Linear stability of a Couette flow for non-monotone stress-power law models

In this paper we investigate the linear stability of a Couette flow driven by a shear stress imposed on the top surface of a fluid layer, assuming that the material obeys an “S-shaped” stress-power law model. The perturbation equation is solved numerically by means of a spectral collocation scheme based on Chebyshev polynomials. We show that there exists a range of Reynolds numbers in which multiple flows are possible. In particular, our results highlight that the solutions belonging to the ascending branches of the constitutive law are unconditionally stable, while those in the descending branch are unconditionally unstable. Graphic abstract: [Figure not available: see fulltext.]