Intermittency features of the Hierarchical Parcel Swapping Model (HiPS) as indicated by turbulent scalar structure functions

Hierarchical Parcel Swapping (HiPS) is a stochastic model of turbulent mixing. HiPS is based on a binary tree structure consisting of nodes emanating from the top level of the tree and terminating in fluid parcels at the bottom level of the tree. Length scales decrease geometrically from level to level and corresponding time scales follow inertial-range scaling. Turbulent advection is modeled by swapping pairs of equal-size subtrees. Swap occurrences are Poisson-sampled at rates corresponding to level time scales. Swaps involving single parcels result in micromixing that changes scalar states. HiPS has recently been validated for pair dispersion and for several scalar mixing regimes over a wide range of Schmidt numbers, addressing scalar spectrum scaling exponents and scalar dissipation statistics. Here, we use HiPS to obtain turbulent scalar structure functions. Scaling exponents up to twentieth order are presented. They compare favorably to DNS results that show anomalous scaling attributed to intermittency. Predicted dependence on the smoothness exponent is compared to Kraichnan-model results.