Viscoelastic Taylor–Couette instability in the Keplerian regime

Abstract

Instability modes of viscoelastic Taylor–Couette flow in the Keplerian regime are investigated using both linear stability analysis and experimental detection of critical states. A generalised Rayleigh criterion has been derived and it allows to separate the zone of potential purely elastic instability modes and the zone of stability. The analogy between the instability of viscoelastic Taylor–Couette flow in the Keplerian regime and the magnetorotational instability (MRI) of conducting magnetic fluids is established. Viscoelastic stress tensor can be represented by a tensor product of magnetic-like vectors. This allows to use the Velikhov-Chandrasekhar criterion of the MRI to predict the elasto-rotational instability (ERI). ERI modes obtained in linear stability and in the experiments are assumed to represent the MRI analogue modes as they are observed in the stable zone according to generalised Rayleigh discriminant.