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.
|Original language||English (US)|
|Number of pages||19|
|Journal||Proceedings of The Royal Society of London, Series A: Mathematical and Physical Sciences|
|State||Published - 1994|
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