A laminar dynamo driven by a steady pressure gradient

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This animation describes the motion of a liquid metal down an infinite helical pipe of rectangular cross-section, driven by a steady, down-pipe pressure gradient. Magnetic field is spontaneously created by the initially steady pipe flow. The field grows exponentially until it reacts back upon the flow and elaborate time-dependent interactions ensue. The top 3 panels show from left to right the cross-pipe field, the down-pipe field and the down-pipe current alongside a time-trace of the magnetic energy. The lower 3 panels show the cross-pipe flow, the down-pipe flow and the downpipe vorticity alongside the kinetic energy.

For these parameters and geometry the solution is a-periodic. It exhibits frequent reversals of the magnetic field direction. Occasionally the field is quenched and reestablishes itself on the slow time-scale of the kinematic eigenfunction.