Pattern Transitions in Unstable Viscous Convective Medium

Abstract

Convection in a thin layer of liquid (gas) with temperature dependent viscosity between poorly heat conducting boundaries is studied within framework of the Proctor-Sivashinsky model. This model is examined in order to study both the flow pattern formation and the second-order structural phase transitions as between patterns with translational invariance as well as between structures with broken translational invariance but keeping a long-range order. The spatial spectrum of arising patterns and estimation of their visual defectiveness are analyzed. The relation between the density of pattern defects and spectral characteristics of the pattern is found. We also discuss the noise effects on the formation of pattern defects. The influence of temperature dependence of viscosity on the process of pattern formation and structure transformations is also discussed. It is shown that the temperature dependence of viscosity inhibits structural transition from regular rolls to square cells