On the realizability of pressure-strain closures

The realizability condition for statistical models of turbulence is augmented to ensure that not only is the Reynolds stress tensor positive semi-definite, but the process of its evolution is physically attainable as well. The mathematical constraints due to this process realizability requirement on the rapid pressure strain correlation are derived. The resulting constraints reveal important limits on the inter-component energy transfer and the consequent flow stability characteristics, as a function of the mean flow. For planar mean flows, the realizability constraints are most stringent for the case of purely sheared flows rather than elliptic flows. The relationship between the constraints and flow stability is explained. Process realizability leads to closure model guidance not only at the two-component (2C) limit of turbulence (as in the classical realizability approach) but throughout the anisotropy space. Consequently, the domain of validity and applicability of current models can be clearly identified for different mean flows. A simple framework for incorporating these process realizability constraints in model formulation is outlined.