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United States Department of Agriculture

Agricultural Research Service

Title: Analytical Expressions for Particle Trajectories above Sinusoidal Terrain

Authors
item Stout, John
item Janowitz, Gerald - NORTH CAROLINA STATE UNIV

Submitted to: Quarterly Journal Royal Meteorological Society
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: July 24, 1996
Publication Date: N/A

Interpretive Summary: As heavy particles fall toward windswept topography, their motion will be governed partly by their physical characteristics, such as particle diameter and mass, and partly by fluid forces resulting from the relative motion of the particles through the spatially varying flow field above the terrain. Here we calculate trajectories of particles falling toward a windswept series of low amplitude hills. It is shown that under the right atmospheric conditions focusing of particle path lines will occur producing alternating regions of increased and decreased particle concentration. Particle motion was obtained analytically by first simplifying the equations of particle motion to kinematic form, then applying perturbation techniques. An extension of the trajectory analysis yields expressions that predict the point of surface impact as a function of the initial release point and knowledge of the flow structure. This finally leads to a method for predicting the point along the surface where deposition is maximum and minimum.

Technical Abstract: As heavy particles fall toward windswept topography, their motion is governed partly by their physical characteristics, such as particle diameter and mass, and partly by fluid forces resulting from the relative motion of the particles through the flow field. Here we calculate trajectories of particles falling toward a windswept series of low amplitude hills. It is shown that under the right atmospheric conditions, alternating regions of convergent and divergent particle path lines will occur. Particle motion was obtained analytically by first simplifying the equations of particle motion to kinematic form, them applying perturbation techniques. The dynamical equations of particle motion are derived in nondimensional form and are shown to simplify to kinematic form when the time scale of fluid motions is much larger than the characteristic response time of the particles. Using perturbation methods, analytical expressions are derived for the trajectories of heavy particles settling under gravity through the spatially varying flow field above sinusoidal topography. An extension of the trajectory analysis yields expressions that predict the point of surface impact as a function of the initial release point. This finally leads to a method for predicting the point along the surface where deposition is either maximum or minimum.

Last Modified: 7/31/2014
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