Exploring the Building Blocks of Chaotic Convection

Exciting progress has been made using powerful ideas from dynamical systems theory to build our physical understanding of chaotic and turbulent fluid flows. Two powerful ideas, in particular, have provided important new fundamental insights: covariant Lyapunov vectors (CLVs) and exact coherent structures (ECS). We will use the Lorenz system to motivate the CLVs and ECS. Due to the computational expense of these calculations for fluid problems, most investigations to date have either used CLVs or ECS. We present our efforts to build a unified investigation of chaotic Rayleigh-Bénard convection using both the CLVs and ECS. We have performed a numerical study to identify a minimal periodic domain that supports chaotic convection for typical parameters of interest. Using this domain, our goal is to compute the backward Lyapunov vectors, the CLVs, and the ECS for this flow field in the spiral defect chaos regime. We present our progress using these quantities to sharpen our understanding of chaotic fluid convection from a geometric point of view rooted in the tangent-space and state-space descriptions.