Abstract
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) |
---|---|
Pages (from-to) | 135-153 |
Number of pages | 19 |
Journal | Proceedings of The Royal Society of London, Series A: Mathematical and Physical Sciences |
Volume | 447 |
Issue number | 1929 |
DOIs | |
State | Published - 1994 |
Externally published | Yes |
ASJC Scopus subject areas
- Engineering(all)