### 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'.

Language | English |
---|---|

Pages | 197-209 |

Number of pages | 13 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 149 |

Issue number | 3 |

DOIs | |

Status | Published - 15 Feb 2001 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Condensed Matter Physics

### Cite this

**A Hopf/steady-state mode interaction in rotating convection : Bursts and heteroclinic cycles in a square periodic domain.** / Dawes, J. H P.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - A Hopf/steady-state mode interaction in rotating convection

T2 - Physica D: Nonlinear Phenomena

AU - Dawes, J. H P

PY - 2001/2/15

Y1 - 2001/2/15

N2 - 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'.

AB - 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'.

KW - 3D convection

KW - 47.20

KW - 47.54

KW - Bursting

KW - Heteroclinic cycle

KW - Mode interaction

KW - Rotation

UR - http://www.scopus.com/inward/record.url?scp=0035252706&partnerID=8YFLogxK

U2 - 10.1016/S0167-2789(00)00201-3

DO - 10.1016/S0167-2789(00)00201-3

M3 - Article

VL - 149

SP - 197

EP - 209

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 3

ER -