Grebenev, V. N.; Oberlack, M. Hidden symmetries to a Hanjalic–Launder semiempirical model of turbulence. (English) Zbl 1164.76346 Regul. Chaotic Dyn. 11, No. 3, 371-381 (2006). Summary: The article is devoted to examining algebraic closure relationships which are used in the Theory of Semiempirical Models of Turbulence. As an example, the dynamics of a far plan turbulent wake is investigated and the so-called locally equilibrium approximation of second-order moments (tangential Reynolds stresses) is considered. Applicability of this algebraic approximation for tangential Reynolds stresses is analyzed by the method of differential constraints in the context of investigation of compatibility of the original mathematical model (the classical \((e,\varepsilon,\langle u'v'\rangle)\)-model of turbulence) with an added differential constraint (i.e. with an algebraic closure relationship for tangential Reynolds stresses). We show that the compatibility condition obtained coincide with the condition that a Hamiltonian vector field generated by the velocity field of the turbulent flow under consideration admits a symplectic symmetry of the canonical transformations. MSC: 76F55 Statistical turbulence modeling 76F60 \(k\)-\(\varepsilon\) modeling in turbulence 35Q35 PDEs in connection with fluid mechanics 35A30 Geometric theory, characteristics, transformations in context of PDEs 35C05 Solutions to PDEs in closed form Keywords:locally equilibrium approximation; turbulent wake; method of differential constraints; compatibility condition PDFBibTeX XMLCite \textit{V. N. Grebenev} and \textit{M. Oberlack}, Regul. Chaotic Dyn. 11, No. 3, 371--381 (2006; Zbl 1164.76346) Full Text: DOI