CAREER: Bispectral mode decomposition for discovery of triadic interactions in laminar-turbulent transition

模态分解技术是从复杂流场的大型实验和数值数据集进行科学发现的最前沿。这些技术包括适当的正交分解（POD）和动态模式分解（DMD），提取能量和动态最相关的流特征。这两种方法产生准确的低维表示复杂的流动动力学。然而，POD和DMD都没有直接和定量的洞察到的非线性相互作用，决定这些动态，和常见的做法仍然是使用功率或交叉谱作为特设指标的非线性相互作用的存在。拟开展的关于双谱模式分解（BMD）的工作直接解决了航空科学、自然科学和环境工程中系统识别和量化非线性现象的能力的更广泛需求。研究活动与全面的教育和推广计划紧密交织在一起，该计划针对早期职业研究人员，非专业人员以及高中和大学的学生。研究方法和成果的广泛传播是通过提供一个免费的，开源的数值工具bispectral mode analysis.BMD是最近开发的模态分解技术，提取与三元非线性相互作用，湍流中的能量传递的基本机制相关联的流结构。首先，零压力梯度边界层的两个经典的过渡方案被重新审视。这些湍流路径的初始阶段在现象学和理论水平上都得到了很好的理解。通过明确分离高保真数值数据的时间和空间尺度参与非线性击穿过程，本研究的目的是完成我们的过渡过程的理解。通过确认或反驳非线性是流向角流早期过渡的根源这一假设，所提出的工作进一步解决了线性模型的理论预测和这种普遍存在的流动的实验观察之间的长期差异。这项工作的一部分是计算直接数值模拟（DNS）数据库中的每个流量调查。最后，BMD作为估算非线性传递函数的一种手段的探索性研究，旨在使未来几代复杂流的降阶模型成为可能。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Modal decomposition techniques are at the forefront of scientific discovery from large experimental and numerical datasets of complex flow fields. These techniques include the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), which extract the energetically and dynamically most relevant flow features. Both methods yield accurate low-dimensional representations of complex flow dynamics. However, neither POD nor DMD give direct and quantitative insight into the nonlinear interactions that dictate these dynamics, and the common practice remains to use peaks in power or cross spectra as ad-hoc indicators for the presence of nonlinear interactions. The proposed work on bispectral mode decomposition (BMD) directly addresses the broader need for the capability to systematically identify and quantify nonlinear phenomena in aeroscience, natural science, and environmental engineering. The research activities are tightly interwoven with a comprehensive education and outreach plan that targets early-career researchers, nonspecialists, and students at the high-school and college levels. The broad dissemination of the research methodology and outcomes is facilitated by providing a free, open-source numerical tool for bispectral mode analysis.BMD is a recently developed modal decomposition technique that extracts flow structures associated with triadic nonlinear interactions, the fundamental mechanism of energy transfer in turbulent flows. First, the two classical transition scenarios of the zero-pressure-gradient boundary layer are revisited. The initial stages of these paths to turbulence are well understood, both on a phenomenological and theoretical level. By unambiguously separating from high-fidelity numerical data the temporal and spatial scales involved in the nonlinear breakdown process, this research aims at completing our understanding of the transition processes. By either confirming or refuting the hypothesis that nonlinearity is at the root of early transition in streamwise corner flows, the proposed work furthermore addresses a long-standing discrepancy between theoretical predictions by linear models and experimental observations of this ubiquitous flow. Part of this effort is the computation of direct numerical simulation (DNS) databases for each flow under investigation. The exploratory study of BMD as a means of estimating nonlinear transfer functions, lastly, aims at enabling future generations of reduced-order models of complex flows.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.