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用于检测和预测高维空间扩展系统中的低维特征的技术，调查系统内的相干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，并增进对这种系统中作为空间尺度函数的不确定性的理解。这项工作的一个动机是希望为复杂的环境系统开发更好的状态估计技术。这项工作的模式系统是浅层热对流模式。该项目将实验室实验与理论和模型相结合。对流不仅是一个很好的模式系统，而且在大气、海洋和地球内部以及工业环境中的许多环境系统中都很重要。热对流表现出多尺度的时空复杂性，实验室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。实验室实验使用二氧化碳作为浅层电池中的对流介质。特定的螺旋缺陷混沌流动模式可以使用计算机控制的激光系统来启动，该系统选择性地加热部分流体。主要的理论工具是状态估计技术，在该技术中，局部集合卡尔曼滤波被应用于数值N-S求解器。随着瑞利数的增加，这将被应用于对流单元表现出的一系列日益复杂的流型。要同化的数据将从对流的阴影图像中获取。该项目的后期阶段将包括在状态估计系统的输出指导下使用选择性加热来控制对流的实验。预计这项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.