Impact of velocity correlations on longitudinal dispersion in space-Lagrangian advective transport models

Space-Lagrangian random walk models conceptualize advective transport in heterogeneous media in terms of collections of particles undergoing fixed-length steps along flow streamlines. We study the impact of velocity correlation structure on longitudinal dispersion for different point velocity statistics. We find that asymptotic equivalence requires the step length of an uncorrelated continuous time random walk to be higher than the correlation length when velocity correlations decay exponentially with distance. We characterize the conditions for equivalence for broad classes of velocity distributions.