We present a full version of the results obtained in Grebenev et al [Doklady Physics 47(7), 518-521 (2002)] wherein the closure formula, that is, the local equilibrium approximation of second-order moments for modeling free turbulent flows was justified by the method of differential constrains. The proposed analysis provides us a point of view from the modern theory of symmetry analysis on the closure problem in turbulence. Specifically, closure relationships in the physical space are interpreted as the (differential) equations of invariant sets (manifolds) in a phase-space. We demonstrate how this concept can be applied for verification of the local equilibrium approximations (LEA) of second-order moments. With this, we obtain the equivalence of LEA and vanishing the Poisson bracket for the defect of the longitudinal velocity component and of the turbulent energy. Numerical experiments carried out in a far turbulent wake confirm this conclusion.
Agradeço, primeiramente à Deus, por sua infinita misericórdia e fidelidade. Aos meus pais, Armando Payares H., e Marlene Guevara H., razão maior da minha existência. À minha esposa e companheira incondicional Mariela Perez A., pela paciência, amor e compreensão nas minhas ausências. Agradeço a CAPES pelo importante apoio financeiro. À minha família, pelo apoio, incentivo, compreensão e paciência. Quero agradecer ao Prof. Dr. Alexandre Grichkov, pela excelente orientação. Aos membros da banca pelas correções, sugestões e orientações, para a versão final da tese. Sou grato aos meus amigos de doutorado, pela força e amizade.
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