On the conditional variance and covariance equations for second-order conditional moment closure

Abstract

The consistency of the conditional variance and covariance equations derived by the decomposition method and by the probability density function method are addressed in this paper. The complete and consistent equations are derived and the limitations of the previous closure hypotheses are discussed. It is shown from a numerical experiment that conditional turbulent fluxes in conserved scalar space, which have been neglected in the previous closure, can have significant contribution to the transport of conditional variances and covariances in conserved scalar space. A gradient transport model for the turbulent fluxes is proposed.