Hopf-Hopf and steady-Hopf mode interactions in Taylor-Couette flow of an upper convected Maxwell liquid

M. Renardy, Y. Renardy, R. Sureshkumar, A. N. Beris

Research output: Contribution to journalArticle

27 Scopus citations

Abstract

In the viscoelastic Taylor-Couette flow, it is known that at certain parameter values, the onset condition can involve more than one mode becoming unstable. We focus on the upper convected Maxwell liquid, and on the situation where two Hopf modes, or a Hopf mode and a steady mode, are simultaneously at criticality. The interaction of such modes is investigated at critical situations. Weakly non-linear amplitude equations are derived for the interaction of these modes, based on a center manifold reduction scheme. The two modes generate a two-parameter bifurcation. The coefficients involved in the equations are determined numerically, based on the physical parameters of the system at criticality. For the cases investigated, it is found that all the bifurcated branches of solutions are unstable. Moreover, direct numerical simulation of the amplitude equations does not lead to bounded solutions.

Original languageEnglish (US)
Pages (from-to)1-31
Number of pages31
JournalJournal of Non-Newtonian Fluid Mechanics
Volume63
Issue number1
DOIs
StatePublished - Mar 1996
Externally publishedYes

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Keywords

  • Hopf-Hopf mode
  • Steady-Hopf mode
  • Taylor-Couette flow
  • Upper convected Maxwell liquid

ASJC Scopus subject areas

  • Chemical Engineering(all)
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanical Engineering
  • Applied Mathematics

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