Stochastic properties of scalar quantities advected by a non-buoyant plume

Abstract

A model probability density equation is obtained by approximating the convective and diffusive terms in a single-point density formulation of homogeneous turbulent scalar transport, with first-order reaction, in a plume. The equation, which includes the intermittency factor of the scalar field explicitly, is then shown to support similarity solutions under some constraining assumptions. Comparison of the similarity solutions with field measurements of conditioned concentrations shows that they can reproduce the general features of the data for both low intermittency and high intermittency measurement regimes. On the basis of these asymptotic results a speculative modelling of the terms representing entrainment at the plume interface is proposed and a class of similarity solutions for the intermittency factor is obtained by numerical integration.