On the realizability of nonlinear stress-strain relationships for Reynolds stress closures
A class of recently developed explicit algebraic stress models based on tensorially quadratic stress-strain relations  is subjected to a systematical realizability analysis. It is found that these models, which are of particular interest for their rigorous derivation from linear second-moment closure models, tend to produce inappropriate unrealizable results like negative turbulence energy components, even in simple shear flows. The cause of the defect is identified in conjunction with a set of realizability-furnishing constraints on the model coefficients. With the exception of the silent normal stress component in accelerated flow, the nature and rationale of the explicit algebraic stress model suggested by Gatski and Speziale  can be extended to maintain the realizability principle. Results obtained from the corresponding quasi-realizable quadratic eddy-viscosity model are reported in comparison with other nonlinear modelling practices.