Mapping Closures for Turbulent Mixing and Reaction
The mapping closure for the one-point pdf of an inert scalar in homogeneous turbulence is explained and developed. Proposed by Chen, Chen & Kraichnan (1989), the mapping closure formalism is based on fundamentally different physical assumptions than previous closures. It is explained here in terms of three fields. The turbulent field is the physical field under study—in this case it is a homogeneous, isotropic, scalar field. At the level of closure considered, the only information known about this field is its one-point pdf. The second field is a specified (and hence completely known) Gaussian field. The third field, the surrogate field, is constructed by a known amplitude mapping from the Gaussian field. This mapping is constructed so that the one-point pdf’s of the turbulent field and the surrogate field are identical. Consequently, at the level of closure, the two fields are indistinguishable. The closure assumption made is that the unknown statistics of the turbulent field are equal to those of the known surrogate field.