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: 2400237
• 负责人: Huixuan Wu
• 金额: $ 32万
• 依托单位: Florida State University
• 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: 2023-10-01 至 2026-09-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2400237&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，不稳定湍流非常复杂，但目前还没有做出太多努力来评估它们到底有多复杂。其复杂性的原因在于，空间和时间方面的流结构模式既包含可预测的元素，也包含随机的元素。然而，预测定律或概率模型无法完全捕捉此类系统的行为。复杂度是流场在非稳态下的确定性或随机性的度量。这项研究将使用先进的数学方法评估复杂程度。通过该项目获得的知识可以应用于涉及复杂性理论的各个其他领域。该项目探索的研究主题将针对本科研究项目进行定制，并将与 K-12 教师共享，以丰富他们的课堂主题。拟议的研究试图建立一个新的理论框架来量化非定常流的复杂性。传统的复杂性估算器通常对 1D 数据进行操作，不足以分析 3D 非稳态现场结果。为了解决这一限制，拟议的研究通过利用大规模流动结构作为分析的基本单位来解决这个问题，这些结构代表了流动在规定时间内的集体运动。这些结构表现出复杂的 3D 空间相互作用，并且可以利用持久同源算法根据其拓扑特征进行分类和符号化。然后使用所得的符号序列来使用超额熵方法来评估复杂性。这种创新方法与传统做法不同，它使用循环时空模式而不是瞬时场作为基本分析单元，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化分离。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，这是通过短时方法（例如有限时间李亚普诺夫指数）或传统统计技术（例如雷诺应力和光谱）。对流动模式之间的时间顺序的检查还可以深入了解相干结构的动力学，揭示诸如纳维-斯托克斯方程不变解之间的关系等基本问题。该奖项反映了 NSF 的法定使命，并被认为值得支持通过使用基金会的智力优点和更广泛的影响审查标准进行评估。