  Parker's mean-field model includes two processes generating large-scale
oscillatory dynamo waves: stretching of magnetic field lines by small-scale
helical flows, and by differential rotation. In this work, we investigate the
capacity of data-driven modal analysis, Dynamic Mode Decomposition, to identify
coherent magnetic field structures of this model. In its canonical form, the
only existing field scale corresponds to the dynamo instability. To take into
account multi-scale nature of the dynamo, the model was augmented with coherent
in time flow field, forcing small-scale magnetic field with a faster temporal
evolution. Two clusters of DMD modes were obtained: the ``slow" cluster,
located near the dynamo wave frequency and associated with its nonlinear
self-interaction, and the ``fast" cluster, centered around the forcing
frequency and resulting from the interaction between the wave and the flow.
Compared to other widely used methods of data analysis, such as Fourier
transform, DMD provides a natural spatiotemporal basis for the dynamo, related
to its nonlinear dynamics. We assess how the parameters of the DMD model, rank
and delay, influence its accuracy, and finally discuss the limitations of this
approach when applied to randomly forced, more complex dynamo flows.
