On the structure of rotational instabilities in non-Newtonian fluids

The stability of an arbitrary base flow to large amplitude disturbances is examined from a theoretical standpoint for incompressible non-Newtonian fluids which are subjected to superimposed rigid body rotations. The non-inertial form of the full nonliner disturbance equations that arise from Cauchy's equations of motion are mathematically analyzed. For non-Newtonian fluids that satisfy the principle of material frame-indifference, it is proved that instabilities which depend on the state of rotation of a fluid must arise exclusively from variations in the velocity disturbances along the axis of rotation of the fluid. How these results are completely consistent with those obtained from the linear stability of rotating Newtonian fluids is demonstrated. Instabilities of the Taylor type in Couette flow and rotating plane Poiseuille flow are examined. The extensions of this analysis to the case of non-Newtonian fluids that violate material frame-indifference is also discussed.