Non-axisymmetric subcritical bifurcations in viscoelastic Taylor-Couette flow

In this paper, the bifurcating families corresponding to each one of the two possible non-axisymmetric patterns emerging at the point of criticality, namely the spirals and ribbons any are calculated and their stability are determined. It is shown that for a narrow gap size, the upper convected Maxwell and Oldroyd-B fluids, at least one of the non-axisymmetric families bifurcates subcritically. This result, in conjunction with theoretical analysis of Hopf bifurcation in presence of symmetries, implies that neither of the bifurcating families is stable. Thus, there is a finite transition corresponding to infinitesimal changes of the flow parameters in the vicinity of the Hopf bifurcation point.