Keywords
modelling, advection-dispersion, particle transport, deposition, hazards
Start Date
1-7-2008 12:00 AM
Abstract
Solid and liquid particles (aerosols) ejected into the atmosphere by volcanic orhydrothermal eruptions, dust and sand swept up by storms or from other pollution sources,and droplets from crop-spraying, are subsequently dispersed by atmospheric wind currents.The particles fall under gravity while being advected by the mean wind and dispersed byturbulence. Particle sizes are generally not uniform, and may also change during flight(perhaps by particle coalescence and/or fragmentation, or, in the case of fluids, byevaporation or condensation) with consequent change to the settling speed. The wind mayalso change with elevation (and with time) and particles may be trapped on crop or forestfoliage as they near the ground.A quantitative model that reflects these influences on particle dispersal is outlined. It isassumed that the wind does not change over the time of particle flight, and that there is nochange of particle size due to evaporation or condensation. However, the other elevationdependentfeatures listed above are included. Changes of conditions with elevation aretreated by using a piecewise-constant wind velocity, associated dominant turbulence lengthscale, settling speed and trapping rates. In any case, this is the way that data are providedfor most of the numerical schemes currently available. When the vertical dispersion isassumed negligible (as is commonly supposed in such modelling), analytic solutions to theadvection-dispersion equations that describe the motion of the particles may be found.Results calculated directly from the analytical formulae provide examples of the method.
Mathematical modelling of aerosol transport and deposition: Analytic formulae for fast computation
Solid and liquid particles (aerosols) ejected into the atmosphere by volcanic orhydrothermal eruptions, dust and sand swept up by storms or from other pollution sources,and droplets from crop-spraying, are subsequently dispersed by atmospheric wind currents.The particles fall under gravity while being advected by the mean wind and dispersed byturbulence. Particle sizes are generally not uniform, and may also change during flight(perhaps by particle coalescence and/or fragmentation, or, in the case of fluids, byevaporation or condensation) with consequent change to the settling speed. The wind mayalso change with elevation (and with time) and particles may be trapped on crop or forestfoliage as they near the ground.A quantitative model that reflects these influences on particle dispersal is outlined. It isassumed that the wind does not change over the time of particle flight, and that there is nochange of particle size due to evaporation or condensation. However, the other elevationdependentfeatures listed above are included. Changes of conditions with elevation aretreated by using a piecewise-constant wind velocity, associated dominant turbulence lengthscale, settling speed and trapping rates. In any case, this is the way that data are providedfor most of the numerical schemes currently available. When the vertical dispersion isassumed negligible (as is commonly supposed in such modelling), analytic solutions to theadvection-dispersion equations that describe the motion of the particles may be found.Results calculated directly from the analytical formulae provide examples of the method.
