Abstract
The dynamics of hexagon patterns in rotating systems are investigated within the framework of modified Swift-Hohenberg equations that can be considered as simple models for rotating convection with broken up-down symmetry, e.g. non-Boussinesq Rayleigh-Bénard or Marangoni convection. In the weakly nonlinear regime a linear stability analysis of the hexagons reveals long- and short-wave instabilities, which can be steady or oscillatory. The oscillatory short-wave instabilities can lead to stable hexagon patterns that are periodically modulated in space and time, or to a state of spatio-temporal chaos with a Fourier spectrum that precesses on average in time. The chaotic state can exhibit bistability with the steady hexagon pattern. There exist regimes in which the steady hexagon patterns are unstable at all wave numbers.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 124-141 |
| Number of pages | 18 |
| Journal | Physica D: Nonlinear Phenomena |
| Volume | 144 |
| Issue number | 1-2 |
| DOIs | |
| State | Published - Sep 15 2000 |
Funding
We gratefully acknowledge helpful discussions with B. Echebarria, A. Golovin, A. Mancho, W. Pesch, and M. Silber. The computations were done with a modification of a code by G. D. Granzow. This work was supported by D.O.E. Grant DE-FG02-92ER14303 and NASA Grant NAG3-2113.
Keywords
- 47.20.Dr
- 47.20.Ky
- 47.27.Te
- 47.54.+r
- Hexagon patterns
- Rotating convection
- Sideband instabilities
- Spatio-temporal chaos
- Swift-Hohenberg equation
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics