Instabilities and Spatio-temporal Chaos of Long-wave Hexagon Patterns in Rotating Marangoni Convection

Abstract

We consider surface-tension driven convection in a rotating fluid layer. For nearly insulating boundary conditions we derive a long-wave equation for the convection planform. Using a Galerkin method and direct numerical simulations we study the stability of the steady hexagonal patterns with respect to general side-band instabilities. In the presence of rotation steady and oscillatory instabilities are identified. One of them leads to stable, homogeneously oscillating hexagons. For sufficiently large rotation rates the stability balloon closes, rendering all steady hexagons unstable and leading to spatio-temporal chaos.