Elastorotational instability in Taylor-Couette flow with Keplerian ratio as analog of the Magnetorotational Instability

The analogy between viscoelastic instability in the Taylor-Couette flow and the magnetorotational instability (MRI) has been found by Ogilvie \& Potter $\left[1\right]$. It relies on the similarity between the governing equations of viscoelastic flows of constant viscosity (Oldroyd-B model equations)and those of Magnetohydrodynamics (MHD). We have performed linear stability analysis of the Taylor-Couette flow with a polymer solution obeying the Oldroyd-B model. A diagram of critical states shows the existence of stationary and helicoidal modes depending on the elasticity of the polymer solution. A generalized Rayleigh criterion determines the potentially unstable zone to pure elasticity-driven perturbations. Experimental results yield four type of modes : one pure elasticity mode and three elastorotational modes that are the MRI-analog modes. Anti-Keplerian case has also been investigated. There is a good agreement between experimental and theoretical results $\left[2\right]$. \\[4pt] [1] G.I. Ogilvie \& A.T. Potter, \textit{Phys. Rev. Lett.} \textbf{100}, 074503 (2008).\\[0pt] [2] Y. Bai, O. Crumeyrolle \& I. Mutabazi, Phys. Rev. E.(2015)