CAREER: Automated physics-based distillation of coherent structures and mechanisms in unsteady and turbulent flows

识别和了解维持非定常和湍流流动的基本机制对于确保在广泛的应用中确保准确的预测和有效的优化和控制非常重要，例如减少空气动力飞行器上的阻力，提高风能收集设备的效率，以及通过心血管流动改善患者的预后。虽然我们对简单流动的这种机制有很好的了解，但需要新的工具才能对与现实世界相关的更广泛的应用程序获得类似程度的理解。该项目将开发能够以自动化和明确的方式识别这种机制的方法，只需最少的数据和计算需求。这些技术发展将与教育和外展倡议相结合，涉及研究社区、课程和研究中的大学生、K-12学生和芝加哥南部当地社区团体的成员。拟议的研究将形成两个中心思想来应对上面确定的挑战，总体目标是开发一种方法，以明确、自动化和计算高效的方式隔离主导的连贯结构和机制。第一个想法涉及将稀疏性提升方法应用于基于物理的建模工具，以发现最小物理模型，而不需要人类的洞察力和/或否则将需要的反复试验。第二个想法考虑了利用波包伪谱理论的思想，使用解析方法而不是数值方法来近似这些机制的行为的方法。这种表述反过来又使有助于研究更广泛类别的机制的其他分析方法成为可能，特别是允许对高度非线性的行为进行建模。为了展示它们的实用性，这些方法将应用于一系列的流体流动，包括不可压缩和可压缩的平行剪切流，具有侧壁诱导的二次平均流分量的流动，以及具有更复杂几何形状的心血管流动。提高识别和操纵湍流中存在的相干结构的能力可以使广泛的应用受益，有可能减少空中、海上和地面运输工具上的摩擦阻力，提高风力涡轮机的效率，并加强对心血管疾病的了解和治疗。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。

Identifying and understanding the fundamental mechanisms that sustain unsteady and turbulent flows is important for ensuring accurate prediction and effective optimization and control across a broad range of applications, such as for reducing drag on aerodynamic vehicles, improving efficiency in wind energy harvesting devices, and improving patient outcomes via cardiovascular flows. While we have a good understanding of such mechanisms for simple flows, new tools will be required to obtain similar levels of understanding for a broader range of applications of real-world relevance. This project will develop methods that enable such mechanisms to be identified in an automated and unambiguous manner, with minimal data and computational requirements. These technical developments will be coupled with educational and outreach initiatives involving the research community, university students in coursework and research, K-12 students, and members of local community groups on Chicago's South Side.The proposed research will develop two central ideas to address the challenge identified above, with an overall goal of developing a methodology to isolate dominant coherent structures and mechanisms in an unambiguous, automated, and computationally efficient manner. The first idea involves applying sparsity-promoting methods to physics-based modeling tools to uncover minimal-physics models without needing the human insight and/or trial-and-error that would otherwise be required. The second idea considers methods to approximate the behavior of these mechanisms using analytic rather than numerical methods, leveraging ideas from wave-packet pseudo-spectral theory. This formulation in turn enables additional analysis methods conducive to studying a broader class of mechanisms, in particular allowing for highly nonlinear behavior to be modeled. To demonstrate their utility, these methods will be applied on a range of fluid flows, including incompressible and compressible parallel shear flows, flows with secondary mean flow components induced by sidewalls, and cardiovascular flows with more complex geometries. An improved ability to identify and manipulate the coherent structures that exist within turbulent flows can benefit a broad range of applications, with the potential to decrease friction drag on air, sea, and ground transport vehicles, increase the efficiency of wind turbines, and enhance understanding and treatment of cardiovascular diseases.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.