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Related Experiment Video

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Magnetically Induced Rotating Rayleigh-Taylor Instability

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

Coexistence of Eckhaus instability in forced zigzag Turing patterns.

Igal Berenstein¹, Alberto P Muñuzuri

¹Group of Nonlinear Physics, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain. igal@fmares.usc.es

The Journal of Chemical Physics

|December 3, 2008

Summary

Pattern-forming systems exhibit Eckhaus and zigzag instabilities when forced with mismatched wavelengths. These instabilities can coexist and interact, leading to pattern reorientation under traveling stripe forcing.

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Area of Science:

Nonlinear dynamics
Pattern formation physics

Background:

Wavelength selection is crucial in pattern-forming systems.
Two primary instabilities, Eckhaus and zigzag, arise from imposed wavelength mismatches.
These instabilities occur when the imposed wavelength is smaller (Eckhaus) or larger (zigzag) than the system's preferred wavelength.

Purpose of the Study:

Investigate the coexistence of Eckhaus and zigzag instabilities in a pattern-forming system.
Analyze the impact of forcing Turing patterns with slowly moving stripes.
Determine if coupled instabilities can induce pattern reorientation.

Main Methods:

Experimental setup involving Turing patterns.
Forcing patterns with slowly moving stripes at a specific wavelength ratio (1.5x preferred).
Observation and analysis of pattern dynamics and instabilities.

Main Results:

Demonstrated the coexistence of Eckhaus and zigzag instabilities under experimental conditions.
Observed that these instabilities occur when the imposed stripe wavelength is approximately 1.5 times the Turing pattern wavelength.
Showcased pattern reorientation resulting from the coupling of these instabilities.

Conclusions:

Eckhaus and zigzag instabilities are not mutually exclusive and can coexist in forced pattern-forming systems.
The interaction between these instabilities can drive significant changes in pattern orientation.
This study provides insights into the complex dynamics of pattern formation under external forcing.