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'.

LanguageEnglish
Pages197-209
Number of pages13
JournalPhysica D: Nonlinear Phenomena
Volume149
Issue number3
DOIs
StatusPublished - 15 Feb 2001

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bursts
convection
pulse detonation engines
cycles
interactions
Prandtl number
infinity
coefficients
simulation

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

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title = "A Hopf/steady-state mode interaction in rotating convection: Bursts and heteroclinic cycles in a square periodic domain",
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'.",
keywords = "3D convection, 47.20, 47.54, Bursting, Heteroclinic cycle, Mode interaction, Rotation",
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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'.

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KW - 47.54

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