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Model for interacting instabilities and texture dynamics of patterns.

A Das¹, K Kumar, N Ganesh

¹Physics and Applied Mathematics Unit, Indian Statistical Institute 203, Barrackpore Trunk Road, Calcutta 700 035, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|July 20, 2001

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This study presents a simple model for thermal convection patterns, revealing how interacting instabilities create complex textures like twisted patchwork quilt. Pattern formation strongly depends on the Prandtl number.

Area of Science:

Physics
Fluid Dynamics
Nonlinear Dynamics

Background:

Thermal convection generates complex patterns.
Understanding pattern formation requires studying interacting instabilities.
Previous models often simplify the dynamics of convective structures.

Purpose of the Study:

To present a simple dynamical model for thermal convection.
To investigate pattern formation, including stripes and patchwork quilt.
To analyze the influence of the Prandtl number on pattern textures.

Main Methods:

A twelve-mode dynamical system derived for a periodic square lattice was used.
Numerical simulations were performed to investigate pattern textures.
The interaction between different pattern types was analyzed.

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Main Results:

The model describes convective patterns such as stripes and patchwork quilt.
Interaction between zigzag stripes and patchwork quilt leads to twisted patchwork quilt patterns.
Pattern textures are strongly dependent on the Prandtl number.
A multicritical point, where four stability boundaries meet, was identified.

Conclusions:

The developed model offers a simplified yet effective way to study interacting instabilities in thermal convection.
The research highlights the crucial role of the Prandtl number in determining pattern textures.
The potential for a multicritical point suggests complex phase transitions in convective systems.