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.     

The exponential probability density function and concentration fluctuations in smoke plumes

Observations of 1-s average concentration fluctuations during two trials of a U.S. Army diffusion experiment are presented and compared with model predictions based on an exponential probability density function (pdf). The source is near the surface and concentration monitors are on lines about 30 to 100 m downwind of the source. The observed ratio of the standard deviation to the mean of the concentration fluctuations is about 1.3 on the mean plume axis and 4 to 5 on the mean plume edges. Plume intermittency (fraction of non-zero readings) is about 50%; on the mean plume axis and 10%; on the mean plume edges. A meandering plume model is combined with an exponential pdf assumption to produce predictions of the intermittency and the standard deviation of the concentration fluctuations that are within 20%; of the observations.     

Statistical characteristics of concentration fluctuations in dispersing plumes in the atmospheric surface layer

Measurements have been made of concentration fluctuations in a dispersing plume from an elevated point source in the atmospheric surface layer using a recently developed fast-response photoionization detector. This detector, which has a frequency response (–6 dB point) of about 100 Hz, is shown to be capable of resolving the fluctuation variance contributed by the energetic subrange and most of the inertial-convective subrange, with a reduction in the fluctuation variance due to instrument smoothing of the finest scales present in the plume of at most 4%.Concentration time series have been analyzed to obtain the statistical characteristics of both the amplitude and temporal structure of the dispersing plume. We present alongwind and crosswind concentration fluctuation profiles of statistics of amplitude structure such as total and conditional fluctuation intensity, skewness and kurtosis, and of temporal structure such as intermittency factor, burst frequency, and mean burst persistence time. Comparisons of empirical concentration probability distributions with a number of model distributions show that our near-neutral data are best represented by the lognormal distribution at shorter ranges, where both plume meandering and fine-scale in-plume mixing are equally important (turbulent-convective regime), and by the gamma distribution at longer ranges, where internal structure or spottiness is becoming dominant (turbulent-diffusive regime). The gamma distribution provides the best model of the concentration pdf over all downwind fetches for data measured under stable stratification. A physical model is developed to explain the mechanism-induced probabilistic schemes in the alongwind development of a dispersing plume, that lead to the observed probability distributions of concentration. Probability distributions of concentration burst length and burst return period have been extracted and are shown to be modelled well with a powerlaw distribution. Power spectra of concentration fluctuations are presented. These spectra exhibit a significant inertial-convective subrange, with the frequency at the spectral peak decreasing with increasing downwind fetch. The Kolmogorov constant for the inertial-convective subrange has been determined from the measured spectra to be 0.17±0.03.     

Recurrence statistics of concentration fluctuations in plumes within a near-neutral atmospheric surface layer

This study examines the statistical properties of the concentration derivative, , for a dispersing plume in a near-neutrally stratified atmospheric surface layer. Towards this goal, the probability density function (pdf) of , and the conditional pdf of given a fixed concentration level, , have been measured. These pdfs are found to be modeled well by a generalizedq-Gaussian (gqG) distribution with intermittency exponent,q, equal to 0.3 and 3/4, respectively. These results highlight the strong intermittency effect (patchiness) of the small-scale concentration eddy structures in the plume. The distribution of time intervals between successive high peaks in the squared derivative process, x², is found to be well approximated by a power-law distribution, implying that occurrences of these high peaks are much more clustered than would be predicted by a Poisson or shot-noise process. The results are used to improve models for the joint pdf of and , and for the expected number of upcrossings per unit time interval of a fixed concentration level that have been proposed by Kristensenet al. (1989). The predictions of the improved models are in accord with observations, and suggest that the intercorrelation between and must be explicitly incorporated if good estimates of the upcrossing intensity are to be obtained.     

Multiscaling properties of concentration fluctuations in dispersing plumes revealed using an orthonormal wavelet decomposition

The dynamical characteristics of concentration fluctuations in a dispersing plume over the energetic and inertial-convective range of scales of turbulent motion are studied using a multiscale analysis technique that is based on an orthonormal wavelet representation. It is shown that the Haar wavelet concentration spectrum is similar to the Fourier concentration spectrum in that both spectra exhibit an extensive inertial-convective subrange spanning about two decades in frequency, with a scaling exponent of -5/3. Analysis of the statistical properties (e.g., fluctuation intensity, skewness, and kurtosis) of the concentration wavelet coefficients (i.e., the concentration discrete detailed signal) suggests that the small scales are always more intermittent than the large scales. The degree of intermittency increases monotonically with decreasing scale within the inertial-convective subrange, reaching a plateau at the very small scales associated with the beginning of the near-dissipation subrange. The probability density function (pdf) of the concentration discrete detailed signal displays stretched exponential tails with an intermittency exponent (tail slope) q that increases as ^a , where is the scale or dilation and a is a power-law exponent that is dependent on downwind distance, plume height, and stratification strength with typical values in the range from about 0.25 to 0.35. It is shown that the concentration variance cascade process requires a phase coherency of eddies between different scales at the small-scale end of the inertial-convective subrange.The variation of the concentration wavelet statistics with height above the ground is investigated. The increased mean shear near the ground smooths the fine-scale plume structure for scales within the inertial-convective subrange, producing a weaker spatiotemporal intermittency in the concentration field compared to that measured higher up in the plume. The pdf of the concentration detailed signal at a fixed scale possesses less elongated tails with decreasing height z. The intermittency exponent q is found to decrease roughly linearly with increasing z.Finally, the results of the wavelet decomposition are combined to provide a conceptual model of the turbulent transport, stirring, and mixing regimes in a dispersing plume. The implications of the results for contaminant texture in a plume are discussed.     

Measurements of level-crossing statistics of concentration fluctuations in plumes dispersing in the atmospheric surface layer

The statistics of level crossings and local extremes in concentration fluctuations in plumes dispersing in the atmosphere have been investigated. A set of concentration fluctuation tracer experiments has been utilized to measure the statistical propertics of the upcrossing interval (inter-arrival time between consecutive concentration bursts), excursion duration (persistence or width of concentration bursts), and concentration amplitude (difference between the maximum and minimum concentrations between successive upcrossings) with respect to a range of concentration crossing levels. In particular, the effect of downwind distance and atmospheric stratification on the level-crossing statistics has been studied in detail. It is shown that the effect of increasing atmospheric stability on level-crossing statistics is similar to the effect of increasing distance from the source in the sense that level-crossing statistics of concentration fluctuations in stable stratification resemble those in neutral stratification, but at a greater downwind distance. It is also found that the distribution of the interval between consecutive upcrossings of a concentration level, as well as the duration of an excursion across a concentration level, can be approximated by a lognormal distribution, whereas the distribution of the concentration amplitude is best characterized by a gamma distribution. Some implications of these results for the modeling of level-crossing statistics of concentration fluctuations are discussed.     

The effect of line averaging on concentration fluctuations

The reduction in variance of concentration fluctuations due to line averaging is estimated assuming that the process is influenced by the integral distance scale, y _I , of ambient turbulence and the scaling width, W, of the time-averaged plume. An analytical formula is derived for the line-averaged variance for situations where the autocorrelogram is exponential and the point variance decreases exponentially with distance from plume centerline. Predictions of concentration fluctuation variance are compared with water tank and field data, with the result that the decrease of variance with averaging distance is well-simulated if the model parameters y _I and W are carefully chosen.     

The structure and magnitude of concentration fluctuations

This paper is concerned with the science of turbulent diffusion and not, except incidentally, with its numerous practical applications. It discusses some recent research, particularly that by the authors and their collaborators. Among the topics considered are (i) the intermittency factor, (ii) the relationship between the mean of the concentration and its variance, and (iii) the interpretation of data. The principal aim of the paper is to draw attention to some outstanding basic questions which would seem promising targets for future research. Without progress on these questions (and others), regulatory modesl of air quality will continue-inevitably-to be unreliable and hardly worth using.     

The effects of mixing and spreading on density in near-field river plumes

Water mass modification in surface-trapped, near-field river plumes is examined using a 1.5-layer reduced gravity model and a three-dimensional numerical model. Solutions to the layer model are shown to be qualitatively similar to previous observations and three-dimensional simulations of near-field plumes. Analytic analysis of the layer model demonstrates how the near-field plume is controlled by the competing processes of mixing and spreading. The two models are then used to explore the parameter space dependence of density changes within the near-field plume and their associated cross-shore length scales. Both the magnitude of density changes and their length scales are proportional to either estuarine discharge or fresh water discharge; density changes are also inversely proportional to the estuary mouth width. One surprising feature of the parameter space solutions is that the density of water exiting the near-field plume, a measure of the net dilution of the entire near-field plume, is shown to be inversely proportional to local mixing rates. This is because when local mixing is lower, the influence of plume spreading becomes greater; this spreading accelerates the plume, requiring more net mixing to bring the plume back to subcritical flow.     

Modelling of concentration fluctuations in canopy turbulence

The knowledge of the concentration probability density function (pdf) is of importance in a number of practical applications, and a Lagrangian stochastic (LS) pdf model has been developed to predict statistics and concentration pdf generated by continuous releases of non-reactive and reactive substances in canopy generated turbulence. Turbulent dispersion is modelled using a LS model including the effects of wind shear and along-wind turbulence. The dissipation of concentration fluctuations associated with turbulence and molecular diffusivity is simulated by an Interaction by Exchange with the Conditional Mean (IECM) micromixing model. A general procedure to obtain the micromixing time scale needed in the IECM model useful in non-homogeneous conditions and for single and multiple scalar sources has been developed. An efficient algorithm based on a nested grid approach with particle splitting, merging techniques and time averaging has been used, thus allowing the calculation for cases of practical interest. The model has been tested against wind-tunnel experiments of single line and multiple line releases in a canopy layer. The approach accounted for chemical reactions in a straightforward manner with no closure assumptions, but here the validation is limited to non-reacting scalars.     

The vertical structure of concentration fluctuation statistics in plumes dispersing in the atmospheric surface layer

This paper describes a study of the vertical structure of concentration fluctuations in a neutrally buoyant plume from an elevated point source in slightly convective to moderately stable meteorological conditions at ranges of between 12.5 and 100 m for a range of source heights between 1 and 5 m. Observations were made of concentration fluctuations in a dispersing plume using a vertical array of sixteen very fast-response photoionization detectors placed at heights between 0.5 and 16 m. Vertical profiles of a number of concentration statistics were extracted, namely, mean concentration, fluctuation intensity, intermittency factor, peak-to-mean concentration ratio, mean dissipation rate of concentration variance, and various concentration time and length scales of dominant motions in the plume (e.g., integral macro-scale, in-plume mid-scale and Taylor micro-scale). The profiles revealed a similarity to corresponding crosswind profiles for a fully elevated plume, but showed greater and greater departure from the latter shapes once the plume had grown in the vertical so that its lower dege began to interact progressively more strongly with the ground. The evolution of the concentration probability density function at a fixed range, but with decreasing height from the ground, is similar to that obtained at a fixed height but with increasing distance from the source. Concentration power spectra obtained at different heights all had an extensive inertial-convective subrange spanning at least two decades in frequency, but spectra measured near the ground had a greater proportion of the total concentration variance in the lower frequencies (energetic subrange), with a correspondingly smaller proportion in the higher frequencies (inertial-convective subrange). It is believed that these effects result from the increased mean shear near the surface, and blocking by the surface. The effect of enhanced shear-induced molecular diffusion on concentration fluctuations is examined.     

Incorporation of internal fluctuations in a meandering plume model of concentration fluctuations

A meandering plume model that explicitly incorporates the effects of small-scale structure in the instantaneous plume has been formulated. The model requires the specification of two physically based input parameters; namely, the meander ratio,M, which is dependent on the ratio of the meandering plume dispersion to the instantaneous relative plume dispersion and, a relative in-plume fluctuation measure,k, that is related inversely to the fluctuation intensity in relative coordinates. Simple analytical expressions for crosswind profiles of the higher moments (including the important shape parameters such as fluctuation intensity, skewness, and kurtosis) and for the concentration pdf have been derived from the model. The model has been tested against some field data sets, indicating that it can reproduce many key aspects of the observed behavior of concentration fluctuations, particularly with respect to modeling the change in shape of the concentration pdf in the crosswind direction.List of Symbols C Mean concentration in absolute coordinates - C _r Mean concentration in relative coordinates - C₀ Centerline mean concentration in absolute coordinates - C _r,0 Centerline mean concentration in relative coordinates - f Probability density function of concentration in absolute coordinates - f _c Probability density function of plume centroid position - f _r Probability density function of concentration in relative coordinates - i Absolute concentration fluctuation intensity (standard deviation to mean ratio) - i _r Relative concentration fluctuation intensity (standard deviation to mean ratio) - k Relative in-plume fluctuation measure:k=1/i _r ² - K Concentration fluctuation kurtosis - M Meander ratio of meandering plume variance to relative plume variance - S Concentration fluctuation skewness - x Downwind distance from source - y Crosswind distance from mean-plume centerline - z Vertical distance above ground - Instantaneous (random) concentration - Crosswind dispersion ofnth concentration moment about zero - _ny Mean-plume crosswind (absolute) dispersion - _y Plume centroid (meandering) dispersion in crosswind direction - _y,c Instantaneous plume crosswind (relative) dispersion - Normalized mean concentration in absolute coordinates:C/C ₀ - Particular value taken on by instantaneous concentration,      

Fractal aspects of integrated concentration fluctuations

Time series of vertically integrated concentrations (VIC) across neutrally buoyant plumes are used to study the fractal and multifractal characteristics of passive scalar fluctuations in turbulent flow fields. Here, the multifractal analysis is based on a novel definition of the singularity spectrum-F() of the time records. Approximations for quantities such as the fractal dimension and the spectral exponent are derived as functions ofF() and are compared with the experimental results. Among other things, we show that VIC records are characterized by two typical subdomains. One domain, which is related to integrated concentration fluctuations, is a subfractal process; whereas the second one, which is directly related to the concentration fluctuations, is a fractal process.     

Conditional concentration statistics for surface plumes in the atmospheric boundary layer

A set of concentration time series from ground-level plumes in the atmosphere has been used to generate conditionally sampled (zeros ignored) plume concentration statistics. These have been compared and contrasted with corresponding unconditionally sampled statistics. It is found that conditional statistics are much less sensitive to the location of the receptor (relative to the mean plume) and to averaging time. Indeed, most of the variation apparent in unconditionally sampled statistics (both explained and unexplained) resides in the intermittency, the fraction of non-zero readings.The data are used to test three commonly used models for the concentration frequency distribution. At the simplest level of modelling, it is assumed that conditional statistics are invariant; then the data are best represented by a clipped-normal distribution. However, an exponential distribution is only slightly conservative and has the advantage of simplicity. A log-normal distribution is clearly not supported by the data. With this simple approach the intermittency remains unspecified and this is a serious deficiency.More advanced modelling must account for the residual variation in conditional statistics, which implies a relationship between these statistics and the intermittency. Although there is evidence for such a relationship in the data, it is not adequately represented by any of the distribution models considered.     

Time series analyses of concentration and wind fluctuations

Analyses of concentration fluctuation (C) spectra from boundary-layer smoke plume experiments at six separate locations show that the spectra from these experiments generally exhibit an inertial subrange at high frequencies with a slope of -5/3 and indicate peak energy at a time period of about 50 to 100 s. These periods of peak energy are a factor of two to five less than those for the peak of the wind speed fluctuation (u or v) spectra. A general spectral formula fits normalized spectra from the U.S. and Australia, where the frequency, n, is made dimensionless by multiplying by the plume dispersion parameter, _y , and dividing by the wind speed, u. Peak energy occurs at a dimensionless frequency of n _y/u equal to about 0.15. The Kolmogorov constant in the inertial subrange is estimated from a set of averaged spectra. Cross-spectra indicate little relation between concentration and wind fluctuations. However, most of the correlation that exists is due to periods larger than about 10 or 20 s.     

Pressure and humidity effects on optical refractive-index fluctuations

Although temperature fluctuations dominate the variance of optical refractive index fluctuations it has been shown recently that humidity fluctuations can also be important (e.g., Friche et al., 1975). This paper reports on simultaneous measurements of temperature, humidity and pressure so that the relative importance of all three can be investigated. For the dry site where the measurements were made, the humidity contribution was less than other investigators had found. The major contribution of the pressure fluctuations was through their covariance with temperature, but this term was found to be between 0.03 and 0.4% of the total variance. The results thus confirmed that pressure fluctuations can be neglected in most circumstances. Both the temperature and humidity spectra displayed -5/3 power laws at small scales while the temperature-humidity cospectrum decreased more rapidly than a -5/3 power law. The temperature-pressure cospectrum decreased even more rapidly than the temperature-humidity cospectrum. The temperature-pressure correlation coefficient was found to be about -0.1. The humidity-pressure correlation was typically between ±0.05 and the cospectrum poorly defined.Contribution of the Bedford Institute of Oceanography.     

Micromixing modelling of concentration fluctuations in inhomogeneous turbulence in the convective boundary layer

The micromixing technique, widely used in engineering calculations of mixing and chemical reaction, is extended to atmospheric boundary-layer flows. In particular, a model based on the interaction-by-exchange-with-the-conditional-mean (IECM) micromixing approach is formulated to calculate concentration fluctuation statistics for a line source and a point source in inhomogeneous and non-Gaussian turbulence in the convective boundary layer. The mixing time scale is parameterised as a linear function of time with the intercept value determined by the source size at small times. Good agreement with laboratory data for the intensity of concentration fluctuations is obtained with a value of 0.9 for the coefficient of the linear term in the time-scale parameterisation for a line source, and a value of 0.6 for a point source. Calculation of higher-order moments of the concentration field for a line source shows that non-Gaussian effects persist into the vertically well-mixed region. The cumulative distribution function predicted by the model for a point source agrees reasonably well with laboratory data, especially in the far field. In the limit of zero mixing time scale, the model reduces to a meandering plume model, thus enabling the concentration variance to be partitioned into meandering and relative components. The meandering component is shown to be more persistent for a point source than for a line source.