A mapping closure for turbulent scalar mixing using a time-evolving reference field

A general mapping-closure approach for modeling scalar mixing in homogeneous turbulence is developed. This approach is different from the previous methods in that the reference field also evolves according to the same equations as the physical scalar field. The use of a time-evolving Gaussian reference field results in a model that is similar to the mapping closure model of Pope (1991), which is based on the methodology of Chen et al. (1989). Both models yield identical relationships between the scalar variance and higher-order moments, which are in good agreement with heat conduction simulation data and can be consistent with any type of epsilon(phi) evolution. The present methodology can be extended to any reference field whose behavior is known. The possibility of a beta-pdf reference field is explored. The shortcomings of the mapping closure methods are discussed, and the limit at which the mapping becomes invalid is identified.