By the "motion" of a magnetic field line, we mean that path in time that is traced out by low energy test electric charges that are initially spread along the field line. The test charges move because they drift in the electric field arising because of the time-changing magnetic field. As time progresses, the test charges move with the "field line" as we have defined it--that is we use the low energy test charge motion to define the concept of field line motion.
Thus the motion we show in our computer visualizations has a physical basis--it is the motion we would observe for low energy test charges initially spread along the various magnetic field lines as the situation evolves in time.
This is a familiar concept in space plasma physics.
The Poynting flux is also in the direction, so that watching the field line motion defined in this way also indicates the direction of energy flow (but of course gives no idea of the magnitude of that flow).
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