The statistical behaviour of the variances, covariance and gradients of the reaction progress variable (
c), and the mixture fraction (
ξ) have been analysed in a pulverised coal jet flame using a three-dimensional carrier phase direct numerical simulation (DNS) dataset. It has been observed that the Favre-probability density functions (PDFs) of
c and
ξ can be parametrised by the standard
β function. Furthermore, the log-normal distribution has been found to accurately represent |?
c| and |?
ξ|. It is also found that ?
c and ?
ξ remain aligned throughout the flame brush. Finally the joint PDF of |?
c| and |?
ξ| has been compared with the product of the PDF of |?
c| and PDF of |?
ξ| extracted from carrier phase DNS, and it has been found that |?
c| and |?
ξ| are not statistically independent in the case investigated.The bivariate log-normal distributions with and without correlation have also been considered, and the former is found to be in better agreement with the carrier phase DNS data.
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