Viscoelastic Taylor-Couette instability as analog of the magnetorotational instability

A linear stability analysis and an experimental study of a viscoelastic Taylor-Couette flow corotating in the Keplerian ratio allow us to elucidate the analogy between the viscoelastic instability and the magnetorotational instability (MRI). A generalized Rayleigh criterion allows us to determine the potentially unstable zone to pure-elasticity-driven perturbations. Experiments with a viscoelastic polymer solution yield four modes: one pure-elasticity mode and three elastorotational instability (ERI) modes that represent the MRI-analog modes. The destabilization by the polymer viscosity is evidenced for the ERI modes.

Figure 1

Curves of critical states for different values of $S$ for $\eta =0.8$ in the Keplerian regime.

Figure 2

Stability diagram for $\eta =0.8$ in the Keplerian regime: solid lines, curves of the critical states predicted by LSA for $S\in 0.5,0.6,0.7,0.8$; closed circles, experimental critical values. The pictures are typical with the cross section of the four modes. Dashed vertical line corresponds to ${\widehat{E}}_0$.