On exchanges between convective modes in a slightly tilted porouscavity

MD Impey, DS Riley

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)

Abstract

We use Liapunov–Schmidt reduction and singularity-theory methods to investigate the bifurcation structure of steady free convection in a finite two-dimensional saturated porous cavity heated from below. In particular, we develop a qualitative model describing the modal exchanges that occur as the aspect ratio of a slightly tilted cavity varies. ℤ2-symmetry breaking bifurcations are involved in these exchanges and the mechanism is significantly different from those in previously studied physical systems. The work is akin to, but distinct from, that of Schaeffer's on the Taylor–Couette problem. We also derive and clearly state conditions for the application of this model to modal exchange in other systems.
Translated title of the contributionOn exchanges between convective modes in a slightly tilted porouscavity
Original languageEnglish
Pages (from-to)395-416
Number of pages22
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume110
Issue number2
DOIs
Publication statusPublished - 1991

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