Frameinvariance of turbulence constitutive relations.
Abstract
The applicability of the principle of material frameindifference to turbulence and its consequences for turbulence modelling are considered. By introducing a distinction between arbitrary timedependent orthogonal transformations of (i) the fluid motion, and (ii) the observer, we find that frameinvariant tensorial measures of the absolute angular velocity and acceleration can be defined. This follows from consideration of a fourdimensional 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 frameindifference. 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.
 Publication:

Astrophysics and Space Science
 Pub Date:
 February 1988
 DOI:
 10.1007/BF00641922
 Bibcode:
 1988Ap&SS.141..159T
 Keywords:

 Constitutive Equations;
 Invariance;
 Reynolds Stress;
 Turbulent Flow;
 Angular Velocity;
 Mathematical Models;
 Tensors;
 Turbulence Models;
 Velocity Distribution;
 Physics (General);
 Fluid Dynamics:Turbulence