Comparison of Wind-tunnel and Water-channel Simulations of Plume Dispersion through a Large Array of Obstacles with a Scaled Field Experiment

We report on measurements of the near-field dispersion of contaminant plumes in a large array of building-like obstacles at three scales; namely, at full-scale in a field experiment, at 1:50 scale in a wind-tunnel simulation, and at 1:205 scale in a water-channel simulation. Plume concentration statistics extracted from the physical modelling in the wind-tunnel and water-channel simulations are compared to those obtained from a field experiment. The modification of the detailed structure of the plume as it interacts with the obstacles is investigated. To this purpose, measurements of the evolution of the mean concentration, concentration fluctuation intensity, concentration probability density function, and integral time scale of concentration fluctuations in the array plume obtained from the field experiment and the scaled wind-tunnel and water-channel experiments are reported and compared, as well as measurements of upwind and within-array velocity spectra. Generally, the wind-tunnel and water-channel results on the modification of the detailed plume structure by the obstacles were qualitatively similar to those observed in the field experiments. However, with the appropriate scaling, the water-channel simulations were able to reproduce quantitatively the results of the full-scale field experiments better than the wind-tunnel simulations.     

Application of a Bivariate Gamma Distribution for a Chemically Reacting Plume in the Atmosphere

The joint concentration probability density function of two reactive chemical species is modelled using a bivariate Gamma distribution coupled with a three-dimensional fluctuating plume model able to simulate the diffusion and mixing of turbulent plumes. A wind-tunnel experiment (Brown and Bilger, J Fluid Mech 312:373–407, 1996), carried out in homogeneous unbounded turbulence, in which nitrogen oxide is released from a point source in an ozone doped background and the chemical reactions take place in non-equilibrium conditions, is considered as a test case. The model is based on a stochastic Langevin equation reproducing the barycentre position distribution through a proper low-pass filter for the turbulence length scales. While the meandering large-scale motion of the plume is directly simulated, the internal mixing relative to the centroid is reproduced using a bivariate Gamma density function. The effect of turbulence on the chemical reaction (segregation), which in this case has not yet attained equilibrium, is directly evaluated through the covariance of the tracer concentration fields. The computed mean concentrations and the O₃–NO concentration covariance are also compared with those obtained by the Alessandrini and Ferrero Lagrangian single particle model (Alessandrini and Ferrero, Physica A 388:1375–1387, 2009) that entails an ad hoc parametrization for the segregation coefficient.     

A Comparison Of The Detailed Structure In Dispersing Tracer Plumes Measured In Grid-Generated Turbulence With A Meandering Plume Model Incorporating Internal Fluctuations

A meandering plume model that explicitly incorporatesinternal fluctuations has been developed and used to model the evolutionof concentration fluctuations in point-source plumes in grid turbulenceobtained from a detailed water-channel simulation. This fluctuating plumemodel includes three physical parameters: the mean plume spread in fixedcoordinates, which represents the outer plume length scale; the meaninstantaneous plume spread in coordinates attached to the instantaneousplume centroid, which represents the inner plume length scale; and, theconcentration fluctuation intensity in the meandering reference frame,which represents the in-plume fluctuation scale. These parameters arespecified in terms of a set of coupled dynamical equations that modeltheir development with downstream distance from the source. Explicitexpressions for the concentration moments of arbitrary integral orderand the concentration probability density function have been obtainedfrom the fluctuating plume model. Detailed comparisons of model predictionsagainst water-channel measurements for the first four concentrationmoments and the concentration probability distributions generally showvery good overall quantitative agreement. Exact quantitative conditions,expressed in terms of the physical parameters of the fluctuating plumemodel, have been derived for the emergence of off-centreline peaks inthe concentration variance profile. These quantitative conditions havebeen illustrated in terms of a diagram of states of the dispersing plume,and the qualitatively different regimes of plume concentration variancebehaviour on this state diagram have been identified and characterized.     

Interaction of a negatively buoyant line plume with a density interface

Laboratory experiments were carried out to investigate the interaction between turbulent line buoyant plumes and sharp density interfaces, with the aim of using the results to interpret oceanic observations pertinent to crack openings in the polar ice-cap (leads). These openings take the form of long narrow channels, and are often modeled as line bouyant plumes. The plumes descend as in a homogenoous fluid, impinge on the density interface, and then spread horizontally as gravity currents. Depending on the Richardson number , where Δb is the buoyancy jump across the interface, l_D is the half-width of the plume before the impingement and q₀is the buoyancy flux per unit length of the source, different flow patterns were identified. When Ri < 0.5, the plumes penetrate deep into the bottom layer, deflect horizontally and then spread while showing little vertical rise. When 0.6 < Ri < 5, the penetration is significant, but the fluid bounces back after entraining heavy fluid from the lower layer and then spreads horizontally above the interface as a gravity current. Appreciable mixing between this current and the lower layer was detected when Ri <1. When Ri > 10, the penetration was small and a sharp-nosed gravity current emerged some time after the impact. Measurements were made on the penetration depth, the velocities of the gravity current and the subsurface flow towards the plume, the entrainment rate and other wave parameters. Possible implications of the results for oceanic cases are also discussed.     

考虑动量和浮力通量耗散的烟气抬升解析模式

环流湍流对烟流抬升有重要的作用。本文考虑了环境湍流引起的烟流的动量和浮力通量耗散，导出了烟流抬升的控制方程，给出了烟流的轨迹方程和中性条件下热浮力烟流的终极抬升高度。在烟囱附近，轨迹方程接近2/3次律；当下风距离增大时，与2/3次律有明显偏离并逐渐变平。与外场试验资料的比较表明，本模式能较好地模拟浮力烟流的轨迹和终极高度。     

The Interference of Higher-Order Statistics of the Concentration Field Produced by Two Point Sources According to a Generalized Fluctuating Plume Model

The higher-order correlation functions for the concentrationfluctuations arising from a two-point-source configuration have beencalculated analytically within the context of the phenomenology of afluctuating plume model (viz., a meandering plume model that explicitlyincorporates internal fluctuations). Explicit expressions for thesecond-, third-, and fourth-order correlationfunctions between the concentrationfluctuations produced by two point sources are given in terms of the sourceseparation d and the five physically based parameters that define thegeneralized fluctuating plume model: namely, the absolute plume dispersion,_a, which determines the outer plume length scale; the relative plume dispersion, _r, which determines the inner plume length scale; the fluctuation intensity, i_r, in relative coordinates, which determines the internal concentration fluctuation level; the correlation coefficient, r,between the positions of the centroids of the two interfering plumes; and,the correlation coefficient, r^*, between the concentration fluctuationsof the two plumes in relative coordinates, which determines the degree ofinternal mixing of the two scalars. Furthermore, the form of the totalconcentration probability density function arising from the interferenceproduced by two point sources is presented. Predictions for the second-ordercorrelation function, , and for the total concentration probabilitydensity function have been compared with some new experimental data fora two-point-source configuration in grid turbulence generated in awater-channel simulation. These results are in good agreement with the dataand suggest that the analytical model for the second-order correlationfunction and the total concentration probability density function canreproduce many qualitative trends in the interaction of plumes from twosources.     

A one-dimensional model for the parameterization of deep convection in the ocean

A one-dimensional penetrative plume model has been constructed to parameterize the process of deep convection in ocean general circulation models (OGCMs). This research is motivated by the need for OGCMs to better model the production of deep and intermediate water masses. The parameterization scheme takes the temperature and salinity profiles of OGCM grid boxes and simulates the subgrid-scale effects of convection using a one-dimensional parcel model. The model moves water parcels from the surface layer down to their level of neutral buoyancy, simulating the effect of convective plumes. While in transit, the plumes exchange water with the surrounding environment; however, the bulk of the plume water mass is deposited at e level of neutral buoyancy. Weak upwelling around the plumes is included to maintain an overall mass balance. The process continues until the negative buoyant energy of the one-dimensional vertical column is minimized. The parameterized plume entrainment rate, which plays a central role in the parameterization, is calculated using modified equations based on the physics of entraining buoyant plumes. This scheme differs from the convective adjustment techniques currently used in OGCMs, because the parcels penetrate downward with the appropriate degree of mixing until they reach their level of neutral stability.     

Design criteria for water tank models of dispersion in the planetary convective boundary layer

Design criteria for laboratory water-analogs of clear-air penetrative convection in the atmosphere are described. Consideration is given to the range of factors relevant to modelling both turbulent penetrative convection and the dispersion of buoyant point-source plumes within the convective boundary layer. Scaling arguments based on mixed-layer and plume scaling show that at typical laboratory scales, saline convection can satisfy the requirements for modelling buoyant plume dispersion under strongly convective (light wind) conditions better than heated water tanks or wind tunnels.     

A Similarity Model for Maximum Ground-Level Concentration in a Freely Convective Atmospheric Boundary Layer

A model of buoyancy- and momentum-driven industrial plumes in a freely convective boundary layer is proposed. The development combines the Lagrangian similarity models of Yaglom for non-buoyant releases in the convective surface layer with the Scorer similarity model for industrial plumes. Constraints on the validity of the extension of Yaglom’s model to the entire convective planetary boundary layer, arrived at by consideration of Batchelor’s formulation for diffusion in an inertial subrange, are often met in practice. The resulting formulation applies to an interval of time in which the entrainment of the atmosphere by the plume is balanced by the entrainment of the plume by the atmosphere. It is argued that during this interval, both maximum plume rise and ground contact are achieved. Further examination of the physical interrelationship with the Csanady-Briggs formulation serves to consolidate the model hypotheses, as well as to simplify the derivation of maximum ground-level concentrations. Experimental evidence is presented for the validity of the model, based on Moore’s published data.     

A similarity model for maximum ground-level concentration in a freely convective atmospheric boundary layer

A model of buoyancy- and momentum-driven industrial plumes in a freely convective boundary layer is proposed. The development combines the Lagrangian similarity models of Yaglom for non-buoyant releases in the convective surface layer with the Scorer similarity model for industrial plumes. Constraints on the validity of the extension of Yaglom’s model to the entire convective planetary boundary layer, arrived at by consideration of Batchelor’s formulation for diffusion in an inertial subrange, are often met in practice. The resulting formulation applies to an interval of time in which the entrainment of the atmosphere by the plume is balanced by the entrainment of the plume by the atmosphere. It is argued that during this interval, both maximum plume rise and ground contact are achieved. Further examination of the physical interrelationship with the Csanady-Briggs formulation serves to consolidate the model hypotheses, as well as to simplify the derivation of maximum ground-level concentrations. Experimental evidence is presented for the validity of the model, based on Moore’s published data.     

The Influence Of Vertical Wind Direction Shear On Dispersion In The Convective Boundary Layer, And Its Incorporation In Coastal Fumigation Models

The mean concentration distributionwithin a plume released from a point source in the atmosphericboundary layer can be greatly influenced by the systematic turningof wind with height (i.e. vertical wind direction shear). Such aninfluence includes a deflection of the plume centroid, with anassociated shearing of the vertical plume cross-section, and anenhancement of dispersion, in the horizontal plane. Wind directionshear is normally not accounted for in coastal fumigation models,although dispersion observations with shear acting as acontrolling parameter are not uncommon. A three-dimensionalLagrangian stochastic model is used to investigate the influenceof uniform wind direction shear on the diffusion of a point-sourceplume within the horizontally homogeneous convective boundarylayer, with the source located at the top of the boundary layer.Parameterisations are developed for the plume deflection andenhanced dispersion due to shear within the framework of aprobability density function (PDF) approach, and compared with theLagrangian model results. These parameterisations are thenincorporated into two applied coastal fumigation models: a PDFmodel, and a commonly used model that assumes uniform andinstantaneous mixing in the vertical direction. The PDF modelrepresents the vertical mixing process more realistically. A moreefficient version of the PDF model, which assumes a well-mixedconcentration distribution in the vertical at large times, isapplied to simulate sulfur dioxide data from the Kwinana CoastalFumigation Study. A comparison between the model results and thedata show that the model performs much better when the wind-sheareffects are included.     

环境湍流对烟云抬升的作用

本文研究了中性层结环境中湍流对烟云抬升的连续作用。取外部湍流卷挟率正比于湍流特征速度并叠加于自身卷挟率,分析表明,即使在抬升的早期,环境湍流对弯曲烟云的路径有不可忽视的影响,并使烟云路径加速变平。电厂烟云的实测资料表明,平均抬升路径实际上不完全符合无湍流环境的三分之二规律,而与本文理论结果更为接近。 本研究也发现,最大抬升高度及其出现的下风距离都是大气湍流度的灵敏函数。据此,我们分析了几个常用抬升公式的局限性,并推荐了一种反映大气湍流度的改型公式。     

A puff model revised by Monte-Carlo method on mesoscale range

A puff model is developed in this study, which simultaneously considers the Monte-Carlo technique, the time and space changes of atmospheric parameters, multiple continuity pollutant sources, linear chemical trans-formation and removal of pollutants, and the effect of complex terrain. The continuously observed turbulent statistical quantities, Lagrangian time scales, mesoscale flow field, and mixing layer depth in the PBL in the Dianchi area in China are directly put into the model, and the diurnal variations of air pollution are forecasted, which are dominated by such mesoscale local circulations as mountain and valley breeze, land and lake breeze, and city heat island (Kunming City). The results show that in the case of inputting the same data, they are in good agreement with the experimental data, as well as with the results of the three-dimensional advection-diffusion model (TD-ADM); the diurnal variation of mesoscale local circulation results in the obvious diurnal variation of mesoscale concentration distribution patterns; the Dianchi lake (appr. 300 km2) has a considerable effect on the distribution of air pollution in the area.     

Effect of Vertical Wind Shear on Concentration Fluctuation Statistics in a Point Source Plume

Measurements of concentration fluctuation intensity, intermittency factor, and integral time scale were made in a water channel for a plume dispersing in a well-developed, rough surface, neutrally stable, boundary layer, and in grid-generated turbulence with no mean velocity shear. The water-channel simulations apply to full-scale atmospheric plumes with very short averaging times, on the order of 1–4 min, because plume meandering was suppressed by the water-channel side walls. High spatial and temporal resolution vertical and crosswind profiles of fluctuations in the plume were obtained using a linescan camera laser-induced dye tracer fluorescence technique. A semi-empirical algebraic mean velocity shear history model was developed to predict these concentration statistics. This shear history concentration fluctuation model requires only a minimal set of parameters to be known: atmospheric stability, surface roughness, vertical velocity profile, and vertical and crosswind plume spreads. The universal shear history parameter used was the mean velocity shear normalized by surface friction velocity, plume travel time, and local mean wind speed. The reference height at which this non-dimensional shear history was calculated was important, because both the source and the receptor positions influence the history of particles passing through the receptor position.     

Convective plumes in the atmospheric boundary layer as observed with an acoustic Doppler sodar

The vertical velocity field and the convective plumes in the atmospheric boundary layer have been observed during morning hours with the acoustic Doppler sounder of the C.R.P.E. A method for plume determination using acoustic soundings in the well-mixed layer is presented. Using Telford's 1970 and Manton's 1975 models, a comparison is made between the predictions of the models and the plume properties as observed by the Doppler sodar. The mean plume velocity is found to be parabolic. It is shown, restricting Monin and Obukhov similarity to conditions inside plumes and using only vertical velocity within plumes, that the observed convective plumes carry nearly sixty percent of the sensible heat flux at the top of the surface layer.     

The vertical profile of concentration fluctuations in near-surface plumes

Field experiments on concentration fluctuations have frequently measured horizontal cross-sections of fluctuation statistics through plumes at fixed heights near the surface, but have not considered the effect of height above the ground in any detail. A set of tracer experiments designed to measure vertical profiles of concentration fluctuations in plumes, with a range of source heights, is described, and profiles of statistics are presented. Considerable variation of the statistics with both source and detector height is found. Near the surface, fluctuation intensity is a minimum and the time and length scales of the fluctuations are greatly increased. Profiles are consistent with the idea that concentration fluctuations near the surface are like those higher up at a greater distance from the source. Lowering the source height reduces the fluctuation intensity at all heights, and also alters the form of the concentration PDF. Results may be explained by the reduced length scale of sheargenerated turbulence near the surface causing enhanced small-scale mixing, which rapidly smooths out much of the fine structure with the plume.     

Extension of a fluctuating plume model of tracer dispersion to a sheared boundary layer and to a large array of obstacles

Fluctuating plume models provide a useful conceptual paradigm in the understanding of plume dispersion in a turbulent flow. In particular, these models have enabled analytical predictions of higher-order concentration moments, and the form of the one-point concentration probability density function (PDF). In this paper, we extend the traditional formalism of these models, grounded in the theory of homogeneous and isotropic turbulent flow, to two cases: namely, a simple sheared boundary layer and a large array of regular obstacles. Some very high-resolution measurements of plume dispersion in a water channel, obtained using laser-induced fluorescence (LIF) line-scan techniques are utilised. These data enable us to extract time series of plume centroid position (plume meander) and dispersion in the relative frame of reference in unprecedented detail. Consequently, experimentally extracted PDFs are able to be directly compared with various theoretical forms proposed in the literature. This includes the PDF of plume centroid motion, the PDF of concentration in the relative frame, and a variety of concentration moments in the absolute and relative frames of reference. The analysis confirms the accuracy of some previously proposed functional forms of model components used in fluctuating plume models, as well as suggesting some new forms necessary to deal with the complex boundary conditions in the spatial domain.     

Some Simple Statistical Models For Relative And Absolute Dispersion

Observations of the dispersion of a contaminant plume in the atmospheric boundary layer, obtained using a Lidar, are analysed in the coordinate frame relative to the instantaneous centre of mass of the plume, as well as the absolute (or fixed) coordinate frame. The study extends the work presented in a previous article, which analysed the structure of the probability density function (pdf) of concentration within the relative coordinate frame. Firstly, the plume displacement component, or plume meander, is analysed and a simple parametric form for the pdf of the plume centreline position is suggested. This is then used to analyse the accuracy and applicability of absolute framework statistical quantities obtained by a convolution of the relative frame statistical quantity with the plume centreline pdf.