Non-axisymmetric subcritical bifurcations in viscoelastic Taylor-Couette flow. (English) Zbl 0826.76034

Sureshkumar, R.; Beris, Antony N.; Avgousti, Marios

Proc. R. Soc. Lond., Ser. A 447, No. 1929, 135-153 (1994).

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.

Reviewer: W.Koch (Göttingen)

MSC:

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

Keywords:

upper convected Maxwell fluid; Hopf bifurcation; axially travelling spirals; azimuthally rotating ribbons; spectral method; Oldroyd-B fluid