Study of a model of thermal convection in cylindrical containers
We propose a generalized Swift-Hohenberg model equation that shows different planforms as observed in experiments in convective layers heated from below. We use this model to study the natural planform when some symmetric inhomogeneities are present on the sidewall boundary conditions. A stability analysis in the one-dimensional case allows us to determine when the rolls parallel to the sidewalls remain stable or perturbations perpendicular to these sidewalls can appear. Having the simple analysis in mind, we study numerical solutions of the model equation in two-dimensional case considering those inhomogeneities.
generalized Swift-Hohenberg model equation
scientific article; zbMATH DE number 493580