COMPARISON OF EXPLICIT AND TRADITIONAL ALGEBRAIC STRESS MODELS OF TURBULENCE

A critical comparison of explicit vs traditional algebraic stress mode ls of turbulence is made in an effort to clear up the confusion that a ppears to have been generated by the recently published literature on the subject, in which disparate approaches are adopted. It is shown th eoretically that the only way that general second-order closures can f ormally lead to fully explicit algebraic stress models, in a global se nse, is in the limit of equilibrium homogeneous turbulence. When these fully explicit models are then applied to turbulent flows that are fa r 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 are shown to have either multiple solutions or singularities, which tends to explain why they have had problems in applications to complex flow s, Thus, it is argued that traditional algebraic stress models are int rinsically ill-behaved and should be abandoned in future applications in favor of regularized, explicit algebraic stress models. It is furth ermore argued that these should be based on the homogeneous equilibriu m hypothesis, which allows for more general second-order closures to b e used to obtain single-valued models.