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. del calculations are compared with the wind tunnel observations in the neutral boundary layer (Fackrell & Robins (1982)  [22]), and with the measurements in decaying homogeneous grid turbulence (Warhaft (1984)  [18]). Good agreement is obtained between observations and model predictions. The model is simple to use and can be applied to non-homogeneous turbulence.