Data-driven modal analysis of nonlinear quantities in turbulent plasmas using multi-field singular value decomposition

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Nonlinear dynamics in the two-dimensional multi-component plasma turbulence described by the Hasegawa–Wakatani equation is investigated by using a data-driven modal analysis with the singular value decomposition (SVD). The conventional SVD is extended to 'multi-field SVD' which can decompose multiple turbulence fields simultaneously by a single set of orthonormal basis functions without imposing a priori scale separations. Then, in addition to the mode amplitude labeled by the singular value, the information on the phase relations in the nonlinear quantities such as a transport flux or a triad energy transfer is extracted in the mode space. Through applications to the two-dimensional plasma turbulence, it is revealed that the multi-field SVD can extract the dominant spatial structures for the turbulent transport and the nonlinear energy transfer, preserving the multi-scale nature of the original turbulent fields. It is also demonstrated that one can reduce the dimensionality or information using the multi-field SVD through comparisons with the conventional Fourier decomposition.

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