On material frame-indifference, intrinsic spin, and certain constitutive relations motivated by the kinetic theory of gases

1983 ◽  
Vol 83 (2) ◽  
pp. 185-194 ◽  
Author(s):  
A. I. Murdoch
Keyword(s):  
Kinetic Theory ◽  
Constitutive Relations ◽  
Kinetic Theory Of Gases ◽  
Frame Indifference ◽  
Material Frame Indifference ◽  
Material Frame

A note on constraints in turbulence modelling

1999 ◽  
Vol 391 ◽  
pp. 373-376 ◽  
Author(s):  
PHILIPPE R. SPALART ◽  
CHARLES G. SPEZIALE
Keyword(s):  
Dimensional Analysis ◽  
Constitutive Relations ◽  
Turbulence Models ◽  
Turbulence Modelling ◽  
Reynolds Stresses ◽  
Frame Indifference ◽  
Material Frame Indifference ◽  
Material Frame ◽  
Viscous Stresses

We show that the class of constitutive relations for turbulence models put forward by Wang (1997) in this journal conflicts with dimensional analysis, unless the turbulent Reynolds stresses were to be tied to the molecular viscous stresses everywhere in the flow. We then reiterate, using counter-examples, that the controversial postulate of material frame-indifference is unfounded for turbulence, and is counter-productive in the quest for accuracy. We add a comment on the role of acceleration.

Constitutive relations for polar continua based on statistical mechanics and spatial averaging

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190407
Author(s):  
Bob Svendsen
Keyword(s):  
Angular Momentum ◽  
Constitutive Relations ◽  
Volume Averaging ◽  
Mass Point ◽  
Momentum Balance ◽  
Spatial Averaging ◽  
Material Frame Indifference ◽  
Phase Space Transport ◽  
Polar Continua ◽  
Material Frame

The purpose of the current work is the formulation of macroscopic constitutive relations, and in particular continuum flux densities, for polar continua from the underlying mass point dynamics. To this end, generic microscopic continuum field and balance relations are derived from phase space transport relations for expectation values of point fields related to additive mass point quantities. Given these, microscopic energy, linear momentum and angular momentum, balance relations are obtained in the context of the split of system forces into non-conservative and conservative parts. In addition, divergence–flux relations are formulated for the conservative part of microscopic supply-rate densities. For the case of angular momentum, two such relations are obtained. One of these is force-based, and the other is torque-based. With the help of physical and material theoretic restrictions (e.g. material frame-indifference), reduced forms of the conservative flux densities are obtained. In the last part of the work, formulation of macroscopic constitutive relations from their microscopic counterparts is investigated in the context of different spatial averaging approaches. In particular, these include (weighted) volume-averaging based on a localization function, surface averaging of normal flux densities based on Cauchy flux theory and volume averaging with respect to centre of mass.

Remarks on material frame-indifference controversy

2013 ◽  
Vol 225 (2) ◽  
pp. 331-348 ◽  
Author(s):  
I-Shih Liu ◽  
Rubens Sampaio
Keyword(s):  
Frame Indifference ◽  
Material Frame Indifference ◽  
Material Frame
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