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Evolution of Staircase Structures in Diffusive Convection
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Stationary localized solutions in binary convection in slightly inclined rectangular cells.
Arantxa Alonso1, Oriol Batiste1, Isabel Mercader1
1Departament de Física, Universitat Politècnica de Catalunya, Mòdul B4, 08034 Barcelona, Spain.
Physical Review. E
|December 23, 2022
Summary
Researchers numerically studied convectons in binary mixtures, discovering new localized solutions with unique spatial features. These findings reveal complex behaviors in snaking diagrams under varying cell inclinations and heating conditions.
Area of Science:
- Fluid dynamics
- Nonlinear dynamics
- Complex systems
Background:
- Convectons, a type of pattern formation, occur in binary mixtures under specific conditions.
- Previous studies focused on convectons in horizontal cells, with less known about their behavior under slight inclinations.
Purpose of the Study:
- To numerically investigate the impact of slight cell inclinations on convectons.
- To identify and characterize novel stationary localized solutions.
- To explore the coexistence and organization of these solutions in snaking diagrams.
Main Methods:
- Numerical analysis of fluid dynamics in two-dimensional elongated rectangular cells.
- Continuation methods to track solutions with respect to cell inclination.
- Exploration of parameter space for moderate to high heating.
Main Results:
- Discovery of novel stationary localized solutions distinct from typical convectons.
- Identification of further solution families organizing into closed branches.
- Observation of a complex coexistence of multiple localized solutions for identical parameters.
- Detailed characterization of solutions in the lowest part of snaking diagrams.
Conclusions:
- Slight cell inclinations introduce significant complexity to convecton behavior.
- New classes of localized structures emerge, expanding the understanding of pattern formation.
- The coexistence of diverse solutions highlights the intricate dynamics in these systems.
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