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An idealised model of turbulent dispersion: one rectangular pulse initial condition
Author(s) -
Mole Nils,
Yeun Hyun Ku
Publication year - 2007
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.824
Subject(s) - kurtosis , probability density function , turbulence , mathematics , dispersion (optics) , statistical physics , advection , skewness , turbulent diffusion , diffusion , range (aeronautics) , probability distribution , random walk , mathematical analysis , pulse (music) , domain (mathematical analysis) , mechanics , statistics , physics , thermodynamics , materials science , detector , optics , composite material
We examine an idealised model of turbulent dispersion which was introduced by Zimmerman and Chatwin. It involves deterministic diffusion in a periodic one‐dimensional domain, for a specified initial concentration field. A stochastic element is introduced by sampling at random across the domain, equivalent to random advection by a velocity which does not vary spatially. We consider initial conditions consisting of a single rectangular pulse, displaced a distance X 0 from the centre of the domain. We present numerical results for the dependence of the variance, skewness, kurtosis and probability density function (pdf) of concentration on X 0 and on time, and we derive the large time asymptotic forms for these quantities. At large time, the pdf is inevitably bimodal, with the peaks at the smallest and largest concentrations. To allow for a range of possible distances between strands of high concentration, as would be expected in a real turbulent flow, we suggest a new model pdf for concentration, obtained by averaging over different values of X 0 . For a uniform distribution of X 0 values, we show that this gives a unimodal concentration pdf at large time, with the peak at the mean concentration. Copyright © 2007 John Wiley & Sons, Ltd.