Simulation of the Askervein Flow. Part 1: Reynolds Averaged Navier–Stokes Equations (k ∈ Turbulence Model)

The neutrally stratified flow over the Askervein Hill was simulatedusing a terrain-following coordinatesystem and a two-equation(k - ) turbulence model. Calculations were performed on awide range of numerical grids to assess, among other things, theimportance of spatial discretization and the limitations of theturbulence model. Our results showed that a relatively coarse gridwas enough to resolve the flow in the upstream region of the hill;at the hilltop, 10 m above the ground, the speed-up was 10% lessthan the experimental value. The flow's most prominent feature wasa recirculating region in the lee of the hill, which determinedthe main characteristics of the whole downstream flow. This regionhad an intermittent nature and could be fully captured only in the caseof a time-dependent formulation and a third-order discretization ofthe advective terms. The reduction of the characteristic roughnessnear the top of the hill was also taken into account, showing theimportance of this parameter, particularly in the flow close to theground at the summit and in the downstream side of the hill.Calculations involving an enlarged area around the Askervein Hillshowed that the presence of the nearby topography affected the flowneither at the top nor downstream of the Askervein Hill.     

Study On Development And Application Of A Regional Pbl Numerical Model

A regional scale (a few km to a few hundred km, minutes to days)planetary boundary layer (PBL) numerical model (RPBLM) has been successfully developed to simulateprecisely the boundary-layer three-dimensional characteristics. The RPBLM model with a high-resolutionnon-hydrostatic E - turbulence closure scheme has been applied to diagnose and prognosticate the PBL characteristicsover a complex underlying surface in the Hong Kong area of 60 km × 48 km. It is shown that the RPBLMmodel can be used to simulate the PBL characteristics including wind, temperature, water vapour andturbulence over such a complex underlying surface and that the simulated result is reasonably in agreementwith observations.     

A k - *epsiv Turbulence Closure Model For The Atmospheric Boundary Layer Including Urban Canopy

A numerical model for the computation of the wind field,air temperature and humidity in the atmospheric boundary layer (ABL) including the urbancanopy was developed for urban climate simulation. The governing equations of the modelare derived by applying ensemble and spatial averages to the Navier–Stokes equation, continuityequation and equations for heat and water vapour transfer in the air. With the spatial averagingprocedure, effects of buildings and other urban structures in the urban canopy can be accounted for byintroducing an effective volume function, defined as the ratio between the volume of air in acomputational mesh over the total volume of the mesh. The improved k - model accounts for the anisotropyof the turbulence field under density stratification. In the improved k - model, the transportof momentum and heat in the vertical direction under density stratification is evaluated based onthe assumption of a near-equilibrium shear flow where transport effects on the stresses andheat fluxes are negligible. The heating processes at surfaces of buildings and ground are alsomodelled. The comparison of the computational results obtained with the present modeland existing observational data and numerical models shows that the present model is capableof predicting the structure of turbulence in the urban canopy layer under density stratification.Numerical experiments with the new model show that the flow behaviour of the air in the urbancanopy layer is strongly affected by the existence of buildings and density stratification.     

AN E – ε – ℓ TURBULENCE CLOSURE SCHEME FOR PLANETARY BOUNDARY-LAYER MODELS: THE NEUTRALLY STRATIFIED CASE

The standard E – model generates aplanetary boundary layerthat appears to be much too deep. The cause of theproblem is traced to the equation for the dissipationrate () of turbulent kinetic energy (E), specifically theparameterization of dissipation production anddestruction. In the context of atmosphericboundary-layer modelling, we argue that a part of thedissipation production should be modelled as the inputto the spectral cascade from the energy-containingpart of the spectrum, with a characteristic length , while the equilibrium imbalancebetween local production and destruction ofdissipation is modelled as proportional toE2/E, as in the standard model. Wepropose an E – – turbulence closurescheme, in which both the mixing length, m, and are prescribed. The importance ofthe equation is diminished, though itstill determines the dissipation rate in the Eequation.     

Gaseous and Particulate Oxidation Products Analysis of a Mixture of α-pinene + β-pinene/O3/Air in the Absence of Light and α-pinene + β-pinene/NOx/Air in the Presence of Natural Sunlight

The gas and particle phase reaction products of a mixture of the atmospherically important terpenes -pinene and -pinene with the atmospheric oxidants O₃ and OH/NO_x were investigated using both gas chromatography-mass spectrometry (GC-MS) and high performance liquid chromatography (HPLC) for identification and quantification of reaction products. The nighttime oxidation of a mixture of -pinene and -pinene in the presence of O₃/air, and the daytime oxidation of a mixture of -pinene + -pinene with NO_x air in the presence of natural sunlight were carried out in the University of North Carolina's large outdoor smog chamber (190 m³) located in Chatham County, North Carolina. Mass balances for gaseous and aerosol reaction products are reported over the course of the reaction. More than twenty-nine products were identified and/or quantified in this study. On average, measured gas and particle phase products accounted for 74 to 80% of the reacted -pinen/-pinene mixture carbon. Measurements show that a number of reaction products were found in both O₃ and NO_x system [pinonaldehyde, pinic acid, pinonic acid, pinalic-3-acid, 4-hydroxypinalic-3-acid, 4-oxonopinone, 1-hydroxy-nopinone, 3-hydroxy-nopinone, and nopinone]. Pinonic acid, pinic acid, pinalic-3-acid, 4-hydroxypinalic-3-acid, and 10-hydroxypinonic acid were observed in the early stage in the aerosol phase and may play an important role in the early formation of secondary aerosols.     

Gas and Particle Products Distribution from the Reaction of β-Caryophyllene with Ozone

Gas and particulate reaction products from the ozonolysis of -caryophyllene (I) in the presence of atmospheric air were investigated using a combination of gas chromatography-mass spectrometry (GC-MS) and high performance liquid chromatography (HPLC). A Scanning Mobility Particle Sizer system (3936, TSI) and a Condensation Particle Counter (3025A, TSI) were used to study secondary organic aerosol formation. The nighttime oxidation was carried out in a large outdoor smog chamber (190 m³). A wide range of ring retaining and ring opening products in the gas and particle phase are reported over the course of the reaction. On average, measured gas and particle phase products accounted for 64% of the reacted -caryophyllene (I) carbon. Measurements show that a number of reaction products with low vapor pressure (e.g., -caryophyllone aldehyde (IV), -norcaryophyllone aldehyde (V), -caryophyllonic acid (VIII), -14-hydroxycaryophyllonic acid (XIV)) were found in the sample taken during the first 20 min of the reaction and may play an important role in the early formation of secondary organic aerosol. A detailed mechanism is proposed to account for most products observed in this investigation.     

A LIMITED-LENGTH-SCALE k-ε MODEL FOR THE NEUTRAL AND STABLY-STRATIFIED ATMOSPHERIC BOUNDARY LAYER

Analytical and numerical models of the neutral and stably-stratifiedatmospheric boundary layer are reviewed. Theoretical arguments andcomputational models suggest that a quasi-steady state is attainable in aboundary layer cooled from below and it is shown how this may be incorporatedwithin a time-steady, one-dimensional model. A new length-scale-limitedk- model is proposed for flows where a global maximum mixing length isimposed by the finite boundary-layer depth or, in stably-stratifiedconditions, by the Obukhov length, whilst still reducing to a form consistentwith the logarithmic law in the surface layer. Simulations compare favourablywith data from the Leipzig experiment and from Cardington airfield inEngland.     

Transport-Dissipation Analytical Solutions to the E-∈Turbulence Model and their Role in Predictions of the Neutral ABL

E- turbulence model predictions of the neutralatmospheric boundary layer (NABL) are reinvestigated to determine thecause for turbulence overpredictions found in previous applications. Analytical solutions to the coupled E and equations for the case of steady balance between transport and dissipation terms, the dominant balance just below the NABL top, are derived. It is found that analytical turbulence profiles laminarizeat a finite height only for values of closure parameter ratio c ₂ /_e equal toor slightly greater than one, with laminarization as z for greater . The point = 2 is additionally foundthat where analytical turbulent length scale (l) profilesmade a transition from ones ofdecreasing ( < 2) to increasing ( > 2)values with height. Numerically predicted profiles near the NABL topare consistent with analytical findings. The height-increasingvalues of l predicted throughout the NABL with standard values ofclosure parameters thus appear a consequence of 2.5(> 2), implied by these values (c ₂ = 1.92, _{= 1.3}, _{e = 1}). Comparison of numericalpredictions with DNS data shows that turbulence overpredictions obtained with standard-valued parameters are rectifiedby resetting and _e to 1.1 and 1.6, respectively, giving, with c ₂ = 1.92, 1.3, and laminarization of the NABL's cappingtransport-dissipation region at a finite height.     

Modification Of The Standard ∈-Equation For The Stable Abl Through Enforced Consistency With Monin–Obukhov Similarity Theory

A condition is derived for consistency of the standard-equation with Monin–Obukhov (MO) similarity theory of thestably-stratified surface layer. The condition is derivedby extending the procedure used to derive the analogous condition forneutral theory to stable stratification. It is shown that consistencywith MO theory requires a function of flux Richardson number, Ri_f, to be absorbed into either of two closure parameters, c ₁ or c ₂.Inconsistency, on the other hand, results if constant values of these are maintained for all Ri_f, as is done in standardapplication of the equation, and the large overpredictions ofturbulence found in such application to the one-dimensionalstable atmospheric boundary layer (1D-SBL) are traced to thisinconsistency. Guided by this, we formulate a MO-consistent-equation by absorbing the aforementioned function intoc ₁, and combine this with a Level-2.5 second-orderclosure model for vertical eddy viscosity and diffusivities.Numerical predictions of the 1D-SBL by the modified model converge to a quasi-steady state, rectifying the predictive failure of the standard -equation for the case.Quasi-steady predictions of non-dimensional variables agree stronglywith Nieuwstadt's theory. Qualitative accuracy of predictionsis inferred from comparisons to field data, large-eddy simulationresults and Rossby-number similarity relationships.     

Partitioning of Semivolatile Organic Compounds in the Presence of a Secondary Organic Aerosol in a Controlled Atmosphere

The gas-particle partitioning of select semivolatile organic compounds (SOCs) was studied by injecting the SOCs into a 190 m3 Teflon film chamber containing a secondary organic aerosol (SOA) generated by volatilizing liquid -pinene into an ozone-concentrated atmosphere. The concentration of total suspended particulates (TSP) and gas and particle-phase SOCs was measured over the course of three experiments spanning a temperature range of 268–297 K and a relative humidity range of 55–100%. An equilibrium partition coefficient, Kp, was calculated for each sampling event. Empirical relationships were then developed to predict the partitioning of the SOCs on the SOA particle source as a function of temperature. Partitioning in this SOA system was compared to that of a SOA generated by the photochemical reaction of NOx with m-xylene. The results indicate that partitioning is similar between the two SOA systems. The effects of multiple particle sources on partitioning was also examined, revealing that a weighted average of predicted Kp values for individual sources can be used to predict partitioning in aerosol mixtures.     

Gas and Particulate Products Distribution from the Photooxidation of α-Humulene in the Presence of NOx, Natural Atmospheric Air and Sunlight

The photooxidation of -humulene in the presence of NO_x, natural sunlight, and rural background air was investigated using a combination of gas chromatography-mass spectrometry (GC-MS) and high performance liquid chromatography (HPLC). Identification and quantification of gas and particulate reaction products were reported over the course of the reaction. The daytime photooxidation was carried out in a large outdoor smog chamber (190 m³). A wide range of ring retaining and ring opening products in the gas and particle phase are reported. On average, measured gas and particle phase products accounted for 44% of the reacted -humulene carbon. Measurements show that a number of reaction products with low vapor pressures (e.g. 3-seco--humulone aldehyde, 7-seco--humulone aldehyde, -humulal aldehyde, -humulene 3-oxide or -humulene 7-oxide, -humulaic/alic acid isomers, and 3-seco--14-hydroxyhumulone aldehyde) were found in the early stage of the reaction and may play an important role in the early formation of secondary organic aerosol. A detailed mechanism is proposed to account for most products observed in this investigation.     

Mass Balance of Gaseous and Particulate Products from β-Pinene/O3/Air in the Absence of Light and β-Pinene/NOx/Air in the Presence of Natural Sunlight

The gas and particle phase products from the reaction of -pinene with the atmospheric oxidants O₃ and OH radicals in the presence of NO_x were investigated using both gas chromatography-mass spectrometry (GC-MS) and high performance liquid chromatography (HPLC) for identification and quantification of reaction products. The nighttime oxidation of -pinene in the presence of O₃/air and the daytime oxidation of -pinene in the presence of NO_x/air and natural sunlight were carried out in the University of North Carolina large outdoor smog chamber (190 m³) located in Chatham County, North Carolina. A Scanning Mobility Particle Sizer system (3936, TSI) and a Condensation Particle Counter (3025A, TSI) were used to study the secondary organic aerosol (SOA) formation, and a filter pack/denuder sampling system was used for simultaneously collecting gas and particle phase products for analysis. A gas chromatograph coupled to a mass spectrometer (GC-EIMS or GC-CIMS) was used for the identification and quantification of gas and aerosol products. A HPLC method was used for the measurement of small carbonyl compounds (aldehydes and ketones) as their 2,4-dinitrophenylhydrazones (DNPH) derivatives. Mass balances for gaseous and aerosol reaction products were reported over the course of the reaction. More than sixteen products were identified and/or quantified in this study. On average, measured gas and particle phase products accounted for 57 to 71% of the reacted -pinene carbon. Measurements showed that a number of reaction products were found in both O₃ and NO_x systems (pinic acid, pinalic-3-acid, 4-hydroxypinalic-3-acid, 4-oxonopinone, 1-hydroxynopinone, 3-hydroxynopinone, and nopinone). Pinic acid, pinalic-3-acid, and 4-hydroxypinalic-3-acid were observed in the early stage in the aerosol phase and may play an important role in the early formation of secondary aerosols. Detailed reaction schemes are presented to account for most of the observed reaction products.     

Laboratory Kinetic Studies of the Reactions of Cl Atoms with Species of Biogenic Origin: δ3-Carene, Isoprene, Methacrolein and Methyl Vinyl Ketone

The rate coefficients for the reaction between atomic chlorine and a number of naturally occurring species have been measured at ambient temperature and atmospheric pressure using the relative rate technique. The values obtained were (4.0 ± 0.8) × 10^-10, (2.1 ± 0.5) × 10^-10, (3.2 ± 0.5) × 10^-10, and (4.9 ± 0.5) × 10^-10 cm³ molecule^-1 s^-1, for reactions with isoprene, methyl vinyl ketone, methacrolein and ³-carene, respectively. The value obtained for isoprene compares favourably with previously reported values. No values have been reported to date for the rate constants of the other reactions.     

Further Studies Of Atmospheric Turbulence In Layers Near The Surface: Scaling The Tke Budget Above The Roughness Sublayer

The second of two experimental studies of the TKE budget conducted on sites of different roughness is described, and results are compared. The first took place within a shallow layer above a small field of mostly bare, cultivated soil; the second was carried out above a roughness sublayer of significant depth on an extensive plain of tall dry grass. Budget terms observed in the second study were scaled with a modified u which compensated for effects of an unusually large stress gradient and ensured that the _m functions would be collinear. By showing that the modification becomes negligible in smaller gradients, it is demonstrated that in normal conditions, budgets observed above significant roughness sublayers should be normalized by scaling in terms of the unreduced Reynolds stress at the sublayer's upper surface. This procedure is shown to be consistent with the expectation that TKE budgets in layers near the surface all scale in fundamentally the same way.Other findings include: (1) the fact that most _m functions previously reported are not quite collinear is attributed to a type of overspeeding known to affect three-cup anemometers; (2) revised _m functions, collinear and largely free of the effects of overspeeding, are determined from a well-established characteristic of the linear _m relation for the stable case; (3) data that define collinear _m functions can also be represented with single hyperbolic curves; (4) dissipation is found to be 10 to 15% too small to balance total TKE production in unstable and neutral conditions and to decrease with increasing z/L in thestable regime; and (5) new relations for based on the observed behaviour of the dissipation deficit provide an improved closure for the set of equations that express the budget terms as functions of _m and z/L.     

Ly(α) absorption cross-section of H2O and O2

The absorption cross-sections of water vapor and oxygen were measured, using a low-pressure radio frequency discharge through traces of hydrogen in argon as a light source for Ly() radiation. The cross-sections are H₂O = 1.59 × 10^–17 cm² and O₂ = 1.13 × 10^–20 + 1.72 × 10^–23 for water and oxygen, respectively, where P is the oxygen pressure in units of Torr. Ly() lamps, such as used for this work, are important light sources for photochemical laboratory work and find applications for trace-gas detection in the atmosphere. For the latter application, accurate cross-sections of water vapor and oxygen are needed.     

A Prediction System for Local Wind Variations in Mountainous Terrain

A three-level model system for the prediction of local flows in mountainous terrain is described. The system is based upon an operational weather prediction model with a horizontal grid spacing of about 10 km. The large-scale flow is transformed to a more detailed terrain, first by a mesoscale model with grid spacing of about 1 km, and then by a local-scale model with a grid spacing of about 0.2 km. The weather prediction model is hydrostatic, while the two other models are non-hydrostatic. As a case study the model system has been applied to estimate wind and turbulence over Várnes airport, Norway, where data on turbulent flight conditions were provided near the runway. The actual case was chosen due to previous experiences, which indicate that south-easterly winds may cause severe turbulence in a region close to the airport. Local terrain induced turbulence seems to be the main reason for these effects. The predicted local flow in the actual region is characterized by narrow secondary vortices along the flow, and large turbulent intensity associated with these vortices. A similar pattern is indicated by the sparse observations, although there seems to be a difference in mean wind direction between data and predictions. Due to fairly coarse data for sea surface temperature, errors could be induced in the turbulence damping via the Richardson number. An adjustment for this data problem improved the predictions.     

Numerical simulation of flow data over two-dimensional hills

We have studied a neutrally-stratified flow over two-dimensional hills using a two-dimensional, non-hydrostatic version of the Regional Atmospheric Modeling System (RAMS). We have implemented three different turbulence closure models: the standardE- model, an Algebraic Reynolds Stress Model (ARSM) and a new model. Model predictions for the mean and turbulence flows using different closure schemes are compared with the data of a wind tunnel experiment containing isolated two-dimensional hills of varying slope. From the comparison, it is concluded that all three models predict the mean flow velocities equally well while only the new closure model accurately predicts the turbulence data statistics.The research reported in this paper was conducted while the first author held a National Research Council (NRC) Associateship.     

The Effect of Vegetation Density on Canopy Sub-Layer Turbulence

The canonical form of atmospheric flows near theland surface, in the absence of a canopy, resembles a rough-wallboundary layer. However, in the presence of an extensive and densecanopy, the flow within and just above the foliage behaves as aperturbed mixing layer. To date, no analogous formulation existsfor intermediate canopy densities. Using detailed laser Dopplervelocity measurements conducted in an open channel over a widerange of canopy densities, a phenomenological model that describesthe structure of turbulence within the canopy sublayer (CSL) isdeveloped. The model decomposes the space within the CSL intothree distinct zones: the deep zone in which the flow field isshown to be dominated by vortices connected with vonKármán vortex streets, butperiodically interrupted by strong sweep events whose features areinfluenced by canopy density. The second zone, which is near thecanopy top, is a superposition of attached eddies andKelvin–Helmholtz waves produced by inflectional instability in themean longitudinal velocity profile. Here, the relative importanceof the mixing layer and attached eddies are shown to vary withcanopy density through a coefficient . We show that therelative enhancement of turbulent diffusivity over its surface-layer value near the canopy top depends on the magnitude of. In the uppermost zone, the flow follows the classicalsurface-layer similarity theory. Finally, we demonstrate that thecombination of this newly proposed length scale and first-orderclosure models can accurately reproduce measured mean velocity andReynolds stresses for a wide range of roughness densities. Withrecent advancement in remote sensing of canopy morphology, thismodel offers a promising physically based approach to connect theland surface and the atmosphere without resorting to empiricalmomentum roughness lengths.     

Note on the Growth Rate of Water Waves Propagating at an Arbitrary Angle to the Wind

The dependence of the turbulent airflow over water waves on the angle,, between mean wind and wavedirections is investigated. To this end,an existing semi-analytical model is extended. In this model, the main simplification of the problem is obtained by using the well-established divisionof the wave boundary layer into inner and outer regions for modelling turbulence. The effect of waves on turbulence is restricted to the thin inner region. Simulations show that the influence of the wind speed component transverse to the wave direction on the air flow, and hence on the growth rate of the waves, is small. This is confirmed by calculations with a numerical model that solves the full Reynolds equations using a second-order turbulence closure scheme. The growth rate of slowly moving waves (as compared to the wind speed) is then proportional to cos², whereas, for faster waves, it has a narrower angular distribution.     

A Mixed Spectral-Integration Model for Neutral Mean Wind Flow Over Hills

A linear model for neutral surface-layer flow over orography is presented. The Reynolds-Averaged Navier-Stokes and E– turbulence closure equations are expressed in a terrain-following coordinate system created from a simple analytical expression in the Fourier domain. The perturbation equations are solved spectrally horizontally and by numerical integration vertically. Non-dimensional solutions are stored in look-up tables for quick re-use. Model results are compared to measurements, as well as other authors’ flow models in three test cases. The model is implemented and tested in two-dimensional space; the equations for a full three-dimensional version are presented.