Elastic turbulence in the Taylor-Couette system with a shear-thinning polymer solution

We have investigated the transition scenario to elastic turbulence for a semi-dilute solution of polyethylene oxide in the Couette-Taylor system with fixed outer cylinder. The control parameters are the Taylor number \textit{Ta}, the elastic number $E$ and the viscosity ratio $S$ = \textit{$\eta $}$_{p}$\textit{/$\eta $}$_{s}$ [1,2]. The solution is shear-thinning i.e. the viscosity decreases as the strain increases. The first instability mode from the base flow appears as a pattern of counterpropagating waves with a strong interaction that leads to large second harmonics in space and in time. We have found two regions in the parameter space with different higher instability modes : for small values $E$, a small increase of \textit{Ta} leads to a pattern dominated by spatiotemporal defects and holes, and a further increase of \textit{Ta} leads to spatiotemporal intermittency with determined critical parameters. For intermediate values of $E$, the pattern bifurcates to a pattern formed by large counter-rotating vortices with a localized strong inflow but a weak outflow. These large vortices are have an irregular size is of about 5$d$ where $d$ is the gap size. These vortices have been previously observed in solutions with constant viscosity [3]. [1] S. Muller, E. Shaqfeh {\&} R. Larson, J. Non-Newtonian Fluid Mech. \textbf{46}, 315(1993) [2] O. Crumeyrolle, I. Mutabazi {\&} M. Grisel, \textit{Phys. Fluids} \textbf{14}, 1681(2002) [3] A. Groisman {\&} V. Steinberg, \textit{Phys. Fluids} \textbf{10}, 2451(1998)