A fast non-Fickian particle-tracking diffusion simulator and the effect of shear on the pollutant diffusion process

Abstract

This paper presents a fast method for the generation of non-Fickian particle paths within a particle-tracking pollutant diffusion model based on a Fourier spectral representation of fractional Brownian motion (fBm), a generalization of ordinary Brownian motion. Correlated diffusive components in a particle-tracking algorithm are modelled using fBm increments that have long-range correlations over numerous spatial and/or temporal scales; hence producing non-Fickian diffusion. A fast algorithm to generate fBm and its increment by using its power spectral density S(f) in a fast Fourier transform algorithm is given. A general equation for the scaling of fBm within a velocity flow field with simple linear shear is presented. An initial numerical study of the nature of fBm shear dispersion has been conducted by incorporating fBm increments into a non-Fickian particle-tracking algorithm. It is shown that the effect of simple (i.e. linear) shear on the diffusion process is to produce enhanced diffusive phenomena with the longitudinal spreading of the plume scaling with exponent ∼1+H, where H is the Hurst exponent used to describe fBm. Finally, a more complex shear zone at the entrance of a coastal bay model is investigated using both a traditional particle-tracking method and the fBm-based method. Copyright © 2000 John Wiley & Sons, Ltd.