Abstract
We review recent computational results for hexagon patterns innon-Boussinesq convection. For sufficiently strong dependence of the fluid parameters on the temperature we find reentrance of steady hexagons, i.e. while near onset the hexagon patterns become unstable to rolls as usually, they become again stable in the strongly nonlinear regime. If the convection apparatus is rotated about avertical axis the transition from hexagons to rolls is replaced by aHopf bifurcation to whirling hexagons. For weak non-Boussinesq effects they display defect chaos of the type described by the two-dimensional (2D)complex Ginzburg-Landau equation. For stronger non-Boussinesq effectsthe Hopf bifurcation becomes subcritical and localized bursting of the whirling amplitude is found. In this regime the coupling of the whirling amplitude to (small) deformations of the hexagon lattice becomes important. For yet stronger non-Boussinesq effects this coupling breaks up the hexagon lattice and strongly disordered states characterized by whirling and lattice defects are obtained.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 279-290 |
| Number of pages | 12 |
| Journal | European Physical Journal: Special Topics |
| Volume | 146 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jul 2007 |
Funding
This paper is dedicated to the memory of Carlos P\u00E9rez-Gar\u0107\u0131a, who was SM\u2019s thesis advisor and who introduced him to the field of pattern formation. SM is grateful for years of friendship and stimulating discussions. We thank W. Pesch for providing us with the numerical codes used in this project and for ongoing support. This research was supported by NSF (DMS-9804673), by the Department of Energy (DE-FG02-92ER14303), and by EU under grant MRTN-CT-2004-005728 (SM).
ASJC Scopus subject areas
- General Materials Science
- General Physics and Astronomy
- Physical and Theoretical Chemistry