# CAIMS Prize Award

Department of Applied Mathematics, University of Western Ontario

Supervisor: P. Sullivan

Thesis title: A New Statistic for the Contaminant Dilution Process in Turbulent Flows

Abstract:

A new statistic, the expected fraction of release mass, is derived for the important practical problem of monitoring the dilution of concentrations that result when a quantity of contaminant is suddenly released in an environmental flow. This new statistic is the expected distribution of the conserved released mass amongst various levels of concentration. The advantage of this approach is that both theoretical prediction and experimental validation are made more tractable. The expected-mass-fraction is defined in terms of a spatial integral over the distributed one-point probability density function of concentration. This definition is shown to lead to a relatively simple differential equation for the moments of the expected-mass-fraction. The features of the definition that there is no spatial reference and all the concentration values in each realization of a cloud are used promote rapid convergence of this new statistic with relatively few experimental cloud releases. Further improvements for laboratory experiments on turbulent diffusion are discussed.