非线性流的双谱模态分解
Bispectral mode decomposition of nonlinear flows
摘要：
三元相互作用是流体流动中能量传递的基本机制。这项工作介绍了双谱模式分解作为一种直接的手段推导流结构，与三元相互作用的实验或数值数据。三元相互作用的特点是二次相位耦合，可以检测的双谱。所提出的方法最大限度地提高了这个三阶统计量的积分测量，以计算与频率三元组相关的模式，以及识别共振三波相互作用的模式双谱。与经典的双谱不同，分解建立了三个频率分量之间的因果关系。这允许的总和和差异的相互作用的区别，并计算的相互作用图，表明区域的非线性耦合。三个例子突出了该方法的不同方面。从圆柱层流的直接数值模拟数据导出了级联三元组及其相互作用区域。它进一步表明，线性不稳定机制，达到一个可观的幅度间接揭示了他们的差异自相互作用。适用于湍流和噪声抑制的粒子图像速度测量数据的大规模分离后证明。将该方法推广到互双谱信息，解释了转捩射流大涡模拟数据中次谐波和高次谐波的产生。
英文摘要：
Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. This work introduces bispectral mode decomposition as a direct means of educing flow structures that are associated with triadic interactions from experimental or numerical data. Triadic interactions are characterized by quadratic phase coupling which can be detected by the bispectrum. The proposed method maximizes an integral measure of this third-order statistic to compute modes associated with frequency triads, as well as a mode bispectrum that identifies resonant three-wave interactions. Unlike the classical bispectrum, the decomposition establishes a causal relationship between the three frequency components of a triad. This permits the distinction of sum- and difference-interactions, and the computation of interaction maps that indicate regions of nonlinear coupling. Three examples highlight different aspects of the method. Cascading triads and their regions of interaction are educed from direct numerical simulation data of laminar cylinder flow. It is further demonstrated that linear instability mechanisms that attain an appreciable amplitude are revealed indirectly by their difference-self-interactions. Applicability to turbulent flows and noise-rejection is demonstrated on particle image velocimetry data of a massively separated wake. The generation of sub- and ultra-harmonics in large eddy simulation data of a transitional jet is explained by extending the method to cross-bispectral information.
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