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.

三重相互作用是流体中能量传递的基本机制。这项工作引入了双谱模式分解，作为从实验或数值数据中得出与三重相互作用有关的流动结构的直接手段。三重相互作用的特征是可以通过双谱检测到的二次相耦合。所提出的方法使该三阶统计量的积分度量最大化，以计算与三重频率相关的模式，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，分解在三重轴的三个频率分量之间建立因果关系。这样可以区分求和相互作用和差相互作用，以及指示非线性耦合区域的相互作用图的计算。三个示例突出了该方法的不同方面。从层流圆柱流的直接数值模拟数据得出了级联三联体及其相互作用的区域。进一步证明，通过它们的差异-自我相互作用间接揭示了达到一定幅度的线性不稳定性机理。在大规模分离的尾流的粒子图像测速数据上证明了湍流和噪声抑制的适用性。通过将方法扩展到跨双谱信息，解释了过渡射流的大涡模拟数据中次谐波和超谐波的产生。从层流圆柱流的直接数值模拟数据得出了级联三联体及其相互作用的区域。进一步证明，通过它们的差异-自我相互作用间接揭示了达到一定幅度的线性不稳定性机理。在大规模分离的尾流的粒子图像测速数据上证明了湍流和噪声抑制的适用性。通过将方法扩展到跨双谱信息，解释了过渡射流的大涡模拟数据中次谐波和超谐波的产生。从层流圆柱流的直接数值模拟数据得出了级联三联体及其相互作用的区域。进一步证明，通过它们的差异-自我相互作用间接揭示了达到一定幅度的线性不稳定性机理。在大规模分离的尾流的粒子图像测速数据上证明了湍流和噪声抑制的适用性。通过将方法扩展到跨双谱信息，解释了过渡射流的大涡模拟数据中次谐波和超谐波的产生。在大规模分离的尾流的粒子图像测速数据上证明了湍流和噪声抑制的适用性。通过将方法扩展到跨双谱信息，解释了过渡射流的大涡模拟数据中次谐波和超谐波的产生。在大规模分离的尾流的粒子图像测速数据上证明了湍流和噪声抑制的适用性。通过将方法扩展到跨双谱信息，解释了过渡射流的大涡模拟数据中次谐波和超谐波的产生。