Spectra of concentration fluctuations: The two time scales of a meandering plume

The integral time scale, T_C, of the concentration fluctuations in a narrow, meandering (intermittent) plume can be much less than the time scale, T_E, of the turbulence in which the plume is immersed, and is generally of the same order of magnitude as the time required for the plume to pass once over a receptor. However the total concentration fluctuation variance is equally strongly influenced by the larger time scale, T_E, associated with meandering caused by ambient turbulence. It is shown that observed energy spectra of concentration fluctuations can be fitted by a linear combination of two Markov spectra, one with the time scale of the meandering motions and another with the time scale of the small scale plume motions. The two components are weighted by I and 1 − I, respectively, where I is the intermittency or fraction of time that non-zero concentrations occur.     

On plume meandering in unstable stratification

Vertical plume meandering of gaseous pollutant is commonly experienced in the daytime atmospheric boundary layer (also know as convective boundary layer, CBL) that arose from the complicated interaction between buoyancy-generated turbulence and gravitational force. It leads to rapid pollutant mixing that cannot be accurately modeled by conventional Gaussian plume model. In the light of explaining the mechanism of plume rises and descents in CBLs, this study employs a direct numerical simulation (DNS) technique to compute the plume behaviors for pollutant emitted from line sources placed parallel to the spanwise direction in an unstably stratified turbulent open channel flow. The DNS results show that the plume meandering is due to the domination of uni-directional mean vertical pollutant fluxes above and below the mean plume height.     

A fluctuating plume model for concentration fluctuations in a plant canopy

A one-particle Lagrangian model for continuous releases in the non-Gaussian inhomogeneous turbulence of a canopy layer is derived based on the fluctuating plume model of Franzese [2003. Lagrangian stochastic modeling of a fluctuating plume in the convective boundary layer. Atmos. Environ. 37, 1691–1701.]. The model equations are filtered by a time-dependent low-pass filter applied to the turbulent kinetic energy in order to obtain a fluctuating plume model able to simulate the vertical meandering of the cloud centroid through non-stationary Lagrangian equations. The model satisfies the well-mixed condition. The relative dispersion of particles and the concentration fluctuation statistics of a passive tracer inside a modeled vegetal canopy are studied. The probability density function of the concentration relative to the plume centroid is parameterized and the mean and variance fields of concentration are simulated and compared with wind-tunnel data and numerical simulations. A skewed, reflected probability density function for the vertical position of the plume centroid is considered.     

Intermittency and conditionally-averaged concentration fluctuation statistics in plumes

A semi-empirical Gaussian plume model is developed which predicts the intermittency factor, and the mean and variance of the non-zero time varying concentration in the plume from a point source. Wind tunnel data are used to verify the theory and to set the empirical constants. Conditionally averaged concentration fluctuation variance, which has zero concentrations removed, is only weakly dependent on source size, while intermittency caused by plume meandering is shown to be strongly dependent on source size. The resulting closed form predictions are presented in a form suitable for estimating risk of exposure to peak concentrations.     

A simple and fast model to compute concentration moments in a convective boundary layer

Recently, a modified meandering plume model for concentration fluctuations in a convective boundary layer has been formulated (Atmos. Environ. 34 (2000) 3599). This model is based on a hybrid Eulerian–Lagrangian approach and it accounts for the skewed and inhomogeneous turbulence characteristics of the convective flow. Using the same hypotheses, but eliminating the need for Lagrangian particle model, we propose a generalised approach, that only requires the knowledge of mean concentration field. The proposed model is independent from the method used to obtain the mean concentration field. The evaluation of the concentration fluctuation field needs a computational time of only few seconds on a standard PC. Therefore, the model is suitable for practical applications.     

Plume behaviors observed using lidar and SF6 tracer at a flat and hilly site

Two field experiments, one at Kincaid, IL, in flat terrain, the other at Bull Run, TN, in rolling terrain, were conducted under the auspices of the Electric Power Research Institute's (EPRI) Plume Model Validation and Development program. Simultaneous observations were made of ground-level SF₆ concentrations; plume cross-sections using light detection and ranging (lidar); turbulence; and routine meteorology at the surface and aloft. Due to terrain influences, surface wind-speeds at the Bull Run site were significantly lower than those at the Kincaid site, whereas thermal winds at Kincaid were generally larger than at Bull Run. At both sites, a reduction in turbulent intensity and an increase in atmospheric stability with height correlate with a substantial decrease in the rate of vertical plume dispersion. SF₆ ground-level concentration (GLC) patterns over distances of 1–50 km from the source were categorized by shape. The GLC patterns at Bull Run were frequently ‘blobby’, when significant GLCs occurred over an azimuth angle exceeding 90°, whereas patterns at Kincaid were generally coherent and nearly elliptical. Plume behavior was examined for 154 h during which both GLCs of SF₆ tracer and lidar cross-sections of the plume were of good quality. Results show that plume looping was rare at Kincaid, but occurred substantially more often at Bull Run (3%: 14%), with the reverse true for meandering (11%: 14%). Inversions that trapped plume material occurred much more often at Kincaid that at Bull Run (11%: <1%). Correlation of cross-wind concentration distributions of the plume aloft with those cross-wind SF₆ concentrations distributions at the ground were poor at both sites.     

Validation studies of turbulence closure schemes for high resolutions in mesoscale meteorological models – A case of gas dispersion at the local scale

This work is a contribution to a large project, aimed at the development of an advanced environmental assessment modelling system to be used in Japan. The modelling system here considered consisted of the RAMS and HYPACT coupled models. The RAMS code was modified to properly simulate local scale phenomena using a fine mesh size of 250 m. In this direction, the main aim here was to investigate the effect of the choice of the turbulence closure scheme on the dispersion of pollutants. Our modified version of the RAMS/HYPACT model chain was validated using field experiments which were carried out by the Japan Atomic Energy Research Institute (JAERI) in the area of Mt. Tsukuba (Japan). The mean flow, turbulence and concentration fields obtained using two alternative turbulence closure schemes are compared. A discussion on the different performances of the turbulence closures is presented and the influence of the closure schemes over the plume dispersion is investigated.     

Experiments on vertical transverse mixing in a large-scale heterogeneous model aquifer

Vertical transverse mixing is known to be a controlling factor in natural attenuation of extended biodegradable plumes originating from continuously emitting sources. We perform conservative and reactive tracer tests in a quasi two-dimensional 14 m long sand box in order to quantify vertical mixing in heterogeneous media. The filling mimics natural sediments including a distribution of different hydro-facies, made of different sand mixtures, and micro-structures within the sand lenses. We quantify the concentration distribution of the conservative tracer by the analysis of digital images taken at steady state during the tracer-dye experiment. Heterogeneity causes plume meandering, leading to distorted concentration profiles. Without knowledge about the velocity distribution, it is not possible to determine meaningful vertical dispersion coefficients from the concentration profiles. Using the stream-line pattern resulting from an inverse model of previous experiments in the sand box, we can correct for the plume meandering. The resulting vertical dispersion coefficient is approximately approximately 4 x 10(-)(9) m(2)/s. We observe no distinct increase in the vertical dispersion coefficient with increasing travel distance, indicating that heterogeneity has hardly any impact on vertical transverse mixing. In the reactive tracer test, we continuously inject an alkaline solution over a certain height into the domain that is occupied otherwise by an acidic solution. The outline of the alkaline plume is visualized by adding a pH indicator into both solutions. From the height and length of the reactive plume, we estimate a transverse dispersion coefficient of approximately 3 x 10(-)(9) m(2)/s. Overall, the vertical transverse dispersion coefficients are less than an order of magnitude larger than pore diffusion coefficients and hardly increase due to heterogeneity. Thus, we conclude for the assessment of natural attenuation that reactive plumes might become very large if they are controlled by vertical dispersive mixing.     

Comparison of PDFs, closure schemes and turbulence parameterisations in Lagrangian stochastic models

Six one-dimensional models, based on the Ito-type stochastic equation, are presented and compared. Four of these take into account up to the fourth order moment of vertical velocity fluctuations, and two up to the third order moment. Four models make use of a bi-Gaussian probability density function (PDF) and the other two are based on a Gram-Charlier series expansion truncated to the third or fourth order. All the models were run with a parameterisation of input turbulence (i.e. w², w³, and τ profiles). Concerning the fourth order moment w⁴, two different parameterisations were considered. Comparisons are made between ground-level concentrations, plume height and plume width observed in the Willis and Deardorff water tank experiments and those predicted by the different models here considered. The goal of this study was to find the models that give greater confidence in their applicability in dispersion studies and to verify the importance of considering the fourth order moment. The main conclusions are: simulation results largely depend on the turbulence parameterisation chosen; the Gram-Charlier PDF gives the best agreement with observations; some combinations of models and turbulence parameterisations perform well in simulating the shape of the ground-level concentration (g.1.c.) trend but fail in correctly simulating the form of the plume (plume height and vertical width); in the case of the Gram-Charlier PDF, the fourth order model reproduced the vertical plume width better than the third order one, whereas the two schemes yielded similar g.1.c. distributions.     

Simulation of large particle transport near the surface under stable conditions: comparison with the Hanford tracer experiments

A plume model is presented describing the downwind transport of large particles (1–100 μm) under stable conditions. The model includes both vertical variations in wind speed and turbulence intensity as well as an algorithm for particle deposition at the surface. Model predictions compare favorably with the Hanford single and dual tracer experiments of crosswind integrated concentration (for particles: relative bias=−0.02 and 0.16, normalized mean square error=0.61 and 0.14, for the single and dual tracer experiments, respectively), whereas the US EPA's fugitive dust model consistently overestimates the observed concentrations at downwind distances beyond several hundred meters (for particles: relative bias=0.31 and 2.26, mean square error=0.42 and 1.71, respectively). For either plume model, the measured ratio of particle to gas concentration is consistently overestimated when using the deposition velocity algorithm of Sehmel and Hodgson (1978. DOE Report PNL-SA-6721, Pacific Northwest Laboratories, Richland, WA). In contrast, these same ratios are predicted with relatively little bias when using the algorithm of Kim et al. (2000. Atmospheric Environment 34 (15), 2387–2397).     

A Theory of Plume Rise Compared with Field Observations

A theory for the rise of a plume in a horizontal wind is proposed in which it is assumed that, for some distance downwind of a high stack, the effects of atmospheric turbulence may be ignored in comparison with the effects of turbulence generated by the plume. The theory, an extension of the local similarity ideas used by Morton, Taylor, and Turner,¹ has two empirical parameters which measure the rate that surrounding fluid is entrained into the plume. Laboratory measurements of buoyant plume motion in laminar unstratified cross flow are used to estimate the empirical parameters. Using this determination of the parameters in the theory, the trajectories of atmospheric plumes may be predicted. To make such a prediction, the observed wind velocity and temperature as functions of altitude, and flow conditions at the stack orifice, are used in numerically integrating the equations. The resulting trajectories are compared with photographs, made by Leavitt, et al.,² of TVA, of plumes from 500 to 600 ft high stacks. Within 10 stack heights downwind of the stack, the root mean square discrepancy between the observed height of the trajectory above ground level and the theoretical value is 14%, which is about the uncertainty in the observed height. The maximum plume rise within the field of observation is within 15% of that predicted by the present theory.     

Monte Carlo simulation of nitrogen oxides dispersion from a vehicular exhaust plume and its sensitivity studies

The pollutant dispersion behavior from the vehicular exhaust plume has a direct impact on human health, particularly to the drivers, bicyclists, motorcyclists, pedestrians, people working nearby and vehicle passengers. A two-dimensional pollutant dispersion numerical model was developed based on the joint-scalar probability density function (PDF) approach coupled with a k–ε turbulence model to simulate the initial dispersion process of nitrogen oxides, temperature and flow velocity distributions from a vehicular exhaust plume. A Monte Carlo algorithm was used to solve the PDF transport equations in order to obtain the dispersion distribution of nitrogen oxides concentration. The model was then validated by a series of sensitivity experimental studies in order to assess the effects of vehicular exhaust tailpipe velocities, wind speeds and chemistry on the initial dispersion of NO and NO₂ mass concentrations from the vehicular exhaust plume. The results show that the mass concentrations of nitrogen oxides decrease along the centerline of the vehicular exhaust plume in the downstream distance. The dispersion process can be enhanced when the vehicular exhaust tailpipe velocity is much larger than the wind speed. The oxidation reaction of NO plays an important role when the wind speed is large and the vehicular exhaust exit velocity is small, which leads to chemical reduction of NO, and the formation and accumulation of NO₂ in the exhaust plume. It is also found that the effect of vehicular exhaust-induced turbulence in the vicinity of the exhaust tailpipe exit is more dominant than the effect of wind turbulence, while the wind turbulence gradually shows a significant role for the dispersion of nitrogen oxides along with the development of exhaust plume. The range of dispersion of nitrogen oxides in the radial direction is increased along with the development of vehicular exhaust plume.     

The Oxidation of Hydrocarbons on Simple Oxide Catalysts

A simple practical scheme for prediction and control of short duration air pollution maxima from a single source is demonstrated for a particular source-site geometry. The method makes use of a number of traditional semi-empirical atmospheric turbulence and diffusion relations in a different application. The concepts stressed in the current example are: (1) the incorporation of interactions of high frequency turbulence and low frequency meandering of the wind into a concentration forecast and (2) the use of source-site geometry to simplify the practical problem as much as possible.     

Integral model of dense gas plume dispersion

The injection of a dense gas stream at ground level into a flowing turbulent atmosphere produces a wide, flat plume that entrains air primarily through its upper surface. A quasi-one-dimensional flow model of an isothermal dense gas plume is developed for the purpose of comparing experiments in wind tunnels and water flumes and field tests in the atmosphere. Comparisons are made for plume width, including the width at the source, and centerline ground plane source gas concentration. All published data are used in this comparison, which cover a factor of about 100 in plume length scale and Reynolds number. Tests conducted by different experimenters were found not to be dynamically similar. Dimensionless model parameters, all of order unity, are selected to give the best agreement among all the experimental data. The dependence of entrainment rate on the plume Richardson number, a key feature of the model, is confirmed in the comparison. The entrainment rate parameter is found to be larger for the field tests than for the laboratory experiments, reflecting the much higher Reynolds number of the former.     

Factors controlling BTEX and chlorinated solvents plume length under natural attenuation conditions

Natural attenuation is presently used at numerous sites where groundwater is contaminated. In order to simulate this attenuation, reactive transport models are often used but they are quite complex and depend on both physical and chemical conditions in the aquifer. As complex numerical models cannot be used to study all possible cases, we develop here analytical solutions to draw general conclusions. Our strategy, called MIKSS (Mixed Instantaneous and Kinetics Superposition Sequence), allows the calculation of the concentrations of all reacting substances in a plume. It is an extension of the superimposition principle that is able to treat the case of joint kinetics and instantaneous reactions. The basic equations have been extended to treat different reactions that occur in the plume core and at its fringe. At first we consider one organic substance degraded under all oxidising conditions (toluene for instance). For this problem the size of the plume depends on the reduced source width and on the ratio of the organic substance concentration to the sum of the electron acceptors' concentrations. For several BTEX substances having different degradation behaviour the formulation is similar, but leads to quite different plume lengths for each substance. Contrary to the case of one substance, the plumes can be quite long and may not satisfy the target risk level. For chlorinated solvents we developed a specific approach to take under consideration all reactions and particularly the competition for hydrogen. A formula is given to assess the size of the plume core, i.e. the zone with highly reducing conditions. The factors influencing the core length are the same as for BTEX (source width, dispersivity, organic carbon content). The size of the TCE plume is calculated from the plume core length and the kinetic constant of TCE degradation. Using assumptions of degradation constants for DCE and VC it is also possible to calculate the longitudinal concentration profile of these substances. The degradation of moderately substituted solvents under oxic conditions reduces the size of their plumes but under these conditions TCE becomes the major threat. Among the conditions studied in this paper, very few chlorinated solvents sites can lead to a negligible risk at an acceptable distance from the source.     

Applied dispersion modelling based on meteorological scaling parameters

A method for calculating the dispersion of plumes in the atmospheric boundary layer is presented. The method is easy to use on a routine basis. The inputs to the method are fundamental meteorological parameters, which act as distinct scaling parameters for the turbulence. The atmospheric boundary layer is divided into a number of regimes. For each scaling regime we suggest models for the dispersion in the vertical direction. The models directly give the crosswind-integrated concentrations at the ground, x_y, for nonbuoyant releases from a continuous point source. Generally the vertical concentration profile is proposed to be other than Gaussian. The lateral concentration profile is always assumed to be Gaussian, and models for determining the lateral spread σ_y are proposed. The method is limited to horizontally homogeneous conditions and travel distances less than 10km. The method is evaluated against independent tracer experiments over land. The overall agreement between measurements and predictions is very good and better than that found with the traditional Gaussian plume model.     

Wind-tunnel study of entrainment in two-dimensional dense-gas plumes at the EPA's fluid modeling facility

This wind-tunnel study has been conducted as part of a collaborative effort to investigate the effect of large surface roughness on the entrainment of air from a neutrally stable simulated atmospheric boundary layer into a continuous dense-gas plume. The present study examined the entrainment rates of dense-gas plumes as they were transported over two surfaces with similar geometry but significantly different roughness lengths (factor of 6). Extensive measurements of the flow and plume structures over a wide range of source Richardson numbers (Ri*) are reported. Carbon dioxide was released from a two-dimensional source in order to obtain a plume with virtually constant Ri*. Over the small roughness, the plume depths were generally large compared with the element heights, whereas over the large roughness, plume depths were comparable with the element heights. Retardation of mean velocities in the lower levels of the dense plumes (with compensating increases in the upper levels) was observed, as well as strong suppression of turbulence over quite large fractions of the boundary-layer depth. These effects increased as Ri* increased. Propagation of dense gas was observed upstream of the source due to gravity spreading. The flow within the plumes was observed to become laminar at the larger Ri*. The primary measurements comprised longitudinal surface concentration profiles. Where the plumes were fully turbulent, the plots of inverse concentration versus downwind distance formed reasonably straight lines. The sought-after entrainment velocities are proportional to the slopes of these lines and were found to diminish quite rapidly with Ri*. More in-depth analyses and intercomparisons with the results of the other laboratories are contained in a companion paper in this same volume (Briggs et al., 2001, Atmospheric Environment 35, 2265–2284).     

Atmospheric dispersion in the presence of a three-dimensional cubical obstacle: Modelling of mean concentration and concentration fluctuations

This paper presents computational simulations of atmospheric dispersion experiments conducted around isolated obstacles in the field. The computational tool used for the simulations was the code ADREA-HF, which was especially developed for the simulation of the dispersion of positively or negatively buoyant gases in complicated geometries. The field experiments simulated involve a single cubic obstacle normal to the mean wind direction and two upwind sources of ammonia and propane, with the ammonia source located at different lateral positions [Mavroidis, I., Griffiths, R.F., Hall, D.J., 2003. Field and wind tunnel investigations of plume dispersion around single surface obstacles. Atmospheric Environment 37, 2903–2918]. Concentrations and concentration fluctuations for both gases were calculated by the model and compared with the experimental results. Certain modelling aspects were studied, such as the effect of using different turbulence closure schemes in the computations. Furthermore, specific characteristics of dispersion were investigated using the computational tool, such as the effect of the lateral displacement of a source on the concentration fluctuations intensity, the effects of natural variability and the sensitivity of concentrations to wind direction fluctuations. The results showed a good level of agreement between calculated and measured concentrations and concentration fluctuations when ensemble averaged data were available from the field experiments. Differences observed between measured and predicted concentrations and concentration fluctuations, in the case of laterally displaced sources, were mainly attributed to the specificities of the experimental cases, such as the interaction of a laterally displaced plume with an obstacle, and to the variability observed in the field. The effect of this variability is indicated by the difference between the predicted-to-observed ratios of ensemble-averaged centreline values for propane and the respective ratios from the single ammonia experiment with co-located gas sources, the latter being higher by upto 30% for concentrations and 70% for concentration fluctuations. Using the computational tool it was shown that, for a laterally displaced source, a change of 5° in the mean wind direction can lead up to a 100% variation in the measured concentrations.     

An interpretation of Taylor's statistical analysis of particle dispersion

We interpret Taylor's equation for plume growth in homogeneous turbulence in terms that have ready intuitive and physical appeal. We show how an understanding of the physical meaning of the Lagrangian time-scale allows a simple derivation of the linear and square root growth laws, which form the basis of most plume spread parametenzations. We then go on to show how this understanding can be used to derive the commonly used expressions for the effects of wind shear on plume spread.