Modelling of anthropogenic pollutant diffusion in the atmosphere and applications to civil protection monitoring

arXiv:0807.0274v1 [physics.flu-dyn] 2 Jul 2008 Modelling of anthropogenic pollutant diffusion in the atmosphere and applications to civil protection monitoring§ Marco Tessarottoa,b,c and Massimo Tessarottoc,d aCivil Protection Agency, Regione Friuli Venezia-Giulia, Palmanova, Italy, bDepartment of Electronics, Electrotechnics and Informatics, University of Trieste, Italy, cConsortium of Magneto-fluid-dynamics, University of Trieste, Italy, dDepartment of Mathematics and Informatics, University of Trieste, Italy (Dated: August 16, 2021) Abstract A basic feature of fluid mechanics concerns the frictionless phase-space dynamics of particles in an incompressible fluid. The issue, besides its theoretical interest in turbulence theory, is important in many applications, such as the pollutant dynamics in the atmosphere, a problem relevant for civil protection monitoring of air quality. Actually, both the numerical simulation of the ABL (atmospheric boundary layer) portion of the atmosphere and that of pollutant dynamics may generally require the correct definition of the Lagrangian dynamics which characterizes arbitrary fluid elements of incompressible thermofluids. We claim that particularly important for applications would be to consider these trajectories as phase-space trajectories. This involves, however, the unfolding of a fundamental theoretical problem up to now substantially unsolved: namely the determination of the exact frictionless dynamics of tracer particles in an incompressible fluid, treated either as a deterministic or a turbulent (i.e., stochastic) continuum. In this paper we intend to formulate the necessary theoretical framework to construct such a type of description. This is based on a phase-space inverse kinetic theory (IKT) approach recently developed for incompressible fluids (Ellero et al., 2004-2008). Our claim is that the conditional frictionless dynamics of a tracer particles - which corresponds to a prescribed velocity probability density and an arbitrary choice of the relevant fluid fields - can be exactly specified. PACS numbers: 47.10.ad,05.20.Dd 1 I. INTRODUCTION This work (together with Refs.[1]) is a part of a research project related to the theoretical description of pollutant dynamics in the atmosphere, a subject relevant for civil protection monitoring of air quality in the atmosphere. Here, we refer in particular to the so-called ABL (atmospheric boundary layer) portion of the atmosphere where the earth surface (land or water) has a direct influence and most of pollution releases occur. In fact, the ability to predict the dynamics of anthropogenic pollutants, especially in order to estimate their con- centration at ground level, is a prerequisite for environmental investigations. A critical issue is therefore the identification of mathematical models, able to give reliable predictions for pollutants concentrations in the presence of complex terrain and for prescribed weather pro- files. This involves the ability to simulate pollutant dynamics in a variety of different physical conditions. In fact in the ABL, sufficiently close to the ground, the atmosphere is mainly characterized by a turbulent flow arising from the wind shear produced by friction with the ground surface. Instead, at the top of the ABL, in the free atmosphere, the wind speed is approximately geostrophic and therefore possibly laminar. The stronger the wind, the more intense is the generated turbulence arising close to the ground, whose properties may be very different, depending on the vertical temperature gradient of the atmosphere. Since turbulence reinforces mixing it tends to homogenize the fluid much more quickly than would a laminar flow, thus preventing local accumulation of pollutants. In addition meteorological parameters (of the atmosphere) are strongly affected by the earth’s surface through dynam- ical processes (friction of the air over the surface and through thermal processes heating or cooling of the air in contact with the ground). Until recently, fully reliable mathematical methods of this type, able to take into account the full complex phenomenology of the at- mosphere and simulate the dynamics of particle or gaseous pollutants in the atmosphere, have been missing. For this reason in the past, most of predictions for pollutant transport in the atmosphere have been based on wind-tunnel experiments. Purpose of the presentation is an overview of the mathematical models currently available and a brief analysis of new theoretical developments in the field. In particular, here we intend to refer to the statistical approach developed by Marco Tessarotto et al. [1] based on the IKT (see also Ellero et al., 2000-2008, [2, 3, 4, 5, 6, 26]). In the sequel, we shall concentrate on those issues that we consider mostly relevant for the present investigation. We intend to show that the IKT 2 approach is a useful theoretical framework that can be used to simulate the dynamics of pollutants in prescribed fluid flows, taking into

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