Large Eddy Simulations of Turbulent and Buoyant Flows in Urban and Complex Terrain Areas Using the Aeolus Model

atmosphere

Article Large Eddy Simulations of Turbulent and Buoyant Flows in Urban and Complex Terrain Areas Using the Aeolus Model

Akshay A. Gowardhan *, Dana L. McGufﬁn , Donald D. Lucas , Stephanie J. Neuscamman, Otto Alvarez and Lee G. Glascoe

Lawrence Livermore National Laboratory, Livermore, CA 94551, USA; [email protected] (D.L.M.); [email protected] (D.D.L.); [email protected] (S.J.N.); [email protected] (O.A.); [email protected] (L.G.G.) * Correspondence: [email protected]

Abstract: Fast and accurate predictions of the flow and transport of materials in urban and complex terrain areas are challenging because of the heterogeneity of buildings and land features of different shapes and sizes connected by canyons and channels, which results in complex patterns of turbulence that can enhance material concentrations in certain regions. To address this challenge, we have developed an efficient three-dimensional computational fluid dynamics (CFD) code called Aeolus that is based on first principles for predicting transport and dispersion of materials in complex terrain and urban areas. The model can be run in a very efficient Reynolds average Navier–Stokes (RANS) mode or a detailed large eddy simulation (LES) mode. The RANS version of Aeolus was previously validated against field data for tracer gas and radiological dispersal releases. As a part of this work, we have validated the Aeolus model in LES mode against two different sets of data: (1) turbulence quantities measured in complex terrain at Askervein Hill; and (2) wind and tracer data from the Citation: Gowardhan, A.A.; Joint Urban 2003 field campaign for urban topography. As a third set-up, we have applied Aeolus to McGuffin, D.L.; Lucas, D.D.; simulate cloud rise dynamics for buoyant plumes from high-temperature explosions. For all three Neuscamman, S.J.; Alvarez, O.; cases, Aeolus LES predictions compare well to observations and other models. These results indicate Glascoe, L.G. Large Eddy Simulations that Aeolus LES can be used to accurately simulate turbulent flow and transport for a wide range of of Turbulent and Buoyant Flows in applications and scales. Urban and Complex Terrain Areas Using the Aeolus Model. Atmosphere Keywords: urban dispersion; large eddy simulation; complex terrain; fast-response dispersion 2021, 12, 1107. https://doi.org/ 10.3390/atmos12091107 modeling; computational fluid dynamics

Academic Editor: Patrick Armand

Received: 9 July 2021 1. Introduction Accepted: 23 August 2021 More than half of the world’s population lives in urban areas and the danger from an Published: 27 August 2021 accidental or deliberate release of hazardous materials can be significant. The transport and dispersion of atmospheric contaminants in urban areas is strongly influenced by surround- Publisher’s Note: MDPI stays neutral ing buildings, which significantly modify the winds, leading to areas of channeling along with regard to jurisdictional claims in the streets, updrafts and downdrafts in the wake of the buildings, and recirculating flow in published maps and institutional affil- street canyons [1,2]. In addition, urban areas create highly heterogeneous regions of wind iations. speed and turbulence intensity. Similarly in complex terrain, the local terrain impacts the flow field significantly, producing similar complex effects which can lead to non-intuitive dispersion patterns. There is a great need to have an accurate and efficient capability to predict dispersion and deposition patterns in these complex scenarios. Copyright: © 2021 by the authors. High-resolution computer models can predict how airborne materials spread around Licensee MDPI, Basel, Switzerland. buildings in urban areas and land features in complex terrain. However, the modeling This article is an open access article tool must be flexible enough to use for a variety of applications, and should be coupled distributed under the terms and to many relevant databases, such as terrain, building shapefiles, land-use characteristics, conditions of the Creative Commons and population. Many fast-response urban dispersion models have been developed to Attribution (CC BY) license (https:// predict transport for these scenarios. Gaussian plume models, which run in seconds on a creativecommons.org/licenses/by/ laptop, have been modified to account for the plume centerline shift that may occur due to 4.0/).

Atmosphere 2021, 12, 1107. https://doi.org/10.3390/atmos12091107 https://www.mdpi.com/journal/atmosphere Atmosphere 2021, 12, 1107 2 of 18

channeling in street canyons [3]. Hall et al. (2000) developed a Gaussian puff model called the Urban Dispersion Model (UDM) for use from neighborhood to city scales [4]. Röckle (1990) derived a diagnostic model that computes three-dimensional (3-D) flow around buildings using empirical equations and mass conservation [5]. Most fast-response models rely on empirical algorithms based on idealized building configurations. This makes it difficult to generalize the accuracy of these models for flow fields in highly heterogeneous urban terrain without many validation exercises [6]. Computational fluid dynamics (CFD) models have been used to compute the flow field in urban areas and complex topography. Comparison of these results with field measurements shows that these models work well in most regions [7–13]. These CFD models, however, are computationally very expensive and prohibitive for applications related to toxic releases in cities or at industrial facilities where turnaround time is very important. Further, before running CFD models, users need to generate detailed grids that account for the 3-D geometry of the surrounding city and terrain. This is usually a time-consuming process, which renders these models useless for an operational response where a quick answer is needed in a small amount of time. Gowardhan et al. (2011) developed a fast-response CFD model which represents an intermediate model type that produces fast runtimes (in the order of minutes for a several-block problem) and a reasonably accurate solution [9]. Neophytou et al. (2011) also evaluated this model and showed these fast-response CFD models can accurately predict the flow features in complex urban configurations [10]. Based on work carried out by Gowardhan (2008) and Gowardhan et al. (2011), we have developed a new fast-response operational dispersion modeling system called Aeolus, which can predict the flow and transport of airborne contaminants in urban areas and complex terrain [9,11]. The model can be run in a very efficient (~minutes) RANS (Reynolds average Navier–Stokes) mode or a detailed (~hours) LES (large eddy simulation) mode. In this paper, we describe the Aeolus model and evaluate its performance in large eddy simulation mode. The LES version is validated for two different cases and applied to a third case to showcase the model capabilities over a wide range of applications. We first present validation results for turbulence generated in neutrally stratified flow over complex terrain case using data from Askervien hill campaign [14]. Next, flow and dispersion in an urban area is validated using wind and tracer data from the Joint Urban 2003 Oklahoma City field experiment [15]. Last, we apply the model’s capability to simulate the cloud rise dynamics of a high-temperature bubble from a nuclear explosion in the troposphere using data from the Upshot-Knothole Dixie test. This test was a high-altitude air burst with an explosive yield of 11 kilotons and a height of burst (HOB) of 1836 m above ground level (AGL).

2. Introduction to Aeolus Modeling System Aeolus is an efficient 3-D CFD code based on a finite volume method. It solves the time-dependent incompressible Navier–Stokes equations on a regular cartesian staggered grid using a fractional step method algorithm. It also solves a scalar transport equation for potential temperature, which is coupled to the flow using an anelastic approximation. The model includes a Lagrangian dispersion model for predicting the atmospheric transport and dispersion of tracers and other materials. The RANS version of Aeolus is used as an operational model in the National Atmospheric Release Advisory Center (NARAC) at Lawrence Livermore National Laboratory (LLNL) for quickly simulating the impacts of airborne hazardous materials in urban areas. NARAC uses Aeolus and other operational atmospheric models to provide the United States Department of Energy information and services pertaining to chemical, biological, radiological, and nuclear airborne hazards [16,17]. NARAC can simulate downwind effects from a variety of scenarios, including fires, industrial and transportation accidents, radiation dispersal device explosions, hazardous material spills, sprayers, nuclear power plant accidents, and nuclear detonations. Atmosphere 2021, 12, 1107 3 of 18

2.1. Large Eddy Simulation Model Aeolus can be run in a high-fidelity mode using an LES model. LES resolves the time-dependent turbulent flow field at both small and large scales, allowing better fidelity than alternative approaches such as RANS. The smallest scales of the solution rely on a Smagorinsky model with a constant of Cs = 0.12 to account for unresolved scales in the flow, rather than resolving them directly as in expensive direct numerical simulation (DNS) methods. This makes the computational cost for applying LES to realistic engineering systems with complex geometry or flow configurations practical and attainable using supercomputers. In contrast, direct numerical simulation, which resolves every scale of the solution, is prohibitively expensive for nearly all atmospheric dispersion problems with complex geometry.

2.2. Numerics The model uses the 3rd order accurate Quadratic Upstream Interpolation for Con- vective Kinematics (QUICK) scheme [18] for the advective terms and 2nd order central difference for the diffusive terms. The scalar transport equation uses a Bounded QUICK (BQUICK) scheme to obtain a bounded solution while maintaining spatial accuracy and reducing dispersion errors. The law of the wall boundary condition is imposed at the rigid surface by applying a free slip boundary condition at the surface. The tangential shear 2 stress is set equal to u∗ . The value of friction velocity u∗ is evaluated using a log-law (u∗ = uk/ln(0.5 × ∆z/z0)), where u is the magnitude of the tangential velocity and z0 is the surface roughness, k is the von Karman constant with a value of 0.4, and ∆z is the vertical grid resolution. The pressure Poisson equation is solved using the successive over-relaxation method (SOR via the methodology described above). A free slip condition is used at the top and side boundaries. The following outﬂow boundary condition is prescribed at the outlet:

∂ϕ ∂ϕ = U (1) ∂t b ∂n where n denotes the direction normal to the boundary face, ϕ is the advected variable, and Ub is a velocity that is independent of the location of the outﬂow surface and is selected so that an overall mass balance is maintained. This boundary condition allows the convection of turbulent structures out of the domain and avoids problems with reﬂection of pressure waves back to the interior of the domain.

2.3. Dispersion Model To model dispersion within the atmosphere, Aeolus models the 3-D, incompressible, advection–diffusion equation with sources and sinks using a Lagrangian framework [19]:

DC = Q − S (2) Dt where the total derivative represents the advection and diffusion that occurs to species in a Lagrangian reference frame, C is the air concentration of the species, Q is the source term, and S is the sink term, which accounts for removal processes such as deposition. The equations for the Lagrangian particle displacement due to advection, diffusion, and settling in the three coordinate directions are:

∂υT υ 1/2 = + Sc + T dxi ueidt dt 2 dWxi (3) dxi Sc

where uei is the wind components in the x, y, and z projection directions, respectively, υT is the eddy diffusivity, Sc is the Schmidt number, dWx,y,z are three independent normal random variates with zero mean and variance dt, which is the timestep of advection of the Lagrangian particle. The stochastic differential equations above are then integrated in Atmosphere 2021, 12, x FOR PEER REVIEW 4 of 18

where 𝑢 is the wind components in the x, y, and z projection directions, respectively, 𝜐 is the eddy diffusivity, 𝑆𝑐 is the Schmidt number, dWx,y,z are three independent normal random variates with zero mean and variance dt, which is the timestep of advection of the Lagrangian particle. The stochastic differential equations above are then integrated in

Atmospheretime2021 ,to12, calculate 1107 an independent trajectory for each Lagrangian particle. The concentra4‐ of 18 tion 𝑐̃, at any time t, can then be calculated from the Lagrangian particle locations at time t and the contaminant mass associated with each particle. The model does not apply ker‐ nel smoothing and timethe togrid calculate cell concentration an independent trajectory depends for on each the Lagrangian number particle. of particles The concentration in the respective grid cell.ce , at any time t, can then be calculated from the Lagrangian particle locations at time t and the contaminant mass associated with each particle. The model does not apply 2.4. Grid Generationkernel smoothing and the grid cell concentration depends on the number of particles in the respective grid cell. The model uses a cartesian grid and straightforward masking approach for generat‐ ing a computational2.4. grid. Grid New Generation model grids can be generated in seconds from geographic information system shapefilesThe model (for uses a a few cartesian kilometers) grid and straightforward and/or building masking data approach available for generating from a computational grid. New model grids can be generated in seconds from geographic the National Geospatialinformation Intelligence system shapeﬁles Agency (forand a United few kilometers) States and/or Geological building Service data available (USGS) from dataset containing thebuilding National data Geospatial for over Intelligence 100 U.S. Agency cities. and Apart United from States the Geological building Service dataset, (USGS) the model also usesdataset the USGS containing national building elevation data for overdata 100 at U.S.10 m cities. resolution Apart from (NED10) the building for ter dataset,‐ rain information whichthe model covers also uses the the 48 USGS contiguous national elevation U.S. states, data at 10Hawaii, m resolution and (NED10) portions for terrainof information which covers the 48 contiguous U.S. states, Hawaii, and portions of Alaska. Alaska. The built‐inThe datasets built-in datasetsand fast and grid fast generation grid generation tools tools are are useful useful for for operational operational applications. ap‐ plications. ExamplesExamples of the grids of the gridsproduced produced for for urban urban areas areas and complex complex terrain terrain areas areas are shown are in shown in Figure 1. Figure1.

Figure 1. Grids produced by Aeolus modeling system for (left) the central business district in Oklahoma City showing the Figure 1. Grids produced by Aeolus modeling system for (left) the central business district in Okla‐ vertical resolution and (right) a region with complex terrain. homa City showing the vertical resolution and (right) a region with complex terrain. Apart from the elevation and building databases, the modeling system also integrates Apart from thedata elevation about land-use and building characteristics, databases, daytime the and modeling nighttime population,system also as wellintegrates as meteoro- data about land‐uselogical characteristics, fields from operational daytime and weather nighttime forecast centerspopulation, and other as sources.well as Allmeteor the above‐ information provides the model with the required initial and boundary conditions and ological fields fromsubsequently operational helps weather to reduce forecast the model centers setup and time other to minutes. sources. The integrated All the above databases information providesalso the ensure model that relevant with the products required can be initial produced and quickly boundary and be distributedconditions to and relevant subsequently helpsauthorities. to reduce the model setup time to minutes. The integrated databases also ensure that relevant2.5. Inflow products Turbulence can be produced quickly and be distributed to relevant . authorities Large eddy simulation models often need a precursor simulation to build a turbulent inflow profile. However, this process can be time consuming and difficult to achieve in an 2.5. Inflow Turbulenceoperational setup. Following DeLeon and Senocak (2017), we have developed a robust inflow turbulence generator which uses temperature perturbations in cells near the inflow Large eddy simulationboundary tomodels produce often a turbulent need a profile precursor [20]. Thesimulation inflow turbulence to build zone a turbulent is contained inflow profile. However,within thethis five process grid cells can nearest be time to consuming the inlet where and a mean difficult velocity to achieve is prescribed. in an The operational setup. buoyancyFollowing effect DeLeon due to the and perturbation Senocak in (2017), the temperature we have field developed propagates toa robust the velocity inflow turbulence generatorfield and produces which theuses requisite temperature turbulent perturbations structures. in cells near the inflow boundary to produce3. Complex a turbulent Terrain profile Validation [20]. The inflow turbulence zone is contained within the five grid cellsThe nearest Aeolus model to the using inlet the largewhere eddy a simulation mean velocity methodology is prescribed. was validated The against buoyancy effect dueexperimental to the perturbation data for three in the different temperature applications: field flow propagates over complex to the terrain, velocity flow and field and produces dispersionthe requisite of tracers turbulent in urban structures. areas, and cloud rise dynamics for buoyant plumes from

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3. Complex Terrain Validation The Aeolus model using the large eddy simulation methodology was validated against experimental data for three different applications: flow over complex terrain, flow Atmosphere 2021, 12, 1107 and dispersion of tracers in urban areas, and cloud rise dynamics for buoyant5 of 18 plumes from high‐temperature explosions. This section covers the complex terrain validation, while the following two sections cover the urban area and cloud rise validations. high-temperatureThe Askervein explosions. Hill project This section [14] was covers a field the complexstudy conducted terrain validation, in 1982 while and 1983 the to study thefollowing boundary two sections‐layer flow cover over the urban low‐ areaprofile and cloudhills. riseIt was validations. performed under a collaborative effortThe under Askervein the auspices Hill project of [ 14the] was International a field study conductedEnergy Agency in 1982 andProgramme 1983 to study for Research the boundary-layer flow over low-profile hills. It was performed under a collaborative andeffort Development under the auspices on Wind of the Energy International Conversion Energy Systems. Agency Programme Askervein for Hill Research is a low, isolated ellipticand Development hill on the on west Wind coast Energy of the Conversion island of Systems. South Uist Askervein in the Hill Outer is a low,Hebrides isolated of Scotland, whichelliptic hillpeaks on theat about west coast 116 of m the above island the of Southground. Uist During in the Outer these Hebrides field campaigns, of Scotland, more than which50 towers peaks were at about deployed 116 m above and instrumented the ground. During for wind these fieldmeasurements campaigns, moreon and than around this low50 towers‐profile were hill, deployed as shown and in instrumented Figure 2. Towers for wind were measurements placed in ontwo and arrays around along this the major axislow-profile of the hill,hill as(lines shown A and in Figure AA),2 .in Towers the prevailing were placed wind in two direction, arrays along and theone major array along the axis of the hill (lines A and AA), in the prevailing wind direction, and one array along minor axis of the hill (line B). Lines A and AA pass through points hilltop (HT) and center the minor axis of the hill (line B). Lines A and AA pass through points hilltop (HT) and pointcenter (CP), point (CP),respectively, respectively, and and along along an an orthogonal orthogonal lineline B. B. A A measurement measurement site site called called refer‐ encereference site site (RS) (RS) was was also also placed placed upstreamupstream of of the the hill hill to characterize to characterize the inflow the inflow conditions. conditions.

(m)

Elevation

Figure 2. 2.Terrain Terrain elevation elevation map map of Askervien of Askervien Hill ﬁeld Hill study field area. study area.

The Aeolus grid was generated by rotating the elevation dataset clockwise by 60 de- greesThe so that Aeolus the inflow grid wind was directiongenerated is orthogonal by rotating to the gridelevation as shown dataset in Figure clockwise2, with by 60 de‐ greesthe vertical so that extent the ofinflow 1 km. wind A uniform direction Cartesian is orthogonal mesh was created to the grid using as a gridshown resolution in Figure 2, with theof ∆ verticalx, ∆y = 20 extent m, and of ∆1z km.= 10 A m uniform resulting Cartesian in~16 million mesh grid was cells. created The inflow using velocity a grid resolution profileof Δx, wasΔy = created 20 m, using and Δ a log-lawz = 10 m profile resulting (u = (u in~16∗/k) ln( millionz/z0)), togrid fit the cells. observed The inflow data velocity profilefrom the was upstream created site using RS as a shown log‐law in Figureprofile3. ( Theu = (u value∗/k) ln of(z/z surface0)), to roughness, fit the observedz0, was data from 0.03 m [14] and the friction velocity u∗ was derived using the velocity reading (u = 14 m/s the upstream site RS as shown in Figure 3. The value of surface roughness,r z0, was 0.03 m at zr = 60 m) at the reference site RS. [14] and the friction velocity u∗ was derived using the velocity reading (ur = 14 m/s at zr = 60 m) at the reference site RS.

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0 0 5 10 15 20 25 30 Wind speed (m/s) 0 0 5 10 15 20 25 30 Wind speed (m/s) Figure 3. Inflow profile for the Aeolus model (black line) overlaid with field data from site RS (red squaresFigure are 3. theInflow time averaged profile forvalues the and Aeolus the red model line represent (black the line) variance). overlaid with field data from site RS (red squares are the time averaged values and the red line represent the variance). FigureFigure 43. shows Inflow the turbulent profile structures for in the the velocity Aeolus magnitude model in a vertical (black slice line) overlaid with field data from site RS (red along linesFigure A and4 shows AA. The the velocity turbulent magnitude structures increases in as the it velocitypasses over magnitude the Askervein in a vertical slice Hill top and the flow separates in the lee side of the hill. It can be observed that a larger wakesquaresalong is created lines are A behind and the AA. the time plane The velocitypassing averaged along magnitude line values A. This increases larger and region as the it of passes redseparation overline the represent Askervein the variance). occursHill topdue andto a steeper the flow drop separates in elevation in thealong lee line side A and of the has hill.been Itobserved can be in observed other that a larger modelwake results, is created as well behind as observed the data. plane passing along line A. This larger region of separation occursWindsFigure due were to simulated a steeper 4 shows for drop2 h, which in the elevation took aboutturbulent along6 h of computer line Astructures andtime on has a quad been‐core observedin the invelocity other magnitude in a vertical slice machine.model results,After a 1.5 as h wellspinup as period, observed Aeolus data. data from the last 30 min of the simulation wasalong time averaged lines for Acomparision and AA.with the Theobserved velocity data. magnitude increases as it passes over the Askervein Hill top and the flow separates in the lee side of the hill. It can be observed that a larger wake is created behind the plane passing along line A. This larger region of separation occurs due to a steeper drop in elevation along line A and has been observed in other model results, as well as observed data. Winds were simulated for 2 h, which took about 6 h of computer time on a quad‐core machine. After a 1.5 h spinup period, Aeolus data from the last 30 min of the simulation was time averaged for comparision with the observed data.

Figure 4. Turbulent structures in the vertical planes passing along line A through point HT (upper) and along line AA through point CP (lower).

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Figure 4. Turbulent structures in the vertical planes passing along line A through point HT (upper) Atmosphere 2021, 12, 1107 and along line AA through point CP (lower). 7 of 18

Observations along lines A and AA are compared with averaged velocities from the Aeolus simulation. Historically, other model simulations have been compared to the AskerveinWinds Hill were dataset simulated in terms for 2 of h, fractional which took speedup about 6 ∆𝑆 h of, which computer is defined time on as a quad-core machine. After a 1.5 h spinup period, Aeolus data from the last 30 min of the simulation 𝑆𝑧 𝑆𝑧 was time averaged for comparision with∆𝑆 the observed data. (4) Observations along lines A and AA are𝑆 compared𝑧 with averaged velocities from thewhere Aeolus S is the simulation. horizontal Historically, wind speed other at a specified model simulations height above have the been surface compared z = 10 m, to and the AskerveinSRS is the wind Hill speed dataset at in the terms reference of fractional site. The speedup fractional∆S ,speedup which is ∆𝑆 defined provides as a measure of the influence of the terrain on the wind field based on the upwind undisturbed inflow. S(z) − S (z) Figure 5 compares the fractional∆S = speedup ∆𝑆RS at 10 m above ground from Aeolus(4) S (z) with field data and two other peer‐reviewed models,RS the standard Weather Research and whereForecastingS is the (WRF) horizontal model wind and speed a version at a specifiedof WRF heightwith an above immersed the surface boundaryz = 10 method m, and S(WRFRS is‐ theIBM) wind [8]. speed For results at the along reference line site. A, Aeolus The fractional compares speedup reasonably∆S provides well with a measure the ob‐ ofserved the influence data and of the the other terrain models. on the It wind correctly field captures based on the the speed upwind‐up undisturbed observed at inflow.the top of hill,Figure as well5 compares as the separation the fractional of the speedup flow on the∆S leeat 10side m of above hill. Aeolus ground is from also Aeolusable to withpredict field the data slight and deceleration two other peer-reviewedin the upwind part models, of hill the reasonably standard well. Weather Predictions Research along and Forecastingline AA have (WRF) been model challenging and a version for many of WRFmodels, with but an here immersed also, Aeolus boundary is able method to predict (WRF- IBM)the key [8]. features For results observed along linein the A, data. Aeolus compares reasonably well with the observed data and theThis other validation models. study It correctly shows captures us that theAeolus speed-up is able observed to predict at the key top flow of hill,features as well in ascomplex the separation terrain and of the this flow makes on the it an lee important side of hill. tool Aeolus for many is also applications able to predict ranging the slight from decelerationwind turbine in optimization the upwind studies part of to hill predicting reasonably dispersion well. Predictions patterns in along regions line with AA havecom‐ beenplex terrain. challenging In future for many work, models, we plan but to validate here also, Aeolus Aeolus for is predicting able to predict flow the and key dispersion features observedpattern in in more the data.complicated terrain involving multiple hills and valleys.

Figure 5.5. Comparison of of fractional fractional speedup speedup predicted predicted by by Aeolus Aeolus along along lines lines A ( topA ()top and) and AA AA (bottom (bot)‐ withtom) ﬁeldwith campaignfield campaign data as data well as as well other as other peer-reviewed peer‐reviewed models. models.

This validation study shows us that Aeolus is able to predict key ﬂow features in complex terrain and this makes it an important tool for many applications ranging from wind turbine optimization studies to predicting dispersion patterns in regions with complex terrain. In future work, we plan to validate Aeolus for predicting ﬂow and dispersion pattern in more complicated terrain involving multiple hills and valleys. Atmosphere 2021, 12, x FOR PEER REVIEW 8 of 18

4. Urban Area Flow and Dispersion Validation Aeolus was validated using data from the Joint Urban 2003 field experiment, which Atmosphere 2021, 12, 1107 was performed in July 2003 in the central business district of Oklahoma8 of 18 City. A large number of meteorological instruments and tracer‐gas air samplers were deployed in the urban area. Meteorological measurements were taken at over 160 different locations [15] 4. Urban Area Flow and Dispersion Validation while tracer measurements were made at over 130 locations [21]. Ten intensive operation Aeolus was validated using data from the Joint Urban 2003 field experiment, which periods (IOPs) were conducted for both daytime and nighttime periods, during which was performed in July 2003 in the central business district of Oklahoma City. A large mostnumber meteorological of meteorological and instruments gas sampler and tracer-gasinstruments air samplers were activated. were deployed During in the the IOPs, the windsurban were area. Meteorologicalpredominantly measurements from the south. were taken Further at over details 160 different about locations the experiment, [15] instru‐ mentwhile types tracer and measurements locations, were and made tracer at over release 130 locations information [21]. Ten can intensive be found operation in Allwine et al. (2004),periods Clawson (IOPs) were et conducted al. (2005), for Flaherty both daytime et al. and (2007), nighttime Nelson periods, et during al. (2007), which mostand Brown et al. meteorological and gas sampler instruments were activated. During the IOPs, the winds (2004)were predominantly[15,21–24]. from the south. Further details about the experiment, instrument types andAeolus locations, results and tracer were release compared information to canfield be data found from in Allwine a continuous et al. (2004), release Clawson of sulfur hex‐ afluorideet al. (2005), (SF Flaherty6) during et al. IOP (2007), 8 trial Nelson 2. As et al. noted (2007), previously, and Brown et the al. (2004)winds [15 were,21–24 predominantly]. from theAeolus south results for werethis release. compared The to field event data was from chosen a continuous because release there of sulfur was hex-little variation in afluoride (SF6) during IOP 8 trial 2. As noted previously, the winds were predominantly thefrom inflow the south wind for direction this release. and The the event edge was of chosen the plume because was there well was captured little variation by the in gas sampler data.the inflowThe portable wind direction wind and detector the edge at of the the city plume post was office well captured (PWID by15), the a gaspropeller sampler anemometer, wasdata. used The to portable record wind the detector ‘wake at‐free’ the city inflow post office profile (PWID for 15), wind a propeller direction anemometer, and wind speed. It waswas located used to recordabout the 500 ‘wake-free’ m upstream inflow profileof the for central wind direction business and district wind speed. at 50 It m was above ground located about 500 m upstream of the central business district at 50 m above ground on a on a 35 m rooftop tower, and was free from building effects. A total of 5488 g of SF6 gas 35 m rooftop tower, and was free from building effects. A total of 5488 g of SF6 gas was wasreleased released continuously continuously for 30 min for from 30 min the Westin from locationthe Westin shown location in Figure shown6. in Figure 6.

Figure 6. SF6 release locations in the Oklahoma City central business district during Joint Urban 2003 Figure(• Park 6. Avenue, SF6 release• Westin, locations and • Botanical). in the TheOklahoma northward City direction central is indicated business by thedistrict black arrow.during Joint Urban 2003 (● Park Avenue, ● Westin, and ● Botanical). The northward direction is indicated by the black The computational domain is displayed in Figure1 (left) and was 1.2 km × 1.4 km × arrow. 0.21 km in the x, y, and z directions discretized on a regular grid (∆x = ∆y = 5 m, ∆z = 3 m). The horizontal grid resolution of 5 m is the minimum grid spacing needed to resolve a typicalThe street computational canyon. The griddomain consists is displayed of about 4.5 millionin Figure cells. 1 Time(left) varying and was input 1.2 for km × 1.4 km × 0.21the km simulation in the x, was y, constructedand z directions using data discretized from the PWIDon a regular 15 anemometer. grid (Δ Sixx = log-lawΔy = 5 m, Δz = 3 m). Theprofiles horizontal using a surfacegrid resolution roughness value of 5 of mz0 is= 0.1the m minimum (5 min average) grid were spacing used in needed the LES to resolve a simulation. Figure7 shows the wind speed and direction measured by the anemometer typical(dashed street lines) canyon. and the fiveThe minute grid consists averaged of values about used 4.5 to million construct cells. the Aeolus Time inputvarying input for thewind simulation profile (solid was line, constructed squares). The using averaged data log-law from profilesthe PWID were 15 used anemometer. to create the Six log‐law profilesmean inflow using profile a surface while roughness the inflow turbulence value of gerator z0 = 0.1 perturbed m (5 min the velcoityaverage) field were to used in the LEScreate simulation. physically Figure realistic 7 turbulent shows features.the wind The speed source and was direction defined as measured a sphere of 1by m the anemom‐ eterradius (dashed and a lines) release and amount the offive 5488 minute g was simulated averaged by values releasing used 0.5 millionto construct lagrangian the Aeolus input particles over the release duration of 30 min. It was found that 0.5 million particels are windsufficient profile to estimate (solid line, 30 min squares). averaged concentrationThe averaged at this log spatial‐law resolution.profiles were used to create the mean inflow profile while the inflow turbulence gerator perturbed the velcoity field to create physically realistic turbulent features. The source was defined as a sphere of 1 m radius and a release amount of 5488 g was simulated by releasing 0.5 million lagrangian particles over the release duration of 30 min. It was found that 0.5 million particels are sufficient to estimate 30 min averaged concentration at this spatial resolution. Similarly to the complex terrain case, the flow field was simulated for 1.5 h, with the initial hour used for spinup and the final 30 min used for analysis and comparison with

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observations. The simulation took about 2 h of computer time to run on a quad‐core ma‐ chine.

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Atmosphere 2021, 12, 1107 9 of 18 observations. The simulation took about 2 h of computer time to run on a quad‐core ma‐ chine.

Figure 7. Five minutes of averaged data from PWID 15 were used to build the inflow profiles for the Figure 7. Five minutesFigure of 7. averaged Five minutes data of averaged from PWID data from 15 PWID were 15 used were usedto build to build the the inflow inflow profiles profiles for for Aeolus LES simulation. the Aeolus LES simulation.the Aeolus LES simulation. Similarly to the complex terrain case, the flow field was simulated for 1.5 h, with Figure 8 shows the velocity vector field for flow around Oklahoma City in the x–y Figure 8 showsthe the initial velocity hour used vector for spinup field and for the flow final around 30 min used Oklahoma for analysis City and comparisonin the x–y planewith at observations. 8 m above ground The simulation level (AGL). took Simulated about 2 h wind of computer vectors timefrom to the run Aeolus on a quad-core model plane at 8 m above(grey groundmachine. arrows) level are overlaid (AGL). with Simulated meteorological wind observations vectors (blackfrom arrows).the Aeolus Longer model ar‐ (grey arrows) are rowsoverlaid inFigure the figurewith8 shows indicate meteorological the velocity higher vector wind fieldspeed.observations for The flow Aeolus around (black wind Oklahoma speed arrows). Cityprediction in theLonger xis– yalsoplane ar‐ represented by the color shading around the buildings, where warmer colors indicate rows in the figure indicateat 8 m above higher ground wind level speed. (AGL). Simulated The Aeolus wind vectorswind fromspeed the prediction Aeolus model is (grey also higherarrows) predicted are overlaid wind withspeed meteorological values. From observationsthis figure, it (black can be arrows). observed Longer that the arrows Aeolus in the represented by themodel figurecolor is able indicate shading to predict higher around the wind important speed. the The flowbuildings, Aeolus features wind reasonablywhere speed predictionwarmer well. iscolors also represented indicate higher predicted windby the speed color shadingvalues. around From the this buildings, figure, where it can warmer be colorsobserved indicate that higher the predicted Aeolus model is able to predictwind the speed important values. From flow this figure,features it can reasonably be observed thatwell. the Aeolus model is able to predict the important flow features reasonably well.

Figure 8. Velocity vectors from Aeolus (gray arrows) and observations (black arrows) for IOP 8 trial 2 during the Joint Urban 2003 field experiment. The simulation shows the horizontal slice (xy plane) at 2 m AGL. The zoomed‐in area highlights urban effects that are predicted well by Aeolus.

The model captures the channeling effects along north–south running streets and predicts the high wind speeds measured in these regions. Aeolus also predicts the reverse flow in the street canyons and wake regions in the domain. The model‐produced velocities Figure 8. Velocity vectorsin from the Aeolus intersection (gray arrows) areas are and in observations good agreement (black arrows) with the for IOPfield 8 trialdata. 2 during the Joint Urban Figure2003 ﬁeld 8. experiment. Velocity vectors The simulation from showsAeolus the (gray horizontal arrows) slice (xy and plane) observations at 2 m AGL. The (black zoomed-in arrows) area for highlights IOP 8 trial 2urban during effects the that Joint are predictedUrban 2003 well by field Aeolus. experiment. The simulation shows the horizontal slice (xy plane) at 2 m AGL. The zoomed‐in area highlights urban effects that are predicted well by Aeolus.

Atmosphere 2021, 12, 1107 10 of 18 Atmosphere 2021, 12, x FOR PEER REVIEW 10 of 18

The model captures the channeling effects along north–south running streets and Figure 9 showspredicts the measured the high wind and speeds predicted measured SF in6 theseair concentration regions. Aeolus alsovalues predicts at ground the reverse level. The colored ﬂowcircles in the represent street canyons the measured and wake regions air concentrations in the domain. The averaged model-produced over the velocities 30 in the intersection areas are in good agreement with the ﬁeld data. min of the continuous release. The colored contours represent the Aeolus prediction of Figure9 shows the measured and predicted SF 6 air concentration values at ground the 30 min averagelevel. air Theconcentration, colored circles with represent higher the measuredpredicted air values concentrations near the averaged source over (red, the 30 orange areas). Themin Aeolus of the model continuous predictions release. The agree colored with contours the experimental represent the results Aeolus predictionwell; the of areas of highest concentrationthe 30 min average and air the concentration, general downwind with higher plume predicted spreading values near are the captured source (red, orange areas). The Aeolus model predictions agree with the experimental results well; the in the simulation results.areas of highest concentration and the general downwind plume spreading are captured in the simulation results.

1 x 10 ‐‐02

5 x 10 ‐‐03

1 x 10 ‐‐03

5 x 10 ‐‐04

1 x 10 ‐‐04

) 3

‐‐05

5 x 10 (g/m

1 x 10 ‐‐05

5 x 10 ‐‐06

Concentration

1 x 10 ‐‐06

5 x 10 ‐‐07

1 x 10 ‐‐07

5 x 10 ‐‐08

3 Figure 9. Contours of 30 min averaged SF6 air concentration (g/m ) from Aeolus overlaid with 30 min averaged field concentration data (filled circles) for IOP 8 trial 2 during the Joint Urban 2003 field experiment. The simulation shows the 3 horizontalFigure slice 9. Contours (xy plane) at of 2 m30 AGL. min averaged SF6 air concentration (g/m ) from Aeolus overlaid with 30 min averaged field concentration data (filled circles) for IOP 8 trial 2 during the Joint Urban 2003 field experiment. The simulationFigure 10 showsdisplays the scatter horizontal plots of slice the paired (xy plane) (point-to-point) at 2 m AGL. values from the Aeolus predictions and the field experiment measurements. Data points (blue circles) that fall on Figure 10 displaysthe solid scatter black diagonalplots of represent the paired perfect (point matching‐to‐point) between values the predicted from the and Aeolus measured values. Points that lie above and below the black line represent values that are over- predictions and theand field under-predicted experiment by measurements. Aeolus, respectively, Data as points compared (blue to circles) the measured that fall data. on The the solid black diagonalgreen, blue, represent and orange perfect colored matching diagonal between lines represent the predicted factors of and 2, 5, andmeasured 10 model– values. Points thatmeasurement lie above and mismatches, below the respectively black line (FAC2, represent FAC5, and values FAC10). that The are scatter over plots‐ and show under‐predicted bygood Aeolus, agreement respectively, between predicted as compared and measured to the values, measured with most data. pairs The falling green, within blue, and orange colored diagonal lines represent factors of 2, 5, and 10 model–measure‐ ment mismatches, respectively (FAC2, FAC5, and FAC10). The scatter plots show good agreement between predicted and measured values, with most pairs falling within the blue FAC5 lines. Figure 10 also indicates that the number of matched zeros, which show how often the model correctly predicts zero‐valued measurements (data below the instru‐ ment minimum level of detection, MLOD = 10−7.5 g/m3). The number of matched zeros shows that the model is able to correctly predict the spread of the plume. Overall, we found that 48.9%, 84.7%, and 91.5% of the simulated points fall within FAC2, FAC5, and FAC10, respectively, indicating excellent performance for predicting dispersion in

Atmosphere 2021, 12, 1107 11 of 18

Atmosphere 2021, 12, x FOR PEER REVIEWthe blue FAC5 lines. Figure 10 also indicates that the number of matched zeros, which 11 of 18 show how often the model correctly predicts zero-valued measurements (data below the instrument minimum level of detection, MLOD = 10−7.5 g/m3). The number of matched zeros shows that the model is able to correctly predict the spread of the plume. Overall, we found that 48.9%, 84.7%, and 91.5% of the simulated points fall within FAC2, FAC5, complexand FAC10, urban respectively, areas indicating which are excellent consistent performance with for the predicting values dispersion suggested in in Hanna and Chang (2012)complex [25]. urban areas which are consistent with the values suggested in Hanna and Chang (2012) [25].

Figure 10. Scatter plot showing points paired in time and space for predicted and observed 30 min Figure 10. Scatter plot showing3 points paired in time and space for predicted and observed 30 min averaged SF6 concentrations (g/m ) for IOP 8 trial 2 during the Joint Urban 2003 ﬁeld experiment. averaged SF6 concentrations (g/m3) for IOP 8 trial 2 during the Joint Urban 2003 field experiment. Further quantitative analysis of our results is given in terms of absolute value of fractional bias (|FB|) and the normalized mean square error (NMSE) for concentration. FractionalFurther bias is quantitative a normalized value analysis of mean errorof our [26 ].results |FB| values is given range in from terms 0 to +2. of A absolute value of frac‐ tionalperfect agreementbias (|FB|) between and model the normalized and measurement mean would square result in error FB = 0. (NMSE) for concentration. Frac‐ tional bias is a normalized value of mean! error [26]. |FB| values range from 0 to +2. A Ci − Ci FB = P o (5) perfect agreement between model andi measurementi would result in FB = 0. 0.5 CP + Co Ci i Ci 𝐶 𝐶 where o is the th observation (measurement), andFB P is the corresponding model predic- (5) tion. NMSE captures the overall absolute departure of the modeled results from measure- 0.5𝐶 𝐶 ments. Lower values of NMSE indicate better agreement between model and experimental values. where 𝐶 is the ith observation (measurement), 2 and 𝐶 is the corresponding model pre‐ 1 ∑ Ci − Ci = n P o diction. NMSE captures NMSEthe overall absolute2 departure of the modeled(6) results from meas‐ urements. Lower values of NMSE indicateCo better agreement between model and experi‐ mentalwhere n is values. the number of valid measurement–model data pairs and Co is the mean measurement value. Hanna and Chang (2012) suggest the following limits on the comparison metrics for acceptable performance of an urban model [251]: ∑𝐶 𝐶 𝑛 (6) NMSE 𝐶

where n is the number of valid measurement–model data pairs and 𝐶 is the mean meas‐ urement value. Hanna and Chang (2012) suggest the following limits on the comparison metrics for acceptable performance of an urban model [25]:  |FB| ≲ 0.67, i.e., the relative mean bias less than a factor of 2.  NMSE ≲ 6, i.e., the random scatter ≲ 2.4 times the mean.  FAC2 ≲ 0.30, i.e., 30% or more of model predicted values are within a factor of two of measured values. The absolute value of the fractional bias (|FB|) was found to be 0.015 and the NMSE for the LES simulation was 0.29, indicating relatively low simulation errors compared to the experimental data. This excellent comparison of the Aeolus model with field measure‐ ments in complex urban areas makes it a very useful tool for predicting flow features and dispersion patterns in these scenarios.

Atmosphere 2021, 12, x FOR PEER REVIEW 12 of 18

Atmosphere 2021, 12, 1107 12 of 18 5. High‐Temperature Nuclear Cloud Rise Dynamics For the final application, we ran Aeolus to simulate the dynamics of a hot nuclear detonation cloud rising in the troposphere with a specified ambient potential temperature • |FB| . 0.67, i.e., the relative mean bias less than a factor of ~2. a profile θ . In this set•‐up,NMSE the source. 6, i.e., is not the random only a scattermass release,. 2.4 times but the also mean. a large temperature perturbation. Therefore,• FAC2 the .initialization0.30, i.e., 30% orrequires more of modelthe temperature, predicted values altitude, are within and a factor size of of two of the fireball formed frommeasured the detonation. values. The Smagorinsky schemeThe absolute in Aeolus value of (see the fractional Section bias 2.1) (|FB|) is useful was found for simulating to be 0.015 and turbu the NMSE‐ for the LES simulation was 0.29, indicating relatively low simulation errors compared to lence at standard atmospheric conditions, but not for including all the relevant turbulence the experimental data. This excellent comparison of the Aeolus model with field measure- scales in a buoyant mentsnuclear in complex cloud. urbanRealistically, areas makes there it a very is additional useful tool for mass predicting and energy flow features ex‐ and change as ambient dispersionair is entrained patterns into in these the scenarios. cloud. In Section 5.3, we describe a new pa‐ rameterization that was added to Aeolus to represent this entrainment process. 5. High-Temperature Nuclear Cloud Rise Dynamics For the final application, we ran Aeolus to simulate the dynamics of a hot nuclear 5.1. Dixie Event Descriptiondetonation cloud rising in the troposphere with a specified ambient potential temperature The Dixie test wasprofile performedθa. In this set-up, during the operation source is not Upshot only a mass‐Knothole release, buton also6 April, a large 1953 temperature at 07:30 local time in Nevadaperturbation. (37°5 Therefore,′5″ N, 116°1 the initialization′5″ W). The requires device the temperature,was detonated altitude, in and the size at‐ of the fireball formed from the detonation. mosphere at 1.84 km AGL (3.1 km above mean sea level) with an explosive yield of 11 The Smagorinsky scheme in Aeolus (see Section 2.1) is useful for simulating turbulence kilotons [27]. These atcharacteristics standard atmospheric result conditions, in a scaled but height not for including of burst all of the 831 relevant m correspond turbulence‐ scales ing to ‘regime 1′ in inwhich a buoyant no soil nuclear or dirt cloud. is Realistically, disturbed theredue isto additional the detonation mass and [28]. energy During exchange as the shot, high‐frequencyambient cameras air is entrained captured into thethe cloud. formation In Section and 5.3 ,propagation we describe a newof the parameterization shock‐ wave and fireball forthat comparison was added to with Aeolus simulations, to represent thissuch entrainment as Miranda process. [29]. Miranda simu‐ lates the initial fireball5.1. size Dixie and Event temperature, Description which is shown in Figure 11 for the timestep directly before the DixieThe cloud Dixie starts test was rising. performed Additionally, during operation the time Upshot-Knothole series of the observed on 6 April, 1953 top and bottom of theat 07:30 Dixie local cloud time were in Nevada recorded (37◦5 0in5” Hawthorne N, 116◦105” W). (1979) The device [30]. was detonated in the Previous modelsatmosphere successfully at 1.84 simulated km AGL (3.1 Dixie km cloud above meanrise. Kanarska sea level) with et al. an (2009) explosive com yield‐ of 11 kilotons [27]. These characteristics result in a scaled height of burst of 831 m correspond- pared predictions from a compressible Eulerian model with a low Mach number compo‐ ing to ‘regime 10 in which no soil or dirt is disturbed due to the detonation [28]. During the nent [31]. More recently,shot, high-frequency Arthur et al. cameras (2021) capturedused the the Weather formation Research and propagation and Forecasting of the shockwave model to simulate Dixieand fireball cloud for rise, comparison finding with good simulations, agreement such with as Miranda observations [29]. Miranda [32]. simulates How‐ the ever, neither of theseinitial prior fireball modeling size and studies temperature, contained which is detonation shown in Figure gas 11and for debris the timestep in the directly cloud, which is includedbefore in the the Dixie Aeolus cloud startssimulation. rising. Additionally, the time series of the observed top and bottom of the Dixie cloud were recorded in Hawthorne (1979) [30].

Figure 11. Temperature proﬁle of the initial hot Dixie bubble used in Aeolus (blue solid line) based on a Miranda prediction (blackFigure dashed 11. line).Temperature profile of the initial hot Dixie bubble used in Aeolus (blue solid line) based on a Miranda prediction (black dashed line). Previous models successfully simulated Dixie cloud rise. Kanarska et al. (2009) compared predictions from a compressible Eulerian model with a low Mach number com- 5.2. Model Setup ponent [31]. More recently, Arthur et al. (2021) used the Weather Research and Forecasting In setting up themodel model to simulate grid, there Dixie cloudis a tradeoff rise, ﬁnding between good agreement having withcells observations that are small [32]. How- enough to resolve the turbulent flow, but not too small because a large domain with many cells is required to simulate cloud rise throughout the troposphere. For this simulation, we selected a model resolution of Δx, Δy, Δz = 30 m in the x‐, y‐, and z‐directions and a domain size of x, y, z = 9000 m, 9000 m, 15,000 m, resulting in 45 million grid cells. The ambient conditions are specified as vertical profiles of temperature and pressure at the detonation location. These input data are at a resolution of 304.8 m, and Aeolus linearly interpolates the temperature and pressure profiles to its vertical grid (Tk, Pk). The

Atmosphere 2021, 12, 1107 13 of 18

ever, neither of these prior modeling studies contained detonation gas and debris in the cloud, which is included in the Aeolus simulation.

5.2. Model Setup In setting up the model grid, there is a tradeoff between having cells that are small enough to resolve the turbulent ﬂow, but not too small because a large domain with many cells is required to simulate cloud rise throughout the troposphere. For this simulation, we selected a model resolution of ∆x, ∆y, ∆z = 30 m in the x-, y-, and z-directions and a Atmosphere 2021, 12, x FOR PEER REVIEW 13 of 18 domain size of x, y, z = 9000 m, 9000 m, 15,000 m, resulting in 45 million grid cells. The ambient conditions are specified as vertical profiles of temperature and pressure at the detonation location. These input data are at a resolution of 304.8 m, and Aeolus linearly profilesinterpolates utilized the for temperature the Dixie andcase pressure from radiosonde profiles to measurements its vertical grid [30] (T kare, Pk shown). The profilesin Fig‐ ureutilized 12. The for potential the Dixie casetemperature from radiosonde of every measurementsgrid cell θi,j,k in [ 30Aeolus] are shown is set according in Figure 12 to. Thethe verticalpotential profile: temperature of every grid cell θi,j,k in Aeolus is set according to the vertical profile:

. 103 𝑚𝑏0.286 𝜃,, 𝑇 10 mb (7) θi,j,k = Tk 𝑃 (7) Pk

Figure 12. Ambient meteorology utilized to simulate the Dixie test. The ambient temperature and Figurepressure 12. vertical Ambient proﬁles meteorology are shown utilized with respectto simulate to height the Dixie above test. ground The ambient level (agl). temperature and pressure vertical profiles are shown with respect to height above ground level (agl).

The source inputs deﬁning the initial hot bubble include the detonation time tdet, 𝑡 bubbleThe diameter source inputsDsrc and defining temperature the initialTsrc hot, the bubble mass includeMsrc and the number detonation of Lagrangian time , 𝐷 𝑇 𝑀 bubbleparticles diameterNp, src representing and temperature materials in the, hotthe bubble,mass the densityand numberρsrc and of Lagrangian size dp,src of particlesmaterials 𝑁 in, the representing hot bubble, materials and the source in the positionhot bubble,(xsrc the, ysrc density, zsrc). Aeolus𝜌 and replaces size 𝑑, the ofambient materials potential in the hot tempertaure bubble, and with the thesource hot position bubble potential𝑥,𝑦 temperature,𝑧. Aeolus at replaces the source the ambientlocation potential based on tempertaureTsrc and the gridwith pressure the hot bubble at tdet. Additionally,potential temperature 1.8 million at Lagrangian the source locationparticles based are released on 𝑇 at and random the grid locations pressure within at 𝑡 the. Additionally, bubble volume, 1.8 representingmillion Lagrangian the hot particlescloud at aretdet .released at random locations within the bubble volume, representing the hot cloud at 𝑡. 5.3. Entrainment Parameterization 5.3. EntrainmentThe momentum Parameterization and energy balances are solved for the velocity and potential temper- atureThe ﬁelds momentum at each grid and cell energy center. balances Turbulent are viscositysolved for is the determined velocity and based potential on the sheartem‐ peraturerate and fields Smagorinsky at each constantgrid cell Ccenter.s, but itTurbulent is also enhanced viscosity by is entrainment determined ofbased ambient on the air shearthat is rate not and tracked Smagorinsky in Aeolus. constant To account Cs, but for theit is inducedalso enhanced mixing by from entrainment entrainment, of ambient we add airan that entrainment is not tracked term in (E Aeolus.i,j,k) to eddy To account viscosity for for the momentum induced mixing and potentialfrom entrainment, temperature we equation (v ) at the grid cell at index i, j, and k in the x-, y-, and z-direction, respectively. add an entrainmenti,j,k term (𝐸,,) to eddy viscosity for momentum and potential tempera‐ 𝑣 𝑖, 𝑗, and 𝑘 ture equation ( ,,) at the grid cell at index in the2 x‐, y‐, and z‐direction, respec‐ p3 tively. vi,j,k = Ei,j,k + Cs ∆x∆y∆z S (8)

𝑣,, 𝐸,, 𝐶 𝛥𝑥𝛥𝑦𝛥𝑧 |𝑆̅| (8)

where 𝑆̅ is contraction of the rate‐of‐strain tensor, 𝑆̅ This enhancement due to entrainment is determined based on the vertical velocity of that cell 𝑤,, the potential temperature of that cell 𝜃,,, the ambient potential tempera‐ ture at that vertical level 𝜃 , and a dimensionless empirical parameter 𝑓 entrainment factor. 𝜃,, 𝜃 𝐸,, 𝑚𝑎𝑥 0, 𝑓 Δ𝑥Δ𝑦Δ𝑧𝑤,, (9) 𝜃

Atmosphere 2021, 12, 1107 14 of 18

∂u where S is contraction of the rate-of-strain tensor, S = 1 ∂ui + j . ij 2 ∂xj ∂xi Atmosphere 2021, 12, x FOR PEER REVIEW This enhancement due to entrainment is determined based on the vertical velocity14 ofof 18

that cell wi,j,k the potential temperature of that cell θi,j,k, the ambient potential temperature a at that vertical level θk , and a dimensionless empirical parameter fent entrainment factor. θ − θa p3 i,j,k k Using the model inputs and entrainmentEi,j,k = max 0, parameterizationfent ∆x∆y∆z wi,j,k described above, we(9) per‐ θa formed seven Aeolus simulations. The model set‐up was identicalk for all seven simula‐ tions except that we variedUsing the𝑓 model between inputs and zero entrainment and one. parameterization An entrainment described factor above, of we zero per- is formed seven Aeolus simulations. The model set-up was identical for all seven simulations equivalent to runningexcept a simulation that we varied withoutfent between the zero entrainment and one. An entrainmentparameterization. factor of zero The is equiv- results are shown in Figurealent 13 where to running the a simulation green profile without corresponding the entrainment parameterization. to 𝑓 of 0.5 The is resultsthe closest are shown in Figure 13 where the green proﬁle corresponding to fent of 0.5 is the closest match match to the observations.to the observations.

Figure 13. Dixie cloud rise dynamics for different entrainment factors. The black dashed profiles, green dotted profile, and Figurecolored solid13. Dixie profiles cloud show the rise observed dynamics cloud top for and different bottom, the entrainment simulated cloud factors. center without The entrainment, black dashed and the profiles, greensimulated dotted cloud profile, center with and varying coloredfent from solid 0.2 to profiles 1, respectively. show the observed cloud top and bottom, the simu‐ lated cloud center without entrainment, and the simulated cloud center with varying 𝑓 from 0.2 The entrained ambient air slows the cloud rise velocity, decreasing the maximum to 1, respectively. cloud height. Additionally, entrainment results in oscillations around the stabilized cloud height since the cloud does not overshoot the tropopause height. The hot cloud rises The entrained aboveambient its neutral air slows buoyancy the height cloud due rise to its velocity, inertia until decreasing the inertia cannot the sustain maximum the imbalance in density between the cloud and environment. At this point, the cloud is cloud height. Additionally,denser than entrainment its surroundings results and it falls, in oscillations carried past stabilization around by the its stabilized momentum. Thecloud height since the cloudoscillations does not continue overshoot as the cloud the height tropopause converges height. to its stabilization The hot height. cloud Theoretically, rises above its neutral buoyancythe height frequency due of to oscillations its inertia in a stratifieduntil the environment inertia cannot can be described sustain with the the imbalance Brunt– Väisälä frequency N. in density between the cloud and environment. At thisg d point,θ the cloud is denser than its N2 = (10) surroundings and it falls, carried past stabilization by itsθ dz momentum. The oscillations con‐ tinue as the cloud heightFigure converges 13 shows to the its cloud stabilization center of mass, height. which isTheoretically, not the best comparison the frequency to the observations of cloud top and bottom. Instead, Figure 14 shows the normalized cloud of oscillations in a stratified environment can be described with the Brunt–Väisälä fre‐ quency 𝑁. 𝑔 𝑑𝜃 𝑁 (10) 𝜃 𝑑𝑧 Figure 13 shows the cloud center of mass, which is not the best comparison to the observations of cloud top and bottom. Instead, Figure 14 shows the normalized cloud mass (𝑓𝑡) calculated from the average concentration in the x‐ and y‐directions for each vertical level 𝑘 (𝐶̅ 𝑡) where 𝑚 is the number of horizontal grid cells in each vertical level. The mean cloud mass is normalized so the maximum value of 𝑓𝑡 is one, so the average concentration is divided by its maximum value across the vertical levels.

𝛴𝛴𝐶,,𝑡 𝐶̅ 𝑡 (11) 𝑚

𝐶̅ 𝑡 𝑓 𝑡 (12) 𝑚𝑎𝑥̅ 𝐶𝑡

Atmosphere 2021, 12, 1107 15 of 18

mass ( fk(t)) calculated from the average concentration in the x- and y-directions for each vertical level k (Ck(t)) where mk is the number of horizontal grid cells in each vertical level. The mean cloud mass is normalized so the maximum value of f (t) is one, so the average Atmosphere 2021, 12, x FOR PEER REVIEW 15 of 18 concentration is divided by its maximum value across the vertical levels.

ΣjΣiCi,j,k(t) C (t) = (11) k m Similar to simulations by Arthur et al.k (2021), the cloud height is underpredicted in

the first 2 min post detonation [32]. AtC laterk(t) times, the majority of the cloud mass is con‐ fk(t) = (12) tained between the observed cloud topmax andC(t )bottom, as shown in Figure 14.

Figure 14. Simulated cloud rise with entrainment factor of 0.5. The average concentration of cloud Figuregas normalized 14. Simulated by the maximum cloud rise value with at each entrainment time is shown factor in the of shaded 0.5. grey,The theaverage center concentration of mass of cloud gasof simulated normalized cloud by is shown the maximum in solid blue value profile, at and each the time red dashed is shown and dash-dottedin the shaded profiles grey, show the center of mass ofthe simulated observed cloud cloud top is and shown bottom. in solid blue profile, and the red dashed and dash‐dotted profiles show the observedSimilar to cloud simulations top and by Arthurbottom. et al. (2021), the cloud height is underpredicted in the first 2 min post detonation [32]. At later times, the majority of the cloud mass is contained betweenFigure the observed 15 shows cloud the top evolution and bottom, of asthe shown cloud in Figuretemperature 14. and gas and debris concen‐ trationsFigure at 151.0, shows 3.5, the6.5, evolution and 11.5 of min the cloudafter temperaturedetonation. and The gas potential and debris temperature concen- is shown acrosstrations the at 1.0, y‐ 3.5,and 6.5, z‐grid and 11.5 cells min at after x = 4.5 detonation. km, which The potentialcorresponds temperature to the is cloud shown center. The gas across the y- and z-grid cells at x = 4.5 km, which corresponds to the cloud center. The andgas and debris debris concentrations concentrations are are averaged averaged over over the x-direction the x‐direction and normalized and normalized by their by their re‐ spectiverespective source source massmass to to determine determine their their dilution dilution ratios ratios shown shown in Figure in 15 Figure. The cloud 15. The cloud ver‐ ticalvertical extent, extent, shown shown in in the the grey grey shaded shaded area, isarea, defined is defined as the altitudes as thezcloud altitudes(t) in which 𝑧𝑡 in which thethe concentrationconcentration is more is more than than 10% of 10% the currentof the maximumcurrent maximum concentration. concentration. cloud n o z (t) ∈ zk s.t. Cj,k(t) > 0.1 max Cj,k(t) (13) 𝑧 𝑡 ∈𝑧 𝑠.𝑡.𝐶,̅ 𝑡 0.1𝑚𝑎𝑥𝐶,̅ 𝑡 (13) The cloud center is defined as the cloud center of mass within the cloud extent, which is shown as the black solid lines in Figure 15. 𝛴𝛴𝛴𝐶,,𝑡 𝑧 𝑡 𝑧𝑡 (14) 𝛴𝛴𝛴𝐶,,𝑡 The observed cloud top and bottom is also shown in Figure 15 as the red dashed lines. The simulated cloud rise matches observations well on average, with an underesti‐ mate of the observed height initially and a slight overestimate at the maximum height near 6.5 min post‐detonation. Additionally, even though the simulated cloud bottom ex‐ tends lower than the observed after about 8 min (as shown in Figure 14), most of the cloud below the observed bottom could be considered the stem instead of the cap.

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Figure 15. Cloud position and extent at several times using f of 0.5. The potential temperature at the cloud center, the Figure 15. Cloud position and extent at several timesent using 𝑓 of 0.5. The potential temperature average gas dilution ratio, and the average debris dilution ratio are shown at 1.0, 3.5, 6.5, and 11.5 min after detonation in panelsat the (A cloud–D), respectively. center, the In theaverage 2D concentration gas dilution ﬁgures, ratio, the shaded and the grey average area shows debris the “cloud dilution vertical ratio extent” are described shown inat the 1.0, text, 3.5, the 6.5, black and solid 11.5 line min shows after the clouddetonation center of in mass, panels and ( theA– redD), dashed respectively. lines show In the the observed 2D concentration cloud top and bottomfigures, height. the shaded grey area shows the “cloud vertical extent” described in the text, the black solid line shows the cloud center of mass, and the red dashed lines show the observed cloud top and bottom height. The cloud center is deﬁned as the cloud center of mass within the cloud extent, which is shown as the black solid lines in Figure 15.

6. Conclusions cloud ΣiΣjΣkCi,j,k(t) zk (t) zcenter(t) = (14) Aeolus is a fast‐running computational fluid dynamicsΣiΣjΣ urbankCi,j,k(t) dispersion model that has been validated using several experimental data sets. Using the Aeolus model, complex The observed cloud top and bottom is also shown in Figure 15 as the red dashed lines. dispersal experimentsThe can simulated be completed cloud rise matcheswith simulation observations run well times on average, small with enough an underestimate for use of in emergency response,the observed to provide height consequence initially and a slight management overestimate information. at the maximum The height model near 6.5is min coupled to all the relevantpost-detonation. databases Additionally, required even to setup though and the simulatedrun the model cloud bottom and produce extends lower products which are thanuseful the for observed first responders. after about 8 min (as shown in Figure 14), most of the cloud below the observed bottom could be considered the stem instead of the cap. In this work, we have simulated flow and dispersion using the large eddy simulation version of the Aeolus6. Conclusionsmodel in three different regimes—complex terrain, urban domain, and high‐temperature cloudAeolus rising is a fast-running into high computational altitudes. This fluid showcases dynamics urban the flexibility dispersion model and that adaptability of the modelhas been in validated different using scenarios. several experimental data sets. Using the Aeolus model, complex dispersal experiments can be completed with simulation run times small enough for use Comparing Aeolusin emergency predictions response, to field to provide experiments, consequence the managementmodel generally information. shows The good model is agreement with the coupledmeasured to all data. the relevant This report databases details required model to setup validation and run to the the model Askervein and produce hill field campaign productsconducted which in are 1982 useful and for 1983, first responders. the Joint Urban field experiments con‐ ducted in 2003 for both Incontinuous this work, we and have instantaneous simulated flow and tracer dispersion gas releases, using the and large explosive eddy simulation version of the Aeolus model in three different regimes—complex terrain, urban domain, cloud rise data fromand the high-temperature Dixie nuclear test cloud conducted rising into high at the altitudes. Nevada This Test showcases Site in the 1953. flexibility Ae‐ and olus results compareadaptability well with of measured the model in data different both scenarios. qualitatively and quantitatively and were found to compare Comparingwell with Aeolusthe data. predictions to field experiments, the model generally shows good Expanding the agreementcapabilities with of the a measuredfast‐running data. Thisurban report dispersion details model model validation and validating to the Askervein its simulation results against field data greatly advances NARAC’s ability to make pre‐ dictions of the fate of material released in an urban environment and complex terrain. The improved and validated Aeolus model represents a significant capability for NARAC, and improved support to the USA’s Department of Energy. In future, we plan to validate the LES model for additional complex terrain regions and other real and mock urban areas. We also plan on validating the model for different release types, including buoyant and dense gas releases in urban areas. Given the simplic‐ ity of the model to adapt to complex grids, we intend to extend the model for modeling flow and dispersion pattern in indoor environments. To further increase the efficiency of the large eddy simulation capability of the Aeolus model, we plan to implement the code

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hill field campaign conducted in 1982 and 1983, the Joint Urban field experiments conducted in 2003 for both continuous and instantaneous tracer gas releases, and explosive cloud rise data from the Dixie nuclear test conducted at the Nevada Test Site in 1953. Aeolus results compare well with measured data both qualitatively and quantitatively and were found to compare well with the data. Expanding the capabilities of a fast-running urban dispersion model and validating its simulation results against field data greatly advances NARAC’s ability to make predictions of the fate of material released in an urban environment and complex terrain. The improved and validated Aeolus model represents a significant capability for NARAC, and improved support to the USA’s Department of Energy. In future, we plan to validate the LES model for additional complex terrain regions and other real and mock urban areas. We also plan on validating the model for different release types, including buoyant and dense gas releases in urban areas. Given the simplicity of the model to adapt to complex grids, we intend to extend the model for modeling flow and dispersion pattern in indoor environments. To further increase the efficiency of the large eddy simulation capability of the Aeolus model, we plan to implement the code on a Graphics Processing Unit (GPU) platform which will truly help in operationalizing the model. In addition, we plan to validate the entrainment parameterization in nuclear cloud rise simulations using other test shots.

Author Contributions: A.A.G., D.L.M. and L.G.G. conceived of the presented ideas. A.A.G. is the main developer of the model. D.D.L., D.L.M. and S.J.N. helped develop and validate parts of the model. D.D.L., D.L.M. and O.A. performed the computations. D.L.M. and L.G.G. encouraged and supervised the findings of this work. All authors discussed the results and contributed to the final manuscript. All authors have read and agreed to the published version of the manuscript. Funding: This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. This research was also partially supported by LLNL Strategic Initiative project number 20-SI-006. Institutional Review Board Statement: This document was reviewed and released by Lawrence Livermore National Laboratory with a release number of LLNL-JRNL-824266. Informed Consent Statement: Not applicable. Data Availability Statement: Processed Aeolus model data used in support of the analyses in this paper will be available at ftp://gdo148.ucllnl.org/pub/aeolus-les (accessed on 1 October 2020). Acknowledgments: We acknowledge Andy Cook and Mindy Cook for their contribution of Miranda simulation results used to initialize the Dixie cloud rise simulations. Conflicts of Interest: The authors declare no conflict of interest.

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