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Realizability of Reynolds-Stress Turbulence Models

Schumann, U. (1977) Realizability of Reynolds-Stress Turbulence Models. Physics of Fluids, 20, pp. 721-725. DOI: 10.1063/1.861942.

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Abstract

It is shown that certain existing phenomenological models of turbulence in terms of differential equations for the Reynolds stresses R<sub>α</sub><sub>β</sub>=(ul<sub>α</sub> ul<sub>β</sub>) do not guarantee realizable solutions. The known realizability conditions are R<sub>α</sub><sub>β</sub> ≥ 0 for α=β and R<sup>2</sup><sub>α</sub><sub>β</sub> ≥ R<sub>α</sub><sub>α</sub>R<sub>β</sub><sub>β</sub> for α≠β. A stronger requirement is that the matrix R<sub>α</sub><sub>β</sub> be positive semi-definite. This implies three conditions like non-negative eigenvalues or non-negative principal invariants. Conditions are given which must be satisfied by the model itself in order to guarantee realizable solutions for any realizable initial and boundary conditions. Some means are proposed which can be used to change the existing models into realizable ones.

Document Type:Article
Title:Realizability of Reynolds-Stress Turbulence Models
Authors:
AuthorsInstitution or Email of Authors
Schumann, U.KFZ Karlsruhe
Date:1977
Journal or Publication Title:Physics of Fluids
Volume:20
DOI:10.1063/1.861942
Page Range:pp. 721-725
Status:Published
Keywords:differential equations, Reynolds stresses
HGF - Research field:other
HGF - Program:other
HGF - Program Themes:other
DLR - Research area:no assignement
DLR - Program:no assignment
DLR - Research theme (Project):other
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Atmospheric Physics
Deposited By: Jana Freund
Deposited On:15 Feb 2008
Last Modified:12 Dec 2013 20:29

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