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Simulations of the probability structure of a dispersing, passive scalar
Author(s) -
Zimmerman William B.
Publication year - 2001
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.484
Subject(s) - mathematics , statistical physics , intermittency , advection , kurtosis , skewness , universality (dynamical systems) , physics , mathematical analysis , statistics , turbulence , mechanics , thermodynamics , quantum mechanics
It is established that there is a time asymptotic dependency of the higher order moments of concentration on the lowest three moments through statistical analysis of field plume releases [Mole and Clarke, 1995]. A microscale model of a diffusion layer randomly buffeted by supercloud size eddies and a model of advection and diffusion in a deterministic helical eddy both demonstrated that this slaving of the higher moments to lower moments obtains time‐asymptotically and collapses with all intermittency factors onto a universal curve for kurtosis against skewness. In this article, this universality with residence time and intermittency factor obtains in two distinct plume models for transverse dispersion – diffusion within a 1‐D lamellae structure and during advection by a 2‐D random streamfunction. In the latter case, some evidence for Chatwin's closure hypothesis relating the expectation of the norm square of the gradient of the concentration, conditional at a given concentration, and the pdf of concentration, is presented. At early residence times in the plume, the power law hypothesis is consistent with simulations to a good degree. At intermediate residence times, however, there are apparently two branches to the proposed relationship, one matching Chatwin's hypothesis. Although not tested here, at long residence times the hypothesis should hold under the simulation scheme as it asymptotes to the assumptions of Chatwin's theory. Copyright © 2001 John Wiley & Sons, Ltd.