The neutral curve for stationary disturbances in rotating disk flow for power-law fluids

• We consider the stability of the 3D boundary layer flow of a rotating power-law fluid.
• We present a linear numerical convective stability analysis.
• We model the stationary spiral instabilities that are observed in the Newtonian case.
• Curves of neutral stability are computed using a sixth-order system of equations.
• We show that shear-thinning fluids have a stabilising effect on the flow.

This paper is concerned with the convective instabilities associated with the boundary-layer flow due to a rotating disk. Shear-thinning fluids that adhere to the power-law relationship are considered. The neutral curves are computed using a sixth-order system of linear stability equations which include the effects of streamline curvature, Coriolis force and the non-Newtonian viscosity model. Akin to previous Newtonian studies it is found that the neutral curves have two critical values, these are associated with the type I upper-branch (cross-flow) and type II lower-branch (streamline curvature) modes. Our results indicate that an increase in shear-thinning has a stabilising effect on both the type I and II modes, in terms of the critical Reynolds number and growth rate. Favourable agreement is obtained between existing asymptotic predictions and the numerical results presented here.