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Exploring spiral defect chaos in generalized Swift-Hohenberg models with mean flow
A Karimi1, Zhi-Feng Huang, M R Paul
1Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 21, 2011
Summary
We investigated spiral defect chaos in fluid dynamics models with mean flow. Stronger flow leads to spatiotemporal chaos, while weaker flow results in coarsening patterns and slowly moving target defects.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Fluid dynamics
Background:
- Spiral defect chaos is a complex pattern observed in various physical systems.
- Generalized Swift-Hohenberg equations model pattern formation in systems with mean flow.
- Understanding pattern dynamics under different flow conditions is crucial.
Purpose of the Study:
- To investigate spiral defect chaos in generalized Swift-Hohenberg models with mean flow.
- To analyze pattern dynamics as a function of mean flow magnitude.
- To compare flow field features with Rayleigh-Bénard convection.
Main Methods:
- Spatially extended domains were used for numerical integration.
- Equations were integrated over very long time scales.
- A continuous parameter adjusted mean flow magnitude, simulating fluid boundary conditions.
Main Results:
- Weak mean flow led to pattern coarsening and large, slow-moving target defects.
- Sufficiently strong mean flow induced spatiotemporal chaos, evidenced by a positive Lyapunov exponent.
- Spatial features near spiral defects were quantified and compared to Rayleigh-Bénard convection.
Conclusions:
- Mean flow significantly alters spiral defect chaos dynamics.
- A transition from coarsening to chaos occurs with increasing mean flow.
- The study provides insights into pattern formation influenced by fluid boundary conditions.
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