Abstract

An economical representation of effects of turbulence on the time-evolving structure of diffusive scalar fields is obtained by introducing a hierarchical (tree) network connecting fluid parcels, with effects of turbulent advection represented by swapping pairs of sub-trees at rates determined by turbulence time scales associated with the sub-trees. The fluid parcels reside at the base of the tree. The tree structure partitions the fluid parcels into adjacent pairs (or more generally, p-tuples). Adjacent parcels intermix at rates governed by diffusion time scales based on molecular diffusivities and parcel sizes. This simple procedure efficiently accomplishes long-standing objectives of turbulent mixing model development, such as generating physically based time histories of fluid-parcel nearest-neighbor encounters and the associated spatial structure of turbulent scalar fields. A strategy for implementing the method as a mixing sub-model like those commonly used in turbulent combustion simulations is outlined. The formulation involves a parameter controlling the tree structure that can be used to set the effective spatial dimensionality, which need not be an integer and can be arbitrarily small, subject to practical limitations. With the introduction of velocity components as well as scalars, this hierarchical parcel-swapping (HiPS) f­ormulation becomes a self-contained flow simulation, as illustrated by its application to fully developed channel flow.