Abstract
The combined effect of mean flow and rotation on hexagonal patterns is investigated using Ginzburg-Landau equations that include nonlinear gradient terms as well as the nonlocal coupling provided by the mean flow. Long- and short-wave side-band instabilities are determined. Due to the nonlinear gradient terms and enhanced by the mean flow, the penta-hepta defects can become unstable to the induced nucleation of dislocations in the defect-free amplitude, which can lead to the proliferation of penta-hepta defects and persistent spatio-temporal chaos. For individual penta-hepta defects the nonlinear gradient terms enhance climbing or gliding motion, depending on whether they break the chiral symmetry or not.
Original language | English (US) |
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Pages (from-to) | 107-124 |
Number of pages | 18 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 176 |
Issue number | 1-2 |
DOIs | |
State | Published - Feb 15 2003 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics
Keywords
- Dislocations
- Ginzburg-Landau equation
- Hexagon pattern
- Mean flow
- Nucleation
- Penta-hepta defect
- Rotating convection
- Spatial-temporal chaos
- Stability