Paul J. Sullivan

Progress in integrated assessment and modelling

Environmental processes have been modelled for decades. However. the need for integrated assessment and modeling (IAM) has,town as the extent and severity of environmental problems in the 21st Century worsens. The scale of IAM is not restricted to the global level as in climate change models, but includes local and regional models of environmental problems. This paper discusses various definitions of IAM and identifies five different types of integration that Lire needed for the effective solution of environmental problems. The future is then depicted in the form of two brief scenarios: one optimistic and one pessimistic. The current state of IAM is then briefly reviewed. The issues of complexity and validation in IAM are recognised as more complex than in traditional disciplinary approaches. Communication is identified as a central issue both internally among team members and externally with decision-makers. stakeholders and other scientists. Finally it is concluded that the process of integrated assessment and modelling is considered as important as the product for any particular project. By learning to work together and recognise the contribution of all team members and participants, it is believed that we will have a strong scientific and social basis to address the environmental problems of the 21st Century.

The effect of aspect ratio on longitudinal diffusivity in rectangular channels

In a recent paper Doshi, Daiya & Gill (1978) showed that the value of Taylors longitudinal diffusivity D for laminar flow in a channel of rectangular cross-section of breadth u and height b is about 8 D 0 , for large values of the aspect ratio a / b , where Do is the value of the longitudinal diffusivity obtained by ignoring all variation across the channel. This superficially surprising result is confirmed by an independent method, and is shown to be caused by the boundary layers on the side walls of the channel. The primary purpose of the paper, however, is to consider the value of D in turbulent flow in a flat-bottomed channel of large aspect ratio, for which arguments based on physics are adduced in support of the formula D ≈[1 + B][1 - λ( b / u )], where B and λ are positive constants independent of b . It is shown that this result is consistent with laboratory experiments by Fischer (1966). The paper concludes with a discussion of the practical effects of aspect ratio on longitudinal dispersion in channels whose cross-section is approximately rectangular.

Longitudinal dispersion within a two-dimensional turbulent shear flow

This paper describes some laboratory and numerical experiments made on the longitudinal dispersion in an open channel flow. Particular attention has been paid to the initial stages of the process. Physical arguments suggest that the streamwise dispersion of a line of marked fluid elements across a two-dimensional turbulent shear flow occurs in three distinct stages. These stages are identified by a change in the form of the distribution of marked fluid elements in the flow direction. The skewed distribution of the first stage is readily identified by a constant value (approximately 1·1) for the ratio of the peak velocity ( V 1 ) of the distribution to the mean-flow velocity

A simple and unifying physical interpretation of scalar fluctuation measurements from many turbulent shear flows

\overline{U}

The intermittency factor of scalars in turbulence

; experiments using dyed fluid, made at this stage of the process, have revealed six identifiable features of the suggested distribution. The distributions suggested for the second and the third stage are consistent with the experimental findings of Elder (1959) for the second stage and Taylor (1954) for the third stage. An attempt has been made to simulate the process numerically using a Markovian model. The results of the simulation confirm features suggested by physical arguments and are in agreement with the open channel experiments. The Lagrangian autocorrelation function is found to be related to the Lagrangian velocity-history of marked fluid released from extreme positions on the flow cross-section. The correlation function, as expressed in terms of the velocity-history function provided by the numerical simulation, is \begin{eqnarray*} && R(t^{\prime}) = \exp (-bt^{\prime})\int_0^{1}U^{+2}dy^{\prime};\\ && t^{\prime} = tu_{*}/d,\quad U^{+} = \frac{U(y^{\prime})-\overline{U}}{u_{*}}, \end{eqnarray*} where u * is the friction velocity and U ( y ′) is the temporal mean velocity at a (non-dimensionalized) distance y′ from the flow boundary. In an open channel flow at a Reynolds number (based on friction velocity and channel depth) of 500, the numerical simulation provides the value of b = 0·536. The results of an experiment, in which the three-dimensional motion of small neutrally buoyant spheres was recorded in many small discrete time intervals, corroborate the theoretical suggestions and simulation results.

A simple representation of a developing contaminant concentration field

It is shown that measurements of the statistical properties of the concentration distributions of dispersing scalars taken from many different turbulent shear flows have a great number of common features. In particular the same simple relationship between the mean concentration and the mean-square fluctuation is shown to hold in all the flows, and this relationship is derived theoretically from well-known results for the unreal case when there is no molecular diffusion by a natural hypothesis about the effects of molecular diffusion. Application of the hypothesis to the higher moments and shape parameters gives results that agree reasonably well with the data (given the unavoidable experimental errors). The hypothesis should be subjected to further experimental analysis, and could simplify the application of turbulence closures and similar models. Extensions of the ideas to the probability density function of the scalar concentration suggest that it becomes self-similar. A final conclusion is that more attention to experimental errors due to instrument smoothing is highly desirable.

THE STRUCTURE AND MAGNITUDE OF CONCENTRATION FLUCTUATIONS

The shortcomings of the standard definition of the intermittency factor of a dispersing scalar in turbulence are summarized. In particular, this definition is not suitable for use in theoretical work. A new definition of the intermittency factor in terms of the mean concentration is given, and this is practically convenient and has a clear physical interpretation. Furthermore, the proposed new intermittency factor has an illuminating role in the structure of the probability density function of the scalar.

High concentrations of a passive scalar in turbulent dispersion

Chatwin & Sullivan have demonstrated that, for a wide range of self-similar scalar fields, the moments of the probability density function of concentration have a very simple form. Here, an extension to this simple form which takes account of the source distribution is developed. This extension has two effects. Firstly it modifies the values of the two parameters appearing in the original theory and in particular explains the observed behaviour of these parameters very near to a line source of heat in grid turbulence. Secondly, it introduces an additional parameter in the description of each moment beyond the second. It is shown that these additional parameters are necessary in order to describe measurements of the first four central moments throughout the concentration field from a continuous line source of heat in grid-generated turbulence

A solution-scheme for the convective-diffusion equation

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 models of air quality will continue - inevitably - to be unreliable and hardly worth using.

Longitudinal dispersion in flows that are homogeneous in the streamwise direction

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.