An estimation of a passive scalar variances using a one-particle Lagrangian transport and diffusion model

In this work the Lagrangian particle diffusion model (LPDM) is extended to include variances and covariances between different passive scalars. This is done by introducing an additional particle variable—the conditional average scalar concentration (CASC) over the particle’s trajectory. In contrast to the particle’s scalar concentration which is conserved, the CASC evolves in time. The model for the evolution equation is compatible with the Eulerian equation for the scalar variance and with the asymptotic behaviour of the particles’ pair probability function.