  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.
