This article is published in Environmetrics as a special issue on TIES 2008: Quantitative Methods for Environmental Sustainability, edited by Sylvia R. Esterby, University of British Columbia Okanagan, Canada.
Special Issue Paper
An idealised model of turbulent dispersion: two and three spatial dimensions†
Article first published online: 12 FEB 2010
Copyright © 2010 John Wiley & Sons, Ltd.
Special Issue: TIES 2008: Quantitative methods for environmental sustainability
Volume 21, Issue 7-8, pages 767–788, November - December 2010
How to Cite
Mole, N. (2010), An idealised model of turbulent dispersion: two and three spatial dimensions. Environmetrics, 21: 767–788. doi: 10.1002/env.1037
- Issue published online: 12 FEB 2010
- Article first published online: 12 FEB 2010
- Manuscript Accepted: 10 NOV 2009
- Manuscript Received: 26 SEP 2008
- turbulent dispersion;
- concentration fluctuations;
- probability density function
In the idealised model of turbulent dispersion introduced by Zimmerman and Chatwin (1995), the probability density function (pdf) of concentration becomes bimodal at large times, with peaks at the smallest and largest concentrations. That model only has one spatial dimension, but here I extend the model to two and three spatial dimensions. I also extend to two and three dimensions the pdf calculation method that was given by Mole and Yeun (2007). I use this method to derive large-time analytical solutions for the pdf, and to show that in two and three dimensions the weight of the pdf shifts from extreme concentrations towards the mean concentration. In the typical three-dimensional case, the large-time pdf is unimodal with the peak at the mean concentration. Copyright © 2010 John Wiley & Sons, Ltd.