An alternative assessment of weakequilibrium
conditions in turbulent closure modeling
type de publication 
article dans une revue internationale avec comité de lecture 
date de publication 
2010 
auteur(s) 
Thompson Roney L.; Mompean Gilmar 
journal (abréviation) 
International Journal of Engineering Science (Int J Comput Eng Sci) 
volume (numéro) 
48 (11) 
 
pages 
1633 – 1640 
résumé 
In formulating polynomial representations of turbulent stress anisotropy tensors,
it is necessary to impose equilibrium conditions on the turbulent eld in order to
reduce the governing transport equations to a set of implicit algebraic equations.
Imposing these conditions on the anisotropy tensor rather than the turbulent stress
tensor directly results in a set of weakequilibrium conditions on the evolution of the
anisotropy tensor. A second kind of assumption is a requirement that the turbulent
transport and viscous diusion be related to the anisotropy tensor in a manner
consistent with both the dynamics and related tensorial properties.
In the study reported here, an alternative analysis of the weakequilibrium hy
pothesis is performed in order to improve the physical interpretation of this as
sumption. One important result of the analysis is that previous turbulent weak
equilibrium hypothesis available in the literature impose that the
ow has reached
a Motion With Constant Relative Principle AnisotropicReynoldsStress 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
ows, is
natural that at equilibrium conditions such motion occurs. However, the eigenval
ues of the Reynolds stress can change in time on turbulent extensional
ows due to
action of the mean
ow in a dierent process from a turbulent relaxation. In this case, the extended weakequilibrium assumption has to be related to an objective
time derivative which is not purely corotational. 
mots clés 
Turbulent equilibrium assumption, Coaxialorthogonal tensor decomposition, Reynolds stress evolution 
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