A model for interacting instabilities and texture dynamics of patterns

Abstract

A simple model to study interacting instabilities and textures of resulting patterns for thermal convection is presented. The model consisting of twelve-mode dynamical system derived for periodic square lattice describes convective patterns in the form of stripes and patchwork quilt. The interaction between stationary zig-zag stripes and standing patchwork quilt pattern leads to spatiotemporal patterns of twisted patchwork quilt. Textures of these patterns, which depend strongly on Prandtl number, are investigated numerically using the model. The model also shows an interesting possibility of a multicritical point, where stability boundaries of four different structures meet.Comment: 4 pages including 4 figures, page width revise