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This article discusses triad transfer analysis via quadratic nonlinearity. To avoid fictitious interactions, symmetrization of the triad transfer is reviewed, including arbitrary orthogonal decomposition and coarse graining. The directional representation of the symmetrized triad transfer is proposed by minimizing the number of edges in a network graph of triad interactions with keeping the energy consistency. The directional representation simplifies visualization and allows us to reduce the energy transfer into a one-to-one relation, while eliminating fictitious interactions in non-symmetrized triad transfer functions. Energy transfer processes among plasma turbulent fluctuations that decompose by the singular value decomposition are analyzed as an application. A network graph visualization clearly demonstrates the importance of symmetrization and the consistency between the symmetrized triad transfer and its directional representation.

On the triad transfer analysis of plasma turbulence: symmetrization, coarse graining, and directional representation