CAREER: Information-Theoretic Approach to Turbulence: Causality, Modeling & Control

许多具有工程意义的流动都是由湍流的存在所主导的，湍流是流体的混沌和多尺度运动。到目前为止，现实世界的湍流限制了我们完全理解、建模和控制复杂系统的能力。缺乏一个严格的框架来评估湍流中的因果相互作用是发现的核心跨领域概念。本提案的目的是通过使用信息论或信息传播学重新阐述因果关系、建模和控制问题，从而推动湍流研究领域的发展。在这个新的框架中，湍流被设想为一个比特序列，其动力学特征是比特在流动变量之间的转移。该项目的理论基础将为解决从飞机空气动力学到地球物理和行星流动等湍流研究中的问题提供一个新的视角。该项目还将利用变革性的项目来促进工程领域的多样性和包容性，包括参加年度暑期研究项目和本科生研究机会，以吸引妇女和代表性不足的少数民族。该项目的目标是利用信息论阐明湍流的因果关系、建模和控制问题。该公式的中心量是香农熵，它衡量系统状态中的信息量。在这个框架内，湍流中的因果关系可以通过感兴趣的变量之间的信息流来量化。降阶建模是一个关于信息守恒的问题，模型的目标是最大限度地保持原始系统的信息量。同样，通过将串联传感器-执行器设想为一种减少待控制状态的未知信息的装置，可以用信息论的术语来描述控制理论。这一新形式将被用来推进湍流中的三个突出问题：(I)湍流叶栅中能量传递的因果关系，(Ii)用于大涡模拟的亚网格尺度模拟，以及(Iii)通过主动流动控制抑制湍流分离气泡。研究的案例范围从典型的平板湍流到复杂的流动，如真实的飞机外形。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Many flows of engineering interest are dominated by the presence of turbulence, which is the chaotic and multiscale motion of fluids. To date, real-world turbulence limits our ability to fully understand, model, and control complex systems. The lack of a rigorous framework to evaluate cause-and-effect interactions in turbulence is a cross-cutting concept at the core of discovery. The goal of the present proposal is to advance the field of turbulence research by reformulating the problems of causality, modeling, and control using information theory or the science of message communication. In this new framework, turbulence is envisioned as a sequence of bits, and its dynamics is characterized by the transfer of bits among flow variables. The theoretical foundations of this project will provide a new perspective to tackle problems in turbulence research ranging from aircraft aerodynamics to geophysical and planetary flows. The project will also leverage transformative programs to promote diversity and inclusion in engineering, including the participation in annual summer research programs and undergraduate research opportunities to engage women and underrepresented minorities.The goal of this project is to formulate the problems of causality, modeling, and control for turbulent flows using information theory. The central quantity of the formulation is the Shannon entropy, which measures the amount of information in the states of the system. Within this framework, causality in a turbulent flow can be quantified by the information flux among the variables of interest. Reduced-order modeling is posed as a problem on the conservation of information, in which models aim at preserving the maximum amount of information from the original system. Similarly, control theory can be cast in information-theoretic terms by envisioning the tandem sensor-actuator as a device reducing the unknown information of the state to be controlled. This new formulation will be exploited to advance three outstanding problems in turbulent flows: (i) causality of the energy transfer in the turbulent cascade, (ii) subgrid-scale modeling for large-eddy simulation, and (iii) suppression of turbulent separation bubbles with active flow control. The cases of study range from canonical flat plate turbulence to complex flows such as realistic aircraft configurations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.