Evaluating the complexity of unsteady turbulent flows using excess entropy

使用过剩熵评估非定常湍流的复杂性

• 批准号: 2327661
• 负责人: Huixuan Wu
• 金额: $ 32万
• 依托单位: University of Kansas Center for Research Inc
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-01 至 2023-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2327661&HistoricalAwards=false
• 关键词: Evaluating; complexity; unsteady; turbulent; flows

Unsteady turbulent flows are known to be very complicated, but there has not been much effort to assess just how complex they are. The reason for their complexity is that the patterns of flow structures in terms of space and time contain both predictable and random elements. However, predictive laws or probability models cannot fully capture the behavior of such systems. The degree-of-complexity is a measure of how certain or random a flow field is in an unsteady state. This research will evaluate the degree-of-complexity using advanced mathematical methods. The knowledge acquired through this project can be applied to various other fields that involve complexity theory. The research topics explored in this project will be tailored to be suitable for undergraduate research programs and will be shared with K-12 teachers to enrich their class topics.The proposed research attempts to establish a new theoretical framework for quantifying the complexity of unsteady flows. Traditional complexity estimators typically operate on 1D data and are inadequate for analyzing 3D unsteady field results. To address this limitation, the proposed research tackles the issue by utilizing large-scale flow structures as the fundamental unit of analysis, which represent the collective motion of the flow over a defined period. These structures exhibit intricate 3D spatial interactions and can be classified and symbolized based on their topological characteristics, utilizing the persistent homology algorithm. The resulting symbolic sequence is then employed to assess complexity using the excess entropy method. This innovative approach diverges from conventional practices by using recurrent spatial-temporal patterns as the fundamental analysis unit instead of instantaneous fields, thereby enabling the separation of spatial interactions within a finite domain from the long-term evolution of the entire system. Furthermore, the proposed methodology investigates how large-scale structures self-organize to shape the flow, a pursuit that is challenging to achieve through short-time methods (e.g., finite-time Lyapunov exponent) or conventional statistical techniques (such as Reynolds stresses and spectrum). The examination of temporal order among flow patterns also yields insights into the dynamics of coherent structures, shedding light on fundamental inquiries such as the relationship between invariant solutions of the Navier-Stokes equation.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.

众所周知，非定常湍流非常复杂，但还没有太多的努力来评估它们到底有多复杂。其复杂性的原因是，流动结构在空间和时间上的模式既包含可预测的元素，也包含随机元素。然而，预测性规律或概率模型不能完全捕获此类系统的行为。复杂程度是对处于非稳定状态的流场的确定性或随机性的衡量。这项研究将使用先进的数学方法来评估复杂程度。通过这个项目获得的知识可以应用到涉及复杂性理论的各种其他领域。本课题所探讨的研究课题将适合本科生的研究项目，并将与K-12教师分享以丰富他们的课堂主题。本研究试图建立一个新的理论框架来量化非恒定流的复杂性。传统的复杂性估计器通常对一维数据进行操作，不足以分析三维非定常场结果。为了解决这一局限性，拟议的研究通过利用大尺度流动结构作为基本分析单位来解决这一问题，大尺度流动结构代表了定义时期内流动的集体运动。这些结构表现出错综复杂的三维空间相互作用，并可以根据它们的拓扑特征进行分类和符号化，利用持久同调算法。然后使用所得到的符号序列来使用超额熵方法来评估复杂性。这种创新的方法与传统做法不同，使用重复的时空模式作为基本分析单位，而不是瞬时场，从而能够将有限域内的空间相互作用与整个系统的长期演变分开。此外，所提出的方法研究了大规模结构如何自组织来塑造流动，这一追求通过短时间方法(例如有限时间Lyapunov指数)或传统统计技术(例如雷诺应力和谱)来实现是具有挑战性的。对流动模式中的时间顺序的研究也为连贯结构的动力学提供了洞察力，揭示了基本问题，如Navier-Stokes方程不变解之间的关系。该奖项反映了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。