Geodesic
Tensor-nonlinear shear flows: Material functions and the diffusion-vortex solutions
Russian journal of nonlinear dynamics, Tome 7 (2011) no. 3, pp. 451-463

Voir la notice de l'article provenant de la source Math-Net.Ru

This work deals with tensor-nonlinear constitutive relations connecting the deviators of stress tensor and strain rate tensor in incompressible isotropic media which are called in continuum mechanics as Reiner–Rivlin fluids. The connections of quadratic and cubic invariants of two tensors, where two material functions involve, are presented. The main attention is given to one-dimensional shear flows in various curvilinear coordinate systems. The scheme of obtaining of the material functions for shear on the basis of the steady Poiseuille flow in a plane layer is described. The self-similar solutions corresponding to the generalized diffusion of vortex layer both in plane and axially symmetric cases are derived.
Keywords: tensor nonlinearity, material function, Reiner–Rivlin fluid, shear, vortex layer.
Mots-clés : invariant, constitutive relation, diffusion of vortex 
@article{ND_2011_7_3_a3,
     author = {Dimitri V. Georgievskii},
     title = {Tensor-nonlinear shear flows: {Material} functions and the diffusion-vortex solutions},
     journal = {Russian journal of nonlinear dynamics},
     pages = {451--463},
     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2011_7_3_a3/}
}
TY  - JOUR
AU  - Dimitri V. Georgievskii
TI  - Tensor-nonlinear shear flows: Material functions and the diffusion-vortex solutions
JO  - Russian journal of nonlinear dynamics
PY  - 2011
SP  - 451
EP  - 463
VL  - 7
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2011_7_3_a3/
LA  - ru
ID  - ND_2011_7_3_a3
ER  - 
%0 Journal Article
%A Dimitri V. Georgievskii
%T Tensor-nonlinear shear flows: Material functions and the diffusion-vortex solutions
%J Russian journal of nonlinear dynamics
%D 2011
%P 451-463
%V 7
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2011_7_3_a3/
%G ru
%F ND_2011_7_3_a3
Dimitri V. Georgievskii. Tensor-nonlinear shear flows: Material functions and the diffusion-vortex solutions. Russian journal of nonlinear dynamics, Tome 7 (2011) no. 3, pp. 451-463. http://geodesic.mathdoc.fr/item/ND_2011_7_3_a3/