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It is shown that the physical interpretation of Elie Cartan three-dimensionalspace torsion as couple asymmetric stress, has the effect of damping,previously Riemannian unstable Couette planar shear flow, leading to stabilityof the flow in the Lagrangean sense. Actually, since the flow speed isinversely proportional to torsion, it has the effect of causing a damping inthe planar flow atenuating the instability effect. In this sense we may saythat Cartan torsion induces shear viscous asymmetric stresses in the fluid,which are able to damp the instability of the flow. The stability of the flowis computed from the sectional curvature in non-Riemannian three-dimensionalmanifold. Marginal stability is asssumed by making the sectional non-Riemanniancurvature zero, which allows us to determine the speeds of flows able to inducethis stability. The ideas discussed here show that torsion plays thegeometrical role of magnetic field in hydromagnetic instability of Couetteflows recently investigated by Bonnano and Urpin (PRE, (2007,in press) can beextended and applied to plastic flows with microstructure defects. RecentlyRiemannian asymmetric stresses in magnetohydrodynamics (MHD) have beenconsidered by Billig (2004).

Non-Riemannian geometrical asymmetrical damping stresses on the Lagrange instability of shear flows