Abstract

We investigate the transition between oscillatory and steady convection at onset in low Prandtl number rotating convection in a plane layer. This transition is dominated by mode interactions which, at one point in parameter space, can be posed on a square lattice. This allows a rigorous reduction to a finite-dimensional bifurcation problem. We construct the normal form and compute the normal form coefficients for this codimension-2 bifurcation directly from the PDEs for Boussinesq rotating convection with stress-free upper and lower boundaries. The dynamics near the codimension-2 point are investigated fully; they explain behaviour found in numerical simulations of the PDEs at parameter values near the transition boundary. In particular, the normal form exhibits bursting dynamics created by a heteroclinic cycle containing points 'at infinity'.

Original languageEnglish
Pages (from-to)197-209
Number of pages13
JournalPhysica D: Nonlinear Phenomena
Volume149
Issue number3
DOIs
Publication statusPublished - 15 Feb 2001

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Keywords

  • 3D convection
  • 47.20
  • 47.54
  • Bursting
  • Heteroclinic cycle
  • Mode interaction
  • Rotation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Condensed Matter Physics

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