### 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 language | English |
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Pages (from-to) | 197-209 |

Number of pages | 13 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 149 |

Issue number | 3 |

DOIs | |

Publication status | Published - 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