Abstract
Three-dimensional pattern selection in a low Prandtl number Boussinesq fluid with stress-free boundaries, where the onset of convection is oscillatory, is explored. Restricting the problem to a square lattice, the normal form coefficients are calculated as functions of τ (the square root of the Taylor number) and the Prandtl number σ. There is a large region of the (σ, τ) plane where a heteroclinic cycle connecting four Travelling Roll states is stable. As σ is decreased the cycle undergoes a transverse loss of stability, creating quasiperiodic orbits which may themselves become chaotic. All these stable dynamics occur at onset. Although conjectured on the basis of general results from symmetric bifurcation theory (and well-known for steady convection as the Kuppers-Lortz instability), cycling behaviour has not previously been demonstrated directly from the hydrodynamic equations in the oscillatory case. A second region of the (σ, τ) plane contains stable Travelling Roll solutions: we examine their stability to perturbations at varying angles and demonstrate the existence of small-angle instabilities of travelling rolls.
Original language | English |
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Pages (from-to) | 336-351 |
Number of pages | 16 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 147 |
Issue number | 3-4 |
DOIs | |
Publication status | Published - 15 Dec 2000 |
Funding
I have benefited from discussions with Michael Proctor and Alastair Rucklidge. The presentation of this work has been greatly improved by many perceptive and helpful comments from two anonymous referees. This work was funded by the UK EPSRC.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Condensed Matter Physics