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Pattern dynamics near inverse homoclinic bifurcation in fluids.
Pinaki Pal1, Krishna Kumar, Priyanka Maity
1Department of Mathematics, National Institute of Technology, Durgapur-713 209, India.
Summary
Researchers observed pattern dynamics in Rayleigh-Bénard convection, showing a transition from nonlocal to local dynamics near an inverse homoclinic bifurcation. This study reveals how pattern selection occurs in complex fluid systems.
Area of Science:
- Fluid Dynamics
- Nonlinear Dynamics
- Pattern Formation
Background:
- Extended dissipative systems exhibit complex pattern dynamics.
- Rayleigh-Bénard convection is a canonical model for studying pattern formation in fluids.
- Inverse homoclinic bifurcations represent critical transitions in dynamical systems.
Purpose of the Study:
- To investigate pattern dynamics near an inverse homoclinic bifurcation in a 3D Rayleigh-Bénard convection system.
- To characterize the transition from nonlocal to local pattern dynamics.
- To develop a simplified model capturing the observed dynamics.
Main Methods:
- Direct numerical simulations of three-dimensional Rayleigh-Bénard convection with stress-free boundary conditions.
- Analysis of pattern selection and temporal evolution of oscillating cross-roll patterns.
- Development and validation of a four-mode model.
Main Results:
- Observed spontaneous breaking of competing cross-roll patterns to a single set above a critical Rayleigh number.
- Demonstrated divergence and scaling behavior of the time period near the bifurcation point.
- Validated the four-mode model's ability to reproduce key pattern dynamics.
Conclusions:
- The study exemplifies a transition from nonlocal to local pattern dynamics associated with an inverse homoclinic bifurcation.
- The findings provide insights into pattern selection mechanisms in extended dissipative systems.
- The developed four-mode model offers a simplified yet effective tool for studying these complex dynamics.
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