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We report experimental observation of an instability in a Couette-Taylor flow of a polymer fluid in a thin gap between two coaxially rotating cylinders in a regime where their angular velocity decreases with the radius while the specific angular momentum increases with the radius. In the considered regime, neither the inertial Rayleigh instability nor the purely elastic instability are possible. We propose that the observed “elasto-rotational” instability is an analog of the magnetorotational instability which plays a fundamental role in astrophysical Keplerian accretion disks.

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