Premium
Local equilibrium approximation in free turbulent flows: Verification through the method of differential constrains
Author(s) -
Grebenev Vladimir N.,
Demenkov Andrew G.,
Chernykh Gennady G.,
Grichkov Alexandre N.
Publication year - 2021
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.202000095
Subject(s) - turbulence , closure (psychology) , differential (mechanical device) , differential equation , poisson bracket , equivalence (formal languages) , space (punctuation) , invariant (physics) , mathematics , statistical physics , mathematical analysis , phase space , physics , classical mechanics , mathematical physics , mechanics , computer science , pure mathematics , quantum mechanics , lie algebra , economics , market economy , thermodynamics , operating system
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.