CAREER: Unraveling predictive and multiscale dynamics in turbulence for flow control

湍流在健康和工程中发挥着至关重要的作用，涉及从气候到航空和心血管疾病等一系列重要问题。因此，更好地了解湍流对人类健康和自然资源的可持续性至关重要。湍流的最基本特征是其混乱和多尺度性质，既带来挑战，也带来机遇。为了应对这一挑战，该项目的主要目的是提供一种新的理论和计算研究途径，使用确定性框架来解开湍流的可预测性和多尺度特性，以进行流量控制。除了提供推进节能流量控制策略所需的基础知识外，该项目还将提供完美的教育平台，以促进学术界的实际劳动力培训，因为湍流和流量控制的现实重要性将激发各级学生的兴趣。为此，我们将开展与产业相关的项目，通过弥合学术工作与产业问题之间的差距，培养高素质的产业劳动力。本项目的目标是应用湍流动力系统观点的最新进展，解决湍流中隐藏的混沌和多尺度问题，以实现严格的流动控制。其核心思想是揭示湍流的可预测性和多尺度相互作用，使用所谓的精确相干解的控制Navier-Stokes方程。所获得的新知识将用于具有成本效益的湍流控制。在追求这一目标，具体的目标是：（i）确定预测动态使用小规模的精确相干的解决方案和（ii）小规模和大规模的精确相干的解决方案之间的多尺度相互作用的特点，并利用它们进行流量控制。直接数值模拟和大涡模拟将分别用于模拟和分析小尺度和大尺度精确相干解，沿着一套分析工具，包括线性不稳定性分析和预解式分析。预测和多尺度动力学存在的发现将导致更严格的控制策略，可以将湍流转向理想的状态，从而通过控制较小的尺度来控制目标较大的尺度。由于各种工业流体系统中的能量损失在很大程度上与湍流阻力有关，因此该项目对充分利用湍流中的预测性和多尺度动力学来有效提高系统的能源效率具有深远的影响。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

Turbulent flow plays a crucial role in health and engineering across a range of important issues, from climate to aviation and cardiovascular disease. A better understanding of turbulence is thus central to human health and the sustainability of natural resources. The most essential features of turbulence are its chaotic and multiscale natures, posing both challenges and opportunities. To address this challenge, the principal aim of this project is to provide a new theoretical and computational research avenue that uses a deterministic framework to unravel predictable and multiscale characteristics in turbulence for flow control. In addition to providing the fundamental knowledge necessary to advance energy-saving flow-control strategies, this project will also provide the perfect educational platform to promote practical workforce training in academia as the real-world importance of turbulence and flow control will excite students at various levels. To this end, industry-relevant projects will be developed to cultivate a highly qualified industrial workforce by bridging the gap between academic work and industrial problems.The goal of this project is to apply recent advances in the dynamical systems viewpoint of turbulence to solve the problem of the chaotic and multiscale nature embedded in turbulence for rigorous flow control. The key idea is to uncover the predictability and multiscale interactions in turbulence using so-called exact coherent solutions to the governing Navier-Stokes equations. The new knowledge obtained will be exploited for cost-effective turbulence control. In pursuit of this goal, the specific objectives are: (i) identify the predictive dynamics using small-scale exact coherent solutions and (ii) characterize the multiscale interactions between small-scale and large-scale exact coherent solutions and exploit them for flow control. Direct numerical simulation and large-eddy simulation will be employed to simulate and analyze small-scale and large-scale exact coherent solutions, respectively, along with a suite of analysis tools, including linear instability analysis and resolvent analysis. The discovery that predictive and multiscale dynamics exist will lead to a more rigorous control strategy that can steer turbulence toward desirable states, whereby targeted larger scales are controlled by controlling smaller ones. As energy losses in various industrial flow systems are largely associated with turbulent drag, this project has far-reaching implications in effectively improving the energy efficiency of the systems by taking full advantage of the predictive and multiscale dynamics in turbulence.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.