Stability of fronts separating domains with different symmetries in hydrodynamical instabilities.

Abstract

A generalization of the Swift-Hohenberg (SH) equation is used to study several stationary patterns that appear in hydrodynamical instabilities. The corresponding amplitude equations allow one to find the stability of planforms with different symmetries. These results are compared with numerical simulations of a generalized SH equation (GSHE). The transition between different symmetries, the hysteretic effects, and the characteristics of the defects observed in experiments are well reproduced in these simulations. The existence of steady fronts between domains with different symmetries is also analyzed. Steady domain boundaries between hexagons and rolls, and between hexagons and squares are possible solutions in the amplitude equation framework and are obtained in numerical simulations for a full range of coefficients in the GSHE.