Frame-invariance of turbulence constitutive relations
type: Item
instance of: scholarly article
title: Frame-invariance of turbulence constitutive relations
zbMATH Open document ID: 0664.76054
DOI: 10.1007/BF00641922
author: S. H. Smith
published in: Astrophysics and Space Science
publication date: 1988-01-01T00:00:00Z
review text: The applicability of the principle of material frame-indifference to turbulence and its consequences for turbulence modelling are considered. By introducing a distinction between arbitrary time-dependent orthogonal transformations of (i) the fluid motion, and (ii) the observer, we find that frame-invariant tensorial measures of the absolute angular velocity and acceleration can be defined. This follows from consideration of a four-dimensional formulation of classical mechanics which formally possesses the property of invariance under arbitrary changes of frame of the observer. These tensors allow the construction of constitutive equations which depend, for example, on the absolute angular velocity of the fluid, and which also satisfy the principle of material frame- indifference. The results of this analysis have application outside the field of turbulence modelling. The invariance properties of some previously published Reynolds stress transport turbulence models are examined and modifications are suggested.
Mathematics Subject Classification ID: 76F99
Mathematics Subject Classification ID: 76A02
zbMATH DE Number: 4087259
zbMATH Keywords: material frame-indifference
zbMATH Keywords: turbulence
zbMATH Keywords: four-dimensional formulation
zbMATH Keywords: Reynolds stress
MaRDI profile type: Publication
cites work: Progress in the development of a Reynolds-stress turbulence closure
cites work: Derivation of the Stochastic Helmholtz Equation for Sound Propagation in a Turbulent Fluid
cites work: Invariance of turbulent closure models
cites work: Galilean invariance of subgrid-scale stress models in the large-eddy simulation of turbulence
description: scientific article; zbMATH DE number 4087259