An analogy between astrophysical magnetorotational instability and a viscoelastic instability in a Taylor-Couette flow of polymer fluids

Magnetorotational instability is thought to play an important role in transporting angular momentum out of astrophysical systems. During the last twenty years, considerable progress has been made in understanding the effects of such instability on differentially rotating flows. A sizable amount of analytic work was devoted to linear analysis of instability thresholds, and extensive numerical simulations of the nonlinear stage of the magnetorotational instability have also been performed. Laboratory investigations of the magnetorotational instability in liquid-metal experiments have been proposed and conducted. However, large resistivity of liquid metals complicates unambiguous laboratory study of the magnetorotational instability and it still remains a challenge to address the ranges of scales relevant for real astrophysical systems.;Polymer molecules exhibit elastic behavior and can be modeled using Hookean springs. This leads to the observation that there is a physical and mathematical similarity between the dynamics of viscoelastic polymer fluids and magnetohydrodynamic fluids. A polymer molecule frozen into a fluid is advected and distorted by a fluid flow and reacts to the flow by its tension and accordingly imparts an elasticity to the fluid much in the same way a magnetic field line frozen into an electrically conducting fluid is advected and distorted by a fluid flow and reacts to the flow by a tension exerted by the magnetic field through the Lorentz force. Indeed in a certain range of parameters, the dynamic equations describing viscoelastic polymer fluids are identical to the magnetohydrodynamic equations describing conducting fluids or plasmas. This analogy provides a new avenue with which to investigate the fundamental astrophysical instability in a simple laboratory setting.;This thesis presents theoretical and laboratory studies of a new type of viscoelastic instability in Taylor-Couette flows of polymer fluids that is proposed to be analogous to the magnetorotational instability. A threshold for this new type of instability of polymer fluids is offered for a broad range of polymer and solvent parameters and the question is addressed as to the observability of the instability in experiments.