Wave-vector field of convective flow patterns

Abstract

Textured convective flow patterns in a large cylindrical layer are studied using digital image processing methods to measure the wave-vector field q(r), a slowly varying two-dimensional field that may be used to characterize complex patterns quantitatively. We describe in some detail the development of this method and its application to the analysis of both steady and time-dependent patterns. The variation of the convective textures with \ensuremath{\epsilon}=(R-${R}_{c}$)/${R}_{c}$, where ${R}_{c}$ is the critical Rayleigh number, is studied using quantities derived from the wave-vector field, such as its divergence and its orientation at the boundary of the container. We also find a useful criterion for the stability of convective patterns: Time-dependent patterns usually have a distribution of wave numbers that lies partially outside the predicted stable band for an infinite layer. Measurements of the Swift-Hohenberg Lyapunov functional show that this quantity varies by up to 25% for different stable patterns at the same value of \ensuremath{\epsilon}. .AE