An alternative assessment of weak-equilibrium conditions in turbulent closure modeling

In the study reported here, an alternative analysis of the weak-equilibrium hypothesis is performed in order to improve the physical interpretation of this assumption. One important result of the analysis is that previous turbulent weak-equilibrium hypothesis available in the literature impose that the flow has reached a Motion With Constant Relative PrincipleAnisotropic-Reynolds-Stress History, which means that the eigenvalues of the anisotropic Reynolds stress tensor do not change in time. Since virtually every geometry used to test this kind of hypothesis do not have a change on the cross sectional area and lead to viscometric flows, is natural that at equilibrium conditions such motion occurs. However, the eigenvalues of the Reynolds stress can change in time on turbulent extensional flows due to action of the mean flow in a different process from a turbulent relaxation. In this case, the extended weak-equilibrium assumption has to be related to an objective time derivative which is not purely co-rotational.