Correlation between non-Gaussian statistics of a scalar and its dissipation rate in turbulent flows

This paper reports an experimental study on the correlation between the deviation from Gaussianity of the probability density function (PDF) of a fluctuating scalar and the dependence of the scalar dissipation on the scalar itself in turbulent flows. The study demonstrates that the departure of the scalar PDF from Gaussianity reflects the degree to which the dissipation rate depends statistically on the scalar. Of important significance, present results obtained from wake and jet flows, together with those deduced from previous work on various turbulent flows, appear to point to a generic expression for the total correlation. This expression suggests that the analytical result of O'Brien and Jiang [Phys. Fluids A 3, 3121 (1991)], derived for homogeneous turbulence, should be also valid for inhomogeneous turbulence. That is, the statistical independence of the scalar dissipation and the scalar itself appears to act as the sufficient and necessary condition for the scalar PDF to be Gaussian in any stationary turbulence. It follows that the independence assumption, often used in combustion modeling, is reasonable only in the flow region where the scalar PDF is closely Gaussian.