Nils Mole

Relationships between higher moments of concentration and of dose in turbulent dispersion

Chatwin and Sullivan (1990) proposed simple results for the relationships between moments of scalar fluctuations in self-similar turbulent shear flows. They showed these relationships to be well satisfied by observations from a range of experiments. Here their theory is extended to the skewness, kurtosis and higher order equivalents. It is shown that the relationships between these normalised moments are parameter-free, and are identical to those for zero molecular diffusion. Experimental observations are presented which show a remarkable degree of collapse when these normalised moments are plotted against each other. The agreement with the theoretical results is reasonably good, and better than for some other standard statistical distributions which are commonly applied to such observations. This is true not only for the concentration, but also for generalised doses. It is concluded that the simple theory provides a satisfactory basis for a model of both the concentration and of dose. Furthermore, the results suggest that the concentration and the dose can be modelled through a perturbation to a two-state model.

Concentration fluctuation data from dispersion experiments carried out in stable and unstable conditions

Experiments have been carried out to investigate the dispersion of plumes at short range in the atmospheric boundary layer during stable and unstable conditions. The experiments and measurement system are described, and the results are compared with those of previous experiments. The slow meandering under stable conditions found by Mylne (1992) is not present here (probably because of topographic effects), so the plume is present on the mean centreline more often, and timescales are shorter, under stable conditions. Associated with this, statistics during stable conditions exhibit greater stability to changes in total sampling time. Intensity is found to be greater under unstable conditions, but there do not appear to be large differences in the shape of the probability density function between stable and unstable conditions. The intermittency is calculated using several variations on the conventional definition. The values obtained vary substantially according to which definition is used (although they are always higher in the stable than in the unstable experiments), demonstrating the sensitivity to both the precise definition and to measurement system characteristics. It is shown that even at very short range the mean and variance of concentration are determined almost entirely by the fluid not emanating from the source. Thus the partition between source and non-source fluid suggested by Chatwin and Sullivan (1989), while providing a more scientifically sound definition of intermittency, does not have an obvious direct practical application.

A Concentration pdf for the Relative Dispersion of a Contaminant Plume in the Atmosphere

Observations of the dispersion of a contaminant plume in theatmospheric boundary layer, obtained using a Lidar, are analysedin a coordinate frame relative to the instantaneous centre of massof the plume. To improve the estimates of relative dispersionstatistics, maximum entropy inversion is used to remove noise fromthe Lidar concentration profiles before carrying out the analysis.A parametric form is proposed for the probability density function(pdf) of concentration, consisting of a mixture of a betadistribution and of a generalised Pareto distribution (GPD). Thispdf allows for the possibility of a unimodal or bimodaldistribution, and is shown to give a satisfactory fit toobservations from a range of positions relative to the source. Thevariation of the fitted parameters with crossplume location isanalysed, and the maximum possible concentration is found todecrease away from the plume centre.

The High Concentration Tails Of The Probability Density Function Of A Dispersing Scalar In The Atmosphere

The distribution function for concentrations of a scalar pollutant dispersing in the turbulent atmosphere has a finite domain that is bounded above and below. Three methods, based on extreme value statistics, are used to obtainestimates for the upper bound and to describe the high concentration tailbehaviour of the distribution; all three methods are applied to concentrationdata obtained from experimental atmospheric releases. Quantile quantile (QQ)plots are used to assess the goodness of fit of the resulting estimates of thedistribution, and also to compare the performance of the three methods. Thepredicted values for the upper bound are orders of magnitude less than thesource concentration, illustrating that molecular diffusion has a large effecton the high concentrations.

High concentrations of a passive scalar in turbulent dispersion

In problems involving the dispersion of hazardous gases in the atmosphere, the distribution of high concentrations is often of particular interest. We address the modelling of the distribution of high concentrations of a dispersing passive scalar at large Peclet number, concentrating on the case of steady releases. We argue, from the physical character of the small-scale processes, and from the statistical theory of extreme values, that the high concentrations can be fitted well by a Generalized Pareto Distribution (GPD). This is supported by evidence from a range of experiments. We show, furthermore, that if this is the case then the ratios of successive high-order absolute moments of the scalar concentration are linearly related to the reciprocal of the order. The linear fit thus obtained allows the GPD parameters to be determined from the moments. In this way the moments can be used to deduce the properties of the high concentrations, in particular the maximum possible concentration θ max = θ max ( x ). We argue, on general physical grounds, that θ max / C 0 (where C 0 = C 0 ( X ) is the centreline mean concentration, and X is the downstream distance from the source) decreases to zero very far from the centreline, but that the decrease takes place on a length scale much larger than the mean plume width (because it is controlled by the relatively slowly acting molecular diffusion, rather than the fast turbulent advection). Thus, over the distances for which accurate measurements can be made, we expect θ max / C 0 to be approximately constant throughout the plume cross-section. On the centreline, we argue that θ max / C 0 increases downstream from the source, reaches a maximum and then decreases, ultimately tending to 1 far downstream. In support of these deductions we present results for some high-quality data for a steady line source in wind tunnel grid turbulence. Finally, we apply to this problem some existing models for the relationships between moments. By considering the behaviour far from the centreline in these models, and linking the moments to the high concentrations, we derive relationships between the model parameters. This allows us to derive an expression for θ max / C 0 which depends on a total of 5 parameters, and (weakly) on C / C 0 (where C = C ( x ) is the local mean concentration). Comparison with the data is encouraging. We also discuss possible methods for modelling the spatial variation of these 5 parameters.

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.

The large time behaviour in a model for concentration fluctuations in turbulent dispersion

Abstract A model for concentration fluctuation moments has previously been developed for a scalar dispersing in a turbulent flow (see Mole et al., 1997). This model assumes that the mean concentration is known as a function of space, and of time t, and that higher moments of concentration for a dispersing cloud can be determined fully by a further two parameters α(t) and β(t) (see Chatwin and Sullivan, 1990a). A closure is used which enables a coupled pair of first-order differential equations for α and β to be written down. Here attention is restricted to cases when the mean concentration is self-similar, with a spatial scale L(t). (It is assumed that L −1 d L/ d t→0 as t→∞, so cloud growth must be slower than exponential.) It is shown that there is a constant αs, dependent on the spatial form of the mean concentration, such that α→αs as t→∞ when αs>0, and α→∞ when αs α−α s ∝(L −1 d L/ d t) 1/2 and β∝(L −1 d L/ d t) 1/2 . In the latter case it shows that α∝(L −1 d L/ d t) −1 and β∝L −1 d L/ d t . These results are supported by the numerical solutions for a variety of cases. Some of the corresponding results for the concentration moments are compared with experimental measurements for line sources in wind tunnels.

A switching poisson process model for high concentrations in short-range atmospheric dispersion

Abstract High concentrations of a pollutant dispersing in a turbulent atmosphere may be described in terms of the times at which concentration exceeds a high threshold and the values it reaches at those times. A stochastic model based on a switching Poisson process is proposed to account for both aspects, extending an earlier model of Mole et al. (1995, Environmetrics 6, 595–606), which described only the magnitudes of high concentrations. The model is fitted by maximum likelihood and is shown to be capable of capturing the broad features of extreme concentrations in a series of atmospheric dispersion experiments. Evidence is found that in some cases parameters of the model vary with time, and it is argued that this lends support to an explanation of the variability of extreme concentrations based on a meandering plume hypothesis.

A Novel Approach to the Solar Interior-Atmosphere Eigenvalue Problem

In this paper we introduce a new approach to study the interaction of solar eigenoscillations, with particular emphasis on the f-mode, with random inhomogeneities caused by flows and magnetic field near the solar surface. We present an initial value method to derive a general dispersion relation for a class of models where the magnetic atmosphere is overlying an arbitrary static solar interior. In these models the interior part is treated parametrically and does not need to be specified before we obtain the dispersion relation. In order to demonstrate the applicability of the proposed method, an analytical solution of the dispersion relation is given for an incompressible interior with constant density.