Coherent Structures and Conditional Statistics in Inhomogeneous Turbulent Mixing

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Abstract
We study the statistics of a passive scalar mixed by a turbulent flow that contains coherent structures (Görtler vortices). These structures entrain the passive scalar in such a way that its one-point probability density function (pdf) has a nonstandard shape that can be explained as a superposition of a background Gaussian mixing on the one hand, and the action of the Görtler vortices on the other. We propose a “mean field” approach to predict this pdf. This study (applicable to a wider class of systems) constitutes the first experimental example for which the conditional expectation of the second temporal derivative of the concentration of a passive scalar given the concentration deviates from a linear behavior.