The Fine Structure of a Slender Scalar Plume in Sheared Turbulence

Abstract

We present measurements of the fine structure of a passive scalar plume in uniformly sheared turbulence generated in a water tunnel. We report on the mixed velocity-scalar statistics of the plume, including the probability density functions of the velocity, scalar, and scalar derivatives, as well as conditional expectations of the velocity and the scalar derivatives, conditioned upon the scalar fluctuations. Such results are particularly relevant to models that are intended to be used for solving the balance equation of the scalar pdf. Specifically, we address the effect of having a highly intermittent scalar field, in which case the scalar pdf is highly skewed, the joint velocity and scalar pdfs are non-Gaussian, and conditional expectations of the velocity components are distinctly non-linear.Details on the fine structure of turbulent mixing are particularly relevant for the modelling of chemical reactions and combustion. A popular approach for analyzing reactive flows is to consider the balance equation of the scalar probability density function (pdf) [1,2,3]. Although these equations have certain advantages over conventional Reynolds-averaged balance equations of velocity and scalar moments, they are complicated by the appearance of conditional expectations of the velocity and the scalar dissipation values, conditioned upon the scalar fluctuations. Most previous studies have focused on flows in which the velocity and scalar are nearly homogeneous and jointly-Gaussian, in which case these conditional expectations would be linear functions of the scalar value [2,3,4]; however, this would not necessarily be the case for inhomogeneous scalar fields as they would appear in indus-