Comparison of Explicit and Traditional Algebraic Stress Models of Turbulence

Abstract

A critical comparison of explicit vs traditional algebraic stress models of turbulence is made in an effort to clear up the confusion that appears to have been generated by the recently published literature on the subject, in which disparate approaches are adopted. The only way that general second-order closures can formally lead to fully explicit algebraic stress models, in a global sense, is in the limit of equilibrium homogeneous turbulence. When these fully explicit models are then applled to turbulent flows that are far from equilibrium, a singularity can arise, which can be removed by a systematic regularization. When solved explicitly either analytically or numerically, the traditional, implicit algebraic stress models have either multiple solutions or singularities, which tends to explain why they have had problems in applications to complex flows. Thus, it is argued that traditional algebraic stress models are intrinsically ill-behaved and should be abandoned in future applications in favor of regularized, explicit algebraic stress models. It is furthermore argued that these should be based on the homogeneous equilibrium hypothesis, which allows for more general second-order closures to be used to obtain single-valued models.