The goals of this project are to develop techniques for the detection and prediction of low-dimensional features in high-dimensional, spatially extended systems, to investigate how coherent structures within the system affect predictability, to test control strategies for high-dimensional, spatially extended systems, and to improve understanding of uncertainty as a function of spatial scale in such systems. One motivation for the work is the desire to develop better state estimation techniques for complex environmental systems. The model system for this work is that of shallow thermal convection. The project combines laboratory experiment with theory and modeling. As well as being a good model system, convection is important in many environmental systems in the atmosphere, ocean and interior of the Earth, and in industrial settings. Thermal convection exhibits multi-scale spatial and temporal complexity and laboratory convection experiments provide plentiful, high quality, observational data under relatively well-controlled conditions. The laboratory experiments use carbon dioxide as the convecting medium in a shallow cell. Specific spiral-defect chaos flow patterns can be initiated using a computer-steered laser system that selectively heats parts of the fluid. The primary theoretical tool is a state estimation technique in which a local ensemble Kalman filter is applied to a numerical Navier-Stokes solver. This will be applied to a range of flow patterns of increasing complexity exhibited by the convection cell as the Rayleigh number is increased. The data to be assimilated will be taken from shadowgraph images of the convection. Later stages of the project will include experiments in control of the convection using selective heating guided by output from the state estimation system. It is anticipated that the results of this work will be applicable to other spatially-extended complex systems.
