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Non-axisymmetric subcritical bifurcations in viscoelastic Taylor-Couette flow. (English) Zbl 0826.76034
Recent linear stability analysis of viscoelastic Taylor-Couette flow has shown that for high enough fluid elasticity the critical disturbances are non-axisymmetric and time-dependent. At the Hopf bifurcation point two possible patterns have been identified: axially travelling spirals and azimuthally rotating ribbons. The present paper extends the stability analysis into the weakly nonlinear regime. Using a spectral method, the equations are solved numerically for a selected set of geometric and kinematic parameters in an upper convected Maxwell or Oldroyd-B fluid. For a narrow gap at least one of the two families of critical flow patterns bifurcates subcritically. For a wider gap size both families become supercritical with the ribbons being stable.

MSC:
76E30 Nonlinear effects in hydrodynamic stability
76E05 Parallel shear flows in hydrodynamic stability
76A10 Viscoelastic fluids
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