manifold. In contrast, in backward time integrations, particles accumulate on an LCS, resulting in an attracting manifold. Examples can be found in the reports by Haller,⁴⁶ Mezić et al.,²⁸ Huntley et al.,²⁹ Shadden et al.,⁴⁷ and Peng and Dabiri.⁴⁸

Using a computed instantaneous Eulerian velocity field $\mathit{u}\left(x,t\right)$, the trajectory of a tracer starting at point ${\mathit{x}}_{\mathbf{0}}$ and time $t_0$ is given by

$$\frac{d\mathit{x}}{dt}=\mathit{u}\left(x,t\right).$$ (11)

Sequentially using every tracer in the domain, the solution of Eq. (11) creates a map that advects a point ${\mathit{x}}_{\mathbf{0}}$ starting at time $t_0$ over the integration time interval, $T.$ The flow map for a given particle in this time interval can be expressed as follows:²²

$${\Phi }_{t_0}^{t_0+T}\left(\mathit{x}\right)={\mathit{x}}_0+{\int }_{t_0}^{t_0+T}\mathit{u}\left(x\left(\tau \right),\tau \right)d\tau .$$ (12)

To calculate the stretching of a tracer, a perturbation of the tracer located an infinitesimal distance away is considered, $\mathit{y}=\mathit{x}+\delta \mathit{x}\left(0\right).$ In a time interval T, this perturbation becomes²²

$$\delta x\left(T\right)={\Phi }_{t_0}^{t_0+T}\left(\mathit{y}\right)-{\Phi }_{t_0}^{t_0+T}\left(\mathit{x}\right)=\frac{d{\Phi }_{t_0}^{t_0+T}\left(\mathit{x}\right)}{d\mathit{x}}\delta \mathit{x}\left(0\right)+O\left({‖\delta \mathit{x}\left(0\right)‖}^2\right).$$ (13)

$O$() is the order of the error term, which tends toward zero in the limit as $\delta x$ approaches zero. The magnitude of the perturbation is calculated using the Euclidean norm as follows:²²

$$‖\delta x\left(T\right)‖=\sqrt{⟨\delta x\left(0\right),{\left(\hspace{0.17em}\frac{d{\Phi }_{t_0}^{t_0+T}\left(\mathit{x}\right)}{d\mathit{x}}\right)}^{*}\hspace{0.17em}\frac{d{\Phi }_{t_0}^{t_0+T}\left(\mathit{x}\right)}{d\mathit{x}}\delta x\left(0\right)〉},$$ (14)

where * is the matrix transpose. For instance, in the case of 2D calculations, the Jacobian of the flow map is approximated as follows:²²

$${\mathrm{D}\Phi }_{t_0}^{t_0+T}=\left[\begin{array}{cc}\frac{\Delta x\left(t_0+T\right)}{\Delta x\left(t_0\right)}& \frac{\Delta x\left(t_0+T\right)}{\Delta y\left(t_0\right)}\\ \frac{\Delta y\left(t_0+T\right)}{\Delta x\left(t_0\right)}& \frac{\Delta y\left(t_0+T\right)}{\Delta y\left(t_0\right)}\end{array}\right]=\left[\begin{array}{cc}\frac{x_{i+1,j}\left(t_0+T\right)-x_{i-1,j}\left(t_0+T\right)}{x_{i+1,j}\left(t_0\right)-x_{i-1,j}\left(t_0\right)}& \frac{x_{i,j+1}\left(t_0+T\right)-x_{i,j-1}\left(t_0+T\right)}{y_{i,j+1}\left(t_0\right)-y_{i,j-1}\left(t_0\right)}\\ \frac{y_{i+1,j}\left(t_0+T\right)-y_{i-1,j}\left(t_0+T\right)}{x_{i+1,j}\left(t_0\right)-x_{i-1,j}\left(t_0\right)}& \frac{y_{i,j+1}\left(t_0+T\right)-y_{i,j-1}\left(t_0+T\right)}{y_{i,j+1}\left(t_0\right)-y_{i,j-1}\left(t_0\right)}\end{array}\right].$$ (15)

${D\Phi }_{t_0}^{t_0+T}$ is the finite-difference approximation of $\frac{d{\Phi }_{t_0}^{t_0+T}\left(\mathit{x}\right)}{d\mathit{x}}$ (see Fig. 1). The right Cauchy–Green deformation tensor, also known as Green's deformation tensor, is obtained as

$$\Delta ={\left({\mathrm{D}\Phi }_{t_0}^{t_0+T}\right)}^{*}{\mathrm{D}\Phi }_{t_0}^{t_0+T},$$ (16)

where all eigenvalues are real positive values.²² The maximum stretching information is contained in the maximum eigenvalue of the deformation tensor. Thus, an FTLE is defined as follows:

$$\sigma \left({\Phi }_{t_0}^{t_0+T};{\mathit{x}}_0\right)=\frac{1}{\left|T\right|}\text{log}\hspace{0.17em}\sqrt{{\lambda }_{\text{max}}\left(\Delta \left({\mathit{x}}_0\right)\right)}.$$ (17)

FIG. 1.

Advection of fluid particle P from time $t_0$ to $t_0+T$ in the context of FTLE calculations.

To obtain the FTLE scalar values over the entire domain, the structured background grid system defines the starting locations of all tracer particles. Starting at time $t_0$ and using the instantaneous velocities in interval T, the FTLE value is calculated for each grid point, which generates a field of FTLE scalars. A ridge in the FTLE field is a line whose minimum curvature is transverse to its direction defining the LCSs. The calculation of the FTLEs in negative time shows the convergence of the tracers to form attracting material lines. In theory, the LCSs are impermeable to the flow, which forces the tracers to remain between adjoining LCSs.²²

Three-dimensional (3D) FTLE calculations require a significant number of seeding points and tracer calculations. To overcome these computationally intensive computations, we sampled over 2D planes of the 3D velocity field. Grath et al.⁴⁹ showed that 2D FTLE calculated by extracting data from an existing 3D flow field by projecting the velocity fields onto a plane are in close agreement with the FTLE obtained on the same plane section in 3D FTLE calculations.⁴⁹ It is important to note that 2D particle trajectory curves cannot produce a complete view of a rich complex 3D flow and, thus, should be approached with caution.¹⁷

III. MODEL VALIDATION

The coupled EL approach is validated on a backward-facing step using an experiment (see Ref. 50) that has the fluid flow entering the initial section of a wind tunnel, that is, 4 cm high, 45.7 cm wide, and 5.2 m long (chamber 1). It is immediately followed by a section, that is, 6.7 cm high, 45.7 cm wide, and 1.4 m long, expanding the flow channel on one side by 26.7 mm (chamber 2). Given that the bulk airflow velocity is 9.39 m/s and the characteristic length is the tunnel height of 4 cm, the Reynolds number is $\sim 2.5\times {10}^4$. Copper particles, with a diameter of 68.2  $\mu \mathrm{m}$ and a density of 8800  $\mathrm{kg}/{\mathrm{m}}^3$, were then released into the airflow. Their speed was measured at several cross sections downstream of the step.

A structured mesh of 325 × 10⁶ grid nodes with a grid resolution of 1.33 mm in all directions was used as the background mesh. The geometry of the wind tunnel's step and wall surfaces were resolved using the immersed boundary method using an unstructured triangular grid system. A temporal step of 0.1 ms was selected to achieve a CFL (Courant–Friedrichs–Lewy) number of 1.0 or smaller. We carried out a precursor LES to develop an adequate inlet boundary condition since the considered length of chamber 1 was not long enough for the LES to generate a realistic turbulent boundary condition. These calculated inlet velocities were then applied as the inlet boundary condition. More details regarding our precursor LES methodology are documented in Ref. 7.

For the coupled EL method simulation, 50 000 particles were released at the inlet over 0.07 s. Particles propagating downwind were tracked and width averaged values of the computed particle streamwise velocity (instantaneous) were compared with the corresponding measured mean values at five cross sections downstream of the step (see Fig. 2). We note that the simulated particle velocities in Fig. 2 represent the instantaneous values for many particles, while the measured values represent the mean velocity of many particles passing through each cross section. Error bars of one-standard deviations to show the 95% confidence bounds of the numerical simulation results were used to account for the instantaneous values and make them more comparable with the mean measured values. As seen in this figure, the computed results of the particle velocity at z/H > 0.75 are in relatively good agreement with the measured data, while the discrepancy between the measured and computed particle velocity is more pronounced in the regions near the bottom wall (i.e., z/H < 0.75), where the shear layer and the secondary flow exist. The resolution of the computational grid system in this region could explain the observed discrepancy as well as the slow response time of the copper particles in the experimental test.⁵⁰

FIG. 2.

Time-averaged measured (orange circles)⁵⁰ and instantaneous computed results (green lines) of the copper particle width-averaged streamwise velocity (normalized with the bulk velocity of ${\mathrm{U}}_0=$ 9.39 m/s) at different cross sections downstream of the step in the wind tunnel. The error bars represent one standard deviation (95% intervals) of the instantaneous computed results. The number in parenthesis corresponds to the location of each cross section downstream of the step. H is the height of the step (=2.7 cm), and z is the vertical coordinate.

IV. COMPUTATIONAL DETAILS

The study area covered the lower tip of Manhattan. In Fig. 3, we show the relevant area and all buildings in this region of the city. Note that the study area represents only a small portion of NYC, and its results should not be extrapolated to the rest of the city. The background grid system has a resolution of 3 m in all directions, resulting in a computational grid system with over 76.5 × 10⁶ grid nodes (Fig. 4). A time step of 0.02 s was selected so that the Courant–Friedrichs–Lewy number could be limited to less than 1. This grid resolution was selected based on a grid sensitivity analysis using grid systems with resolutions of 8, 6, and 3 m. The digital map of the city was reconstructed using the buildings and ground data obtained from an aerial survey in 2014 (https://www.openstreetmap.org; https://www1.nyc.gov/site/doitt/initiatives/3d-building.page). The study area included 360 buildings with various dimensions and geometries (Fig. 3). Given the direction of the prevailing wind, the southern and northern faces of the study area were set as Dirichlet-type inlet and Neumann-type outlet boundary conditions, respectively. A precursor simulation was run to develop turbulent inflow boundary condition with a mean flow velocity of 3.58 m/s. The so-obtained turbulent inflow was then instantaneously imposed at the inlet of the study area. The western, eastern, and top faces of the study area were treated as free-slip boundaries, where the boundary normal velocity component is set to zero and a zero gradient is applied for the velocity components parallel to the boundary.

FIG. 3.

Three-dimensional view of study area in New York City, which is limited to lower Manhattan. The computational domain is 2.5 long, 1.8 wide, and 0.6 km high in windwise (South–North), spanwise (West–East), and vertical directions, respectively.

FIG. 4.

Schematic of area from top view showing background grid system and immersed building bodies (a). Buildings, roads, and other cityscape features are discretized with unstructured triangular grid systems (in black) and treated as sharp-interface immersed bodies embedded in the flow domain, which is discretized with a structured Cartesian grid system (white lines). Buildings are shown in brown, whereas roads and ground are in green. For clarity, every 30th structured grid cell is shown. (b) Zoomed-in section centered on contaminant release point location marked with a red dot.

The simulated particles had a diameter of 30.0  $\mu \mathrm{m}$ and a density twice that of air. Overall, 120 000 particles were released and uniformly dispersed over 46.5 min. The particles were released at random locations within a 24-m sphere 50 m above the ground to resemble a contaminant cloud on the East side of the New York Stock Exchange [red circle in Fig. 4(b)]. After all particles were released, the simulation was continued until all particles propagated out of the study area.

V. RESULTS AND DISCUSSIONS

In this section, we present the LES results of the wind flow field and the contaminant transport from a source point released in lower Manhattan. We also discuss the importance of our findings regarding the impacts of point-source contaminations with concentration levels that can be experienced in populated urban areas. Figure 5 shows the locations of the vertical planes within the study area where the simulation results are discussed. Note that the numerical model used in this study has been extensively validated for biological, geophysical, and atmospheric flows (for more details, see Refs. 7, 30, 36, and 51–57).

FIG. 5.

Locations of various planes used to show the simulation results in the study area from the top view. Line P₁ marks the location of the plane passing through the particle release point in the North–South direction. Line P₂ shows the location of the vertical particle used to illustrate the particle motion from the updraft on the lee side of the buildings.

A. Wind velocity field

We first present the instantaneous simulation results of the flow field in the study area. Figure 6(a) shows the contours of the LES-computed instantaneous velocity magnitude (normalized with the mean flow velocity of the dominant wind, i.e., 3.58 m/s) on the vertical plane, P₁, shown in Fig. 5. The skyscrapers impede the wind, creating an urban canopy over the entire study area. A distinct shear layer over the urban canopy and low-momentum regions on the lee side of the city buildings are noticeable. Additionally, the shorter buildings, which serve as ground roughness, generate local turbulence shear layers while being shielded by the taller upwind buildings. Figure 6(b) presents the contours of the LES-computed instantaneous normalized velocity magnitude on a horizontal plane approximately 20 m above the mean ground level. At this level, the wind flow enters the street channels without obstructions. In particular, the highly expansive street canyons, particularly those aligned with the wind flow direction (South to North), experience significantly elevated flow velocities. For instance, the West Street channel gradually narrows [Fig. 6(b)]. In contrast, the wind velocity decreases significantly in the city interior, particularly in the dense areas with narrow-street channels, which offer high resistance to the fluid flow. As discussed in Sec. V B, these velocity fields have important consequences for the contaminant particle transport within the study area.

FIG. 6.

Contours of instantaneous velocity magnitude, normalized with mean-flow velocity of dominant wind (=3.58 m/s), at t =23.3 min, from side (a) and top (b) views. Side view (a) is shown on a vertical plane along line P₁ in Fig. 5. Top view (b) shows the horizontal plane approximately 20 m above mean ground level. Buildings and the ground are shown in gray. The tallest building in (a) is one liberty plaza. In both views, wind flows from South (left) to North (right).

The time-averaged wind flow field of the study area was obtained by averaging the instantaneous flow field for two flow-through cycles. One flow-through cycle is the time required for a fluid particle to travel from the inlet to the outlet of the study area. Given the length of the study area in the windwise direction (2.5 km) and the mean flow velocity of the dominant wind, the one flow-through cycle of the study area lasts for approximately 12 min. Figure 7(a) depicts the time-averaged velocity magnitude, normalized with the mean flow velocity on the vertical plane P₁ shown in Fig. 5. A dominant turbulent shear layer above the urban canopy and low-momentum regions on the lee side of the buildings and at lower elevations are observed. Many low-lying areas are marked with very low wind flow velocities (less than 0.04 when scaled by the dominant wind speed). Such low-momentum regions can potentially contribute to high resident times of contaminant particles in the city. Figure 7(b) shows the time-averaged velocity field on a horizontal plane. These results are in agreement with the previous results, which show that the air flows through the street channels that are aligned with the wind velocity without any major obstructions. In general, the wind has a lower momentum in the interior areas, and specifically, the shielding effect of the buildings induces a near-zero momentum on their lee sides.

FIG. 7.

Contours of time-averaged velocity magnitude, normalized with mean flow velocity of dominant wind (=3.58 m/s), from side (a) and top (b) views. Side view in (a) is shown on a vertical plane along line P₁ in Fig. 5. Top view in (b) shows the horizontal plane approximately 20 m above mean ground level. Buildings and the ground are shown in gray. In both views, wind flows from South (left) to North (right). The tallest building in (a) is one liberty plaza.

B. Contaminant particle transport

In addition to the LES-computed velocity field, particle momentum equations were solved to obtain the Lagrangian particle trajectories from a release point, which is illustrated by a red dot in Fig. 4(b). The dominant wind flow in the study area propagated the particles North through lower Manhattan. Overall, 120 000 particles were uniformly injected into the flow domain over 46.6 min. The simulation was continued until 99.9% suspended particles exited the study area. We divided the simulations into three parts: ascending, dynamic equilibrium, and descending phases. The ascending phase encompasses the time from when the first particle is released until it reaches the outlet at t = 15.4 min. Immediately following the ascending phase, the dynamic equilibrium phase begins and continues until the contaminant release at the point source is stopped at t = 46.6 min. Finally, the descending phase covers the time frame starting from when the particle release is stopped until the end of the simulation at t = 78.2 min, i.e., when 99.9% particles were propagated out of the flow domain. This final phase delineates the varying rate at which the contaminant particles leave the study area.

1. Ascending phase

Immediately after the release of the contaminant, a plume of particles with a relatively high concentration formed near the injection point. Figure 8 depicts the instantaneous locations of the contaminant particles, which are colored according to their concentrations, during the ascending phase on a vertical plane along line P₁ shown in Fig. 5. The evolution of the contaminant transport in the ascending phase is also shown in Fig. 9 (Multimedia view), which was created using snapshots of particle trajectories. The multimedia view in Fig. 9 is 60 times faster than the physical time. The instantaneous and time-averaged contaminant concentrations were calculated as follows. First, all articles were projected onto either a vertical or a horizontal plane of interest. Second, the total number of particles in each 2D cell was calculated, and the concentration in each cell was quantified by dividing the number of particles in each cell by the total number of the particles in the study. As shown in Fig. 8, after the contaminant release, the contaminant particles propagate downwind, reaching the end section of the domain (i.e., the northern face of the study area) (after t ∼15 min). The mean propagation speed of the particles reaching the end of the study area is approximately 1.8 m/s, which is 50.2% of the dominant wind velocity. The vertical rise of the contaminant plume is strictly limited by the urban canopy, preventing the contaminant particles from crossing the dominant shear layer, as shown in Fig. 7(a).

FIG. 8.

Side view of contaminant particles (colored with their concentration) during ascending phase of transport concentrations. View (from East to West) is taken from the vertical plane along line P₁ in Fig. 5. (a)–(f) correspond to t = 0.5, 4.6, 8.7, 12.8, 16.9, and 20.0 min after the start of the release. The flow is from South (left) to North (right).

FIG. 9.

The evolution of the contaminant transport in the ascending phase shown on the vertical plane along line P₁ in Fig. 5 and viewed from East to West. Particles are colored with their local concentration. The multimedia view is 60 times faster than the physical time. The flow is from South (left) to North (right). Multimedia view: https://doi.org/10.1063/5.0098503.1 Download video file ^{(8.6MB, mov)} DOI: 10.1063/5.0098503.1

To examine the horizontal transport of the contaminant particles and their spanwise expansion, we captured snapshots of particle trajectories from the top view (Fig. 10). The evolution of the particle trajectories from the top view can be seen in Fig. 11 (Multimedia view), which was created using the snapshots of particle locations. This multimedia view is 60 times faster than the physical time. As seen in Figs. 10 and 11 (Multimedia view), the particles initially disperse through the street canyons and side streets that are slightly diagonal or transverse to the predominant wind flow direction. This dispersion pattern is random owing to the random nature of the turbulent wind flow in the urban area. At later times and farther downwind of the release point, particles at smaller elevations also follow the roads. These roads extend North, channelizing the particle plume boundaries laterally eastward (Fig. 10). The width of the particle plume rapidly increases downwind of the release point, reaching several blocks in the spanwise direction. As seen in Fig. 7, low-momentum regions of the flow are located near the ground level; at higher elevations, the wind velocity markedly increases. Similarly, as particles travel further away from the release point and at greater elevation, owing to the random upward drifts, they are carried in the northern direction with a high velocity.

FIG. 10.

Top view of contaminant particles (colored with their concentration) during ascending phase of transport concentrations. (a)–(f) correspond to t = 0.5, 4.6, 8.7, 12.8, 16.9, and 20.0 min after the start of the release. The flow is from South (left) to North (right).

FIG. 11.

The evolution of the contaminant transport in the ascending phase shown from top view. Particles are colored with their local concentration. The multimedia view is 60 times faster than the physical time. The flow is from South (left) to North (right). Multimedia view: https://doi.org/10.1063/5.0098503.2 Download video file ^{(9MB, mov)} DOI: 10.1063/5.0098503.2

2. Dynamic equilibrium phase

After the first contaminant particle exits the domain, the dynamic equilibrium phase commences, wherein particles propagate along coherent but dynamically changing paths. For instance, at t = 25.6 min, on a horizontal plane, the contaminant trajectories primarily occur from South (left) to North (right) following the prevailing wind [Fig. 12(b)]. However, close to the source, the particles are still at low elevations and follow the street canyons that are diagonally offset from the prevailing wind direction. Owing to this diagonal propagation, some of the particles move farther East [i.e., the downward direction in Fig. 12(b)], rather than along the main body of the particle plume, which is located at a higher elevation to them and tends to remain within a transverse band centered on the release location. Near the center of the study area, the width of the contaminant cloud slightly narrows before dispersing over a maximum width of approximately eight city blocks near the outlet. With regard to the distribution of the vertical particle concentrations downwind from the contaminant release point, the particles remain near the release elevation for a short distance and then rise to approximately thrice this elevation [Fig. 12(a)]. Subsequently, many contaminant particles ascend to near the height of the surrounding skyscrapers, maintaining a uniform height until reaching the one World Trade center. The particle concentrations vary inversely with height throughout this region, with high concentrations observed at low elevations. Downwind from the one World Trade center, the concentration density gradually decreases as the particles move away farther North (right) from the release point and disperse both laterally and vertically [for more details, see Fig. 9 (Multimedia view)].

FIG. 12.

Contaminant particle distribution during dynamically steady phase of transport at t = 25.6 min from side (a) and top (b) views. The vertical plane in (a) is located over line P₁ in Fig. 5. Particles are colored according to their local concentration. The flow is from South (left) to North (right).

The FTLE fields were computed in backward time using the LES-computed velocity fields to identify the flow patterns induced by the buildings of the urban area. Backward-time FTLEs were calculated starting at 65.2 min and integrated backward in time over the entire prior physical time of the numerical simulation. As shown by Shadden et al.,²² the consideration of a long integration time in the simulation provides a good estimate of the LCSs within the study area. The computed FLTE fields along the horizontal and vertical planes are shown in Fig. 13. In Fig. 13(a), the FTLE fields are plotted over a vertical plane (along line P1 in Fig. 5). The turbulent shear layers at the tops of the skyscrapers produce ridges having maxima FTLEs and attracting material lines. The most prominent one is generated by the southernmost building [Fig. 13(a)], which lies directly in the path of the prevailing wind. At this building, the material line forms the boundary of the urban canopy, which continues through the rest of the study area. This LCS and other turbulent shear layers confine the contaminant particles under the urban canopy and at elevations comparable to the heights of the skyscrapers. Figure 13(b) depicts contours of FTLE on a horizontal plane nearly 50 m above ground level. As seen, the most salient feature of the calculated LCSs is that the buildings, which do not obstruct the wind flow, induce attracting material lines along their front and side walls that extend leeward, shielding their lee-side areas. This is particularly apparent on the southeastern shore, where wide road channels are absent. Inland from the coast, at approximately three or four blocks, the material lines interact, forming intricate pathways for the wind flow and, consequently, for the material particles to follow. Farther away from the coast, many locations have no discernable material lines, except the buildings on the lee side of large open areas where front, leeward, and side material lines are formed. Exceptions to the deficit of material lines in the interior are street channels that are parallel to the flow field. At these locations, material lines form on the road channel wall, and many block the flow from the side streets. Consistent with the findings of Hanna et al.,¹³ the calculated LCSs on the windward and lee sides of the buildings constitute channels that direct the material flow downward on the windward side and upward on the lee side.

FIG. 13.

Contours of FTLE fields obtained with backward time integration from side (a) and top (b) views. Top view shows a horizontal plane 50 m above mean ground elevation. (b) is taken from the vertical plane shown by line P₁ in Fig. 5. Ridges of maximum FTLE mark the attracting manifolds of 2D particle trajectories. Gray regions show buildings and the ground. The flow is from South (left) to North (right).

In the following, we focus on the local flow patterns around individual buildings to determine the particle transport in these regions. Figure 14 depicts the velocity vectors of the wind flow on a vertical plane located over line P₂ in Fig. 5. The velocity vectors show upward and downward flow patterns along the sides of the buildings. Consequently, the contaminant particles propagate upward on the lee sides and downward on the windward sides of the buildings. The downward flowing particles are subsequently captured in the recirculating vortical structures in the individual buildings. Figure 15 (Multimedia view) shows this phenomenon from a point of view close to the release point; in this multimedia view, particles are colored according to their elevation.

FIG. 14.

Snapshot of wind velocity vectors colored with velocity magnitude (normalized with dominant wind speed). Vector field marks time-varying up and downdrafts that form around the skyscrapers. The location of this figure is shown by line P₂ in Fig. 5. The flow is from South (left) to North (right).

FIG. 15.

The upward and downward propagation of contaminant particles along the sides of the buildings from a point of view near the release point. Particles are colored according to their elevation. Multimedia view: https://doi.org/10.1063/5.0098503.3 Download video file ^{(9.2MB, mov)} DOI: 10.1063/5.0098503.3

Figure 16(a) shows the distributions of the skyscrapers in the southern and northern sides in terms of their heights, where buildings taller than 170 m are designated as skyscrapers and shown using red color. The southern side has significantly more skyscrapers than the northern side, which contains mainly shorter buildings of approximately equal height. Consequently, the flow on the southern side is obstructed by many tall buildings, which produce strong updrafts and downdrafts. The updrafts and obstructions generate an upward flow that transports numerous particles up to the height of the tallest building. The downdrafts generate recirculation zones on the lee sides of the buildings. Additionally, some contaminant particles traverse this area with little elevation gain. On the northern side, the lack of strong mixing of the flow from the tall buildings allows particles to traverse this side horizontally with only minor upward movements [see Fig. 9 (Multimedia view)]. Overall, the flow and, consequently, the particle transport in the southern side of the study area are dominated by (i) turbulent upward and downward drafts and (ii) shear layers induced by the skyscrapers, as shown by the material lines in Fig. 13(a). However, particle transport in the northern part of the study area is dominated by a near-horizontal wind flow with a slight upward trajectory.

FIG. 16.

Contaminant particle distribution during the dynamic equilibrium phase. (a) shows a snapshot of 3D contaminant particle distribution at t = 46.6 min. Red color in (a) marks buildings taller than 170 m. Particles in (a) are colored according to velocity magnitude. (b) depicts contaminant particles and their concentrations (in logarithmic scale) averaged over the dynamic equilibrium phase, on a horizontal plane 2 m above the mean ground level. The flow is from South (left) to North (right).

Figure 16(b) shows the particle plume colored with concentration contours, averaged over the dynamic equilibrium phase, at approximately 2 m above the mean ground level. The concentration on the southern side of the study area is higher than that on the northern side; thus, a gradual reduction in concentration is expected to occur based on the distance from the release point. The contaminants disperse in the spanwise direction; at the regions near the exit of the outlet, they cover approximately eight city blocks. The distribution is skewed to the East by the meandering plume, particularly in the area immediately South of the North/South border. The concentration level distribution near the ground is important because higher concentrations can have more severe effects on the health of individuals on the ground.

3. Descending phase

After the cessation of the contaminant particle release, the particles propagated out of the domain, and the plume gradually dissipated. The particle release was stopped after t = 46.6 min, marking the beginning of the descending phase. In this section, the physical times and related figures are presented relative to the time of cessation of the particle release. The simulations ended when solely 0.1% of the particles remain active. As soon as the particle feeding stopped, the concentration levels started decreasing. The receding of the contaminant particle plume can be seen in the plots of the instantaneous particle plumes in Fig. 17. After approximately 48.5 min, the study area is cleared of the particles, resulting in a mean particle velocity of 0.6 m/s, which is 16.8% dominant wind velocity. Specifically, the resident time of the contaminants is approximately thrice longer than the elapsed time of the ascending phase. The contaminant particles at higher elevations exit the study area much faster than those near the ground level, owing to the higher wind velocity at these elevations, and clear the study area in approximately 37.2 min. The particles at lower elevations required significantly longer times to exit the study during the descending phase. This is because they trapped on the lee sides of the buildings within the recirculation zones and/or the flow momentum was minimal at these elevations. The particles trapped in the recirculation zones either propagate out of the study area at a prolonged rate or become attached to the buildings or the solid surfaces of the grounds. The delay in their departure from the urban area illustrates the critical role of buildings and other cityscape features in delaying the complete removal of contaminants from an urban area.

FIG. 17.

Snapshots of contaminant concentrations during the descending phase. [(a)–(d)] show the vertical views along line P₁ in Fig. 5, whereas [(e)–(h)] show top views. Panels labeled [(a) and (e)], [(b) and (f)], [(c) and (g)], and [(d) and (h)] correspond to 0, 9.3, 13.9, and 23.2 min after particle release cessation, respectively. The flow is from South (left) to North (right).

Most urban contaminant transport numerical studies employ EE methods.^13,58 Such EE models frequently utilize a continuum convection–diffusion transport for contaminant scalar transport. We compared the computational results of the current coupled EL model with those of EE models to obtain insight into the similarities and differences between these two modeling approaches. In a different study,⁷ we simulated the present study area with the same computational grid system, geometry, and boundary conditions using a coupled EE model (for more details, see Ref. 7), the results of which are compared with those of the present EL model. Our comparative analysis showed that the EE and EL methods yielded slightly different durations for the ascending and descending phases, and the durations estimated from the EL model were approximately 19% and 17% shorter than those from the EE model, respectively. Furthermore, the comparisons of the contaminant concentration fields show a slight disagreement in the range of volume fractions. This can be attributed to the limited number of contaminant particles used in this study. Specifically, more particles are needed to obtain better statistical results that are consistent with those of the EE model.

Despite the differences between the EE and EL modeling results, the obtained shapes and dimensions of the contaminant plumes showed good agreement. This is highlighted in Fig. 18, in which the simulation results of the two modeling approaches are presented. The EE results are shown as isosurfaces of contaminant concentrations of 0.01 (dark red) and 0.001 (light red). The isosurfaces are set to be translucent so that the particles of EL simulation are visible. The top and side views of the instantaneous concentration plumes are taken at t = 25.6 min, i.e., during the dynamic equilibrium phase of the transport. The horizontal and vertical extents of the plumes from the two modeling approaches seem quantitatively similar. Moreover, the distributions of the concentrations obtained from both modeling approaches decrease further away from the release point. Overall, this comparison shows that EE modeling approaches could yield results that are comparable to those of EL modeling frameworks, despite being computationally less demanding.

FIG. 18.

Snapshots of contaminant transport using coupled EL and EE models at t = 25.6 min from side (a) and top (b) views. The side view represents a vertical view of the domain along line P₁ in Fig. 5. EL simulation results of this study are shown in blue dots superimposed by the iso-surfaces of concentration [=0.01 (dark red) and 0.001 (light red)] from EE modeling approach. This view is from East to West. The flow is from South (left) to North (right).

VI. CONCLUSION

We conducted a coupled EL modeling of the dominant wind in the southern tip of NYC to investigate the transport mechanisms of contaminant particles released from a point source within the city. We also studied the formation of LCSs around the buildings and other urban features in the area by examining the particle trajectories and more rigorously, obtaining contours of the FTLEs. Numerous such structures were observed as dominant sets of attracting material lines generated at the tops of the skyscrapers in the area, including one that formed an urban canopy, with material boundaries showing channels in which flow moved upward or downward close to the walls of the buildings. Additionally, we observed the differences among the turbulence characteristics of the North and South sides of the model area. The South side showed significant turbulent fluctuations in the elevations of the particles and an increase in the ground contaminant concentration, both of which were caused by the skyscrapers. On the northern side, the contaminant particle plume moved mostly horizontally with an increase in the elevation; however, no extreme changes occurred on the southern side with a corresponding decrease in the number of skyscrapers.

Immediately after the contaminant particles were released, they propagated downwind and expanded in the spanwise direction to approximately 0.5 km, with the concentration decreasing as they traveled northward. After approximately 15 min, the first contaminant particle reached the end of the study area, with a mean propagation speed of 1.8 m/s, which was 50.2% dominant wind speed. At later times, during the ascending and dynamic equilibrium phases, the particle concentration fields remained high at the release point; on the lee sides of both tall and short buildings, they were close to the release point. With the cessation of the particle release and the beginning of the descending phase, the contaminants started to recede from the urban area. Approximately 48 min were required until the study area was clear from the contaminant particles. Considering the resident time of the particles in this phase of transport, the propagation speed of the particles averaged 0.6 m/s, which was approximately 17% of the dominant wind velocity. This was attributed to the particles stopping in the recirculation zones on the lee sides of the buildings and to the low velocity of the particles near the ground level. Note that, because of shear layers forming at the tops of the skyscrapers, the contaminant particles remained within the urban canopy during the transport phases.

Based on the results of this study conducted within a 2.5 km (South–North) by 1.8 km (East–West) region within lower Manhattan under a point-source release of contaminant particles under a South to North wind of 3.58 m/s, the following conclusions can be drawn:

• (i)The contaminant particles gradually propagated downwind with a lateral dispersion covering eight city blocks.
• (ii)The concentration was highest at the release point and remained relatively constant while decreasing downwind.
• (iii)The maximum propagation speed of the particles during the ascending phase was approximately 50% of the dominant wind speed.
• (iv)The minimum speed of the particles during the descending phase was approximately 17% dominant wind speed.
• (v)Particles trapped in recirculation zones and low-momentum regions near the ground increased the resident time of the contaminant plume.
• (vi)Because of their relatively long resident time, the contaminant particles filled the study area much faster than they exited it after the cessation of their release.

To the best of our knowledge, this study is the first to investigate contaminant transport in a real-life urban environment using a coupled EL and FTLE approach as well as to conduct a comparative analysis of the coupled EL and EE approaches for contaminant transport in such urban areas. Although the simulated results of this study may not be extrapolated outside of the study area of NYC, the general observations can be used for locations with similar topologies. Additionally, this study is limited to a unidirectional wind condition owing to the high computational cost of the simulations. A more comprehensive understanding of the flow requires simulations of different wind directions.

AUTHOR DECLARATIONS

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

Wayne R. Oaks: Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing - original draft (equal). Seokkoo Kang: Methodology (equal); Software (equal); Writing - original draft (equal); Writing - review and editing (equal). Xiaolei Yang: Formal analysis (equal); Methodology (equal); Software (equal); Writing - original draft (equal). Ali Khosronejad: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Writing - original draft (equal); Writing - review and editing (equal).

DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.