Eolian Sediment Transport as a Stochastic Process: The Effects of a Fluctuating Wind on Particle Trajectories

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Abstract
Particle response to turbulent velocity fluctuations of the wind may be characterized by a response time that is strongly dependent upon grain diameter. While very small particles respond quickly to all wind velocity fluctuations and follow essentially fluid element paths, larger particles respond only to the lower frequency air velocity fluctuations, and hence diverge significantly from fluid element paths. A realistic model of the history of the wind velocity fluctuations to which an airborne particle is subjected, incorporating both the vertical structure of the turbulence in the atmospheric boundary layer and the effects of particle "slip" relative to the air, combined with a simple linear differential equation for the particle response to step changes in wind velocity, allows calculation of suspension trajectories. Ensembles of such trajectories produce concentration profiles that compare favorably with power-law concentration profiles predicted using continuum suspension theory. The same fluctuation field acts to modify trajectories of larger particles previously modeled as being determined entirely by the mean wind profile, the modifications diminishing as particle size increases. The spectrum of particle behavior is therefore shown to be continuous, with saltation and suspension its idealized end-members.

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