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Proper invariant turbulence modelling within one-point statistics

Frewer, Michael (2009):
Proper invariant turbulence modelling within one-point statistics.
In: Journal of Fluid Mechanics, Cambridge University Press, pp. 37-64, 639, ISSN 0022-1120,
[Online-Edition: http://journals.cambridge.org/action/displayAbstract?fromPag...],
[Article]

Abstract

A new turbulence modelling approach is presented. Geometrically reformulating the averaged Navier–Stokes equations on a four-dimensional non-Riemannian manifold without changing the physical content of the theory, additional modelling restrictions which are absent in the usual Euclidean (3+1)-dimensional framework naturally emerge. The modelled equations show full form invariance for all Newtonian reference frames in that all involved quantities transform as true 4-tensors. Frame accelerations or inertial forces of any kind are universally described by the underlying four-dimensional geometry.

By constructing a nonlinear eddy viscosity model within the k−ε family for high turbulent Reynolds numbers the new invariant modelling approach demonstrates the essential advantages over current (3+1)-dimensional modelling techniques. In particular, new invariants are gained, which allow for a universal and consistent treatment of non-stationary effects within a turbulent flow. Furthermore, by consistently introducing via a Lie-group symmetry analysis a new internal modelling variable, the mean form-invariant pressure Hessian, it will be shown that already a quadratic nonlinearity is sufficient to capture secondary flow effects, for which in current nonlinear eddy viscosity models a higher nonlinearity is needed. In all, this paper develops a new unified formalism which will naturally guide the way in physical modelling whenever reasonings are based on the general concept of invariance.

Item Type: Article
Erschienen: 2009
Creators: Frewer, Michael
Title: Proper invariant turbulence modelling within one-point statistics
Language: English
Abstract:

A new turbulence modelling approach is presented. Geometrically reformulating the averaged Navier–Stokes equations on a four-dimensional non-Riemannian manifold without changing the physical content of the theory, additional modelling restrictions which are absent in the usual Euclidean (3+1)-dimensional framework naturally emerge. The modelled equations show full form invariance for all Newtonian reference frames in that all involved quantities transform as true 4-tensors. Frame accelerations or inertial forces of any kind are universally described by the underlying four-dimensional geometry.

By constructing a nonlinear eddy viscosity model within the k−ε family for high turbulent Reynolds numbers the new invariant modelling approach demonstrates the essential advantages over current (3+1)-dimensional modelling techniques. In particular, new invariants are gained, which allow for a universal and consistent treatment of non-stationary effects within a turbulent flow. Furthermore, by consistently introducing via a Lie-group symmetry analysis a new internal modelling variable, the mean form-invariant pressure Hessian, it will be shown that already a quadratic nonlinearity is sufficient to capture secondary flow effects, for which in current nonlinear eddy viscosity models a higher nonlinearity is needed. In all, this paper develops a new unified formalism which will naturally guide the way in physical modelling whenever reasonings are based on the general concept of invariance.

Journal or Publication Title: Journal of Fluid Mechanics
Volume: 639
Publisher: Cambridge University Press
Divisions: 16 Department of Mechanical Engineering > Fluid Dynamics (fdy)
16 Department of Mechanical Engineering
Date Deposited: 24 Aug 2011 18:13
Official URL: http://journals.cambridge.org/action/displayAbstract?fromPag...
Additional Information:

DOI: 10.1017/S0022112009991133

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