Sensitivity of convective structures to mean flow boundary conditions: A correlation between symmetry and dynamics

Abstract : Various simple structures have been proposed for modeling the transition to time dependence of convective patterns in extended geometries. In order to further question their relevance to the dynamics of complex structures ͑textures͒, we introduce a change of boundary conditions from both an experimental and a theoretical side. It consists in keeping the same roll structure but in separating the boundaries of the mean flows from those of the roll flows. This induces negligible effects on symmetric structures ͑straight rolls and foci͒ but dramatic changes on asymmetric ones ͑focus pairs and textures͒, especially regarding the onset of time dependence. Both kinds of sensitivity to this change of boundary conditions are recovered from the Cross-Newell equations. They reveal a correlation between symmetry and dynamics that prevents symmetric structures from modeling asymmetric ones. On the opposite side, they point to focus pairs as a plausible prototype of the mechanisms of time-dependence at work in textures.