  Coherent structures are found in many different turbulent flows and are known
to drive self-sustaining processes in wall turbulence. Identifying the triadic
interactions which generate coherent structures can provide insights beyond
what is possible with linearized models. There are infinite possible
interactions that may generate a given structure. Thus, a method to
systematically study those, ranking them in terms of their contribution to the
structure of interest, is essential. We here use the resolvent-based extended
spectral proper orthogonal decomposition (RESPOD) approach (Karban, U. et al.
2022 Self-similar mechanisms in wall turbulence studied using resolvent
analysis. Journal of Fluid Mechanics 969, A36) to rank the triadic interactions
which give rise to the dominant coherent structures in minimal Couette flows at
Reynolds number 400 and 1000. Our analysis identifies that six triadic
interactions dominate the most energetic coherent structure, revealing the
capability of the methodology to identify and rank nonlinear interactions. The
approach can be used to analyse the energy exchange in turbulent flows and may
guide the construction of reduced-order models based on the interplay between
different flow modes. Based on this framework, we introduce a modelling
strategy where the interactions increasing or reducing the energy of a given
mode are grouped as sources and sinks, respectively. The effect of the sinks is
embedded in the resolvent operator by using an eddy viscosity model. The
sources are used for driving this modified resolvent operator and are shown to
yield accurate flow predictions at zero frequency. We discuss that this
strategy can be useful when analysing nonlinear interactions or modelling
forcing at high-Reynolds-number flows.
