Individual Particle Based Description of Atmospheric Dispersion: a Dynamical Systems Approach
We argue that a proper treatment of material dispersion should be based on individual particle tracking using realistic size and density. The effect of turbulent diffusion and the scavenging of particles by precipitation are shown to be treatable as stoch
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A–ELTE Theoretical Physics Research Group, P´ azm´ any P. s. 1/A, H-1117 Budapest, Hungary Department of Theoretical Physics, E¨ otv¨ os Lor´ and University, P´ azm´ any P. s. 1/A, H-1117 Budapest, Hungary Abstract We argue that a proper treatment of material dispersion should be based on individual particle tracking using realistic size and density. The effect of turbulent diffusion and the scavenging of particles by precipitation are shown to be treatable as stochastic perturbations of the deterministic Newtonian equation of motion. This approach enables one to investigate the chaotic aspects of particle dispersion by means of dynamical systems concepts. Topological entropy is shown to be in this context the growth rate of material lines, which can be considered to provide a novel characterization of the state of the atmosphere. The deposition process is found to be well characterizable by the escape rate (being a measure of the strength of the exponential decay of the number of particles not yet reached the surface), which might depend on local turbulence and rain intensity. The variability of the dispersion process due to the difference between different meteorological forecasts within an ensemble forecast are also illustrated. Examples are taken from volcanic eruptions and the Fukushima accident.
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Introduction
The concepts of chaos theory apply to any nonlinear system. Nowadays they are also widely used in different treatments of climate dynamics, as some chapters of this book also illustrate. The most appropriate appearance of dynamical systems theory is in conceptual climate models since chaos is basically a low-dimensional phenomenon. Primarily, it is a feature of temporal dependence without any spatial extension. Chaos is thus a property of systems describable by ordinary differential equations. The often heard statement that weather is chaotic should therefore be interpreted A. Provenzale et al. (Eds.), The Fluid Dynamics of Climate, CISM International Centre for Mechanical Sciences DOI 10.1007/ 978-3-7091-1893-1_4 © CISM Udine 2016
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T. Haszpra and T. Tél
in a symbolic sense: weather, in which spatial features are essential, is more complex than chaotic. It is basically turbulent in accordance with the fact that weather is described by the partial differential equations of hydrodynamics. (In spite of the differences between chaos and turbulence, some features might be in common, like e.g. the fact that both phenomena are unpredictable.) As a consequence, all aspects of climate dynamics related to essential spatial features and requiring thus a description in terms of partial differential equations are more complicated than chaotic. There is one class of phenomena, relevant both in weather- and climaterelated contexts, namely the dispersion of particles, which is a chaotic process. This is so because the traditional description of any flow occurs in the Eulerian picture, and implies the determination of the velocity field. The advection of particles can, however, be treated as a phenomenon sitting on top of t
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