THE VANISHING EFFECT OF MOLECULAR DIFFUSIVITY ON TURBULENT DISPERSION- IMPLICATIONS FOR TURBULENT MIXING AND THE SCALAR FLUX

In 1921 G. I. Taylor introduced (with little discussion) the notion th at the dispersion of a conserved passive scalar in a turbulent flow is determined by the motion of fluid particles (independent of the molec ular diffusivity). Here, a hypothesis of diffusivity independence is i ntroduced, which provides a sufficient condition for the validity of T aylor's approach. The hypothesis, which is supported by DNS data, is t hat, at high Reynolds number, the mean of the scalar conditional on th e velocity is independent of the molecular diffusivity. From this hypo thesis it is shown that (at high Reynolds number) the conditional Lapl acian of the scalar is zero. This new result has several significant i mplications for models of turbulent mixing, and for the scalar flux. P rimarily, a model of turbulent scalar mixing that is independent of ve locity is inconsistent with the hypothesis, and gives rise to a spurio us source or (more likely) sink of the scalar flux.