Collaborative Research: MSPA-CSE: State Estimation and Predictability of High-Dimensional Complex Systems--Theory and Experiment

该项目的目标是开发高维空间扩展系统中低维特征的检测和预测技术，研究系统内的连贯结构如何影响可预测性，测试高维空间扩展系统的控制策略，并提高对不确定性作为空间尺度函数在此类系统中的理解。这项工作的动机之一是希望为复杂的环境系统开发更好的状态估计技术。本工作的模式系统为浅层热对流模式系统。该项目将实验室实验与理论和建模相结合。对流不仅是一个很好的模式系统，而且在大气、海洋、地球内部以及工业环境等许多环境系统中也很重要。热对流具有多尺度的时空复杂性，室内对流实验在相对较好的控制条件下提供了丰富、高质量的观测数据。在实验室实验中，二氧化碳作为对流介质在一个浅细胞。使用计算机控制的激光系统可以选择性地加热部分流体，从而启动特定的螺旋缺陷混沌流模式。主要的理论工具是一种状态估计技术，其中局部集合卡尔曼滤波器应用于数值Navier-Stokes解算器。这将适用于随着瑞利数的增加，对流单元所表现出的越来越复杂的流动模式的范围。待同化的数据将取自对流的阴影图像。该项目的后期阶段将包括使用状态估计系统输出引导的选择性加热来控制对流的实验。预计本工作的结果将适用于其他空间扩展的复杂系统。

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.