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Hydrodynamic coarsening in striped pattern formation with a conservation law
1Statistical Mechanics Laboratory, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606-8585, Japan. shiway@kit.ac.jp
Summary
Numerical simulations reveal that hydrodynamic flow, when combined with striped-pattern instability and a zero mode, creates distinct upflow and downflow hexagonal domains. This interaction is crucial for pattern formation in fluid dynamics.
Area of Science:
- Fluid dynamics
- Pattern formation
- Instability phenomena
Background:
- Fluid flow can exhibit complex pattern formation.
- Instabilities drive transitions in fluid behavior.
- Zero modes can influence system dynamics.
Purpose of the Study:
- To investigate the emergence of hexagonal domain patterns in numerical simulations.
- To understand the role of hydrodynamic flow and specific instabilities in pattern generation.
Main Methods:
- Numerical simulations were employed.
- The interaction between striped-pattern-forming instability and a neutrally stable zero mode was analyzed.
Main Results:
- The study observed the coexistence of upflow and downflow hexagonal domains.
- These patterns were found to be dependent on the presence of hydrodynamic flow.
- The interaction of the specified instability and zero mode was identified as the key mechanism.
Conclusions:
- Hydrodynamic flow is essential for the formation of coexisting upflow and downflow hexagonal domains.
- The interplay between striped-pattern instability and a zero mode dictates the observed domain patterns.