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

模式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前沿技术。这些技术包括本征正交分解(POD)和动态模式分解(DMD)，它们提取能量和动态最相关的流动特征。这两种方法都产生了复杂流动动力学的准确低维表示。然而，POD和DMD都不能直接和定量地了解决定这些动力学的非线性相互作用，通常的做法仍然是使用功率或互谱中的峰值作为存在非线性相互作用的特别指示器。拟议的双谱模式分解(BMD)工作直接满足了对航空科学、自然科学和环境工程中的非线性现象进行系统识别和量化的能力的更广泛的需求。研究活动与一个全面的教育和推广计划紧密交织在一起，该计划针对的是早期职业研究人员、非专业人员以及高中和大学水平的学生。通过为双谱模式分析提供免费、开源的数值工具，促进了研究方法和结果的广泛传播。BMD是最近发展起来的一种模式分解技术，它提取与三元非线性相互作用相关的流动结构，三元非线性相互作用是湍流中能量传递的基本机制。首先，回顾了零压力梯度边界层的两种经典转折情景。无论是在现象学层面还是在理论层面上，这些通向湍流的路径的初始阶段都是很好的理解。通过明确地从高保真数值数据中分离出参与非线性击穿过程的时间和空间尺度，本研究旨在完善我们对转变过程的理解。通过证实或驳斥非线性是流向角流早期转变的根源这一假设，建议的工作进一步解决了线性模型的理论预测与这种普遍存在的流动的实验观测之间的长期差异。这项工作的一部分是为调查中的每一股水流计算直接数值模拟(DNS)数据库。BMD作为一种估计非线性传递函数的方法的探索性研究，最后，旨在使未来几代复杂流动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。

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.