From symmetry to asymmetry:

It has been established, from previous (analytical) work, that the exact symmetry of a standard (k=1) ABC flow is not conserved when the wavenumber increases to k=2. The dominant mode for the magnetic field that leads to a very fast exponential growth (compared to the k=1 case) is a symmetry breaking eigenmode. The transition from a symmetric mode to an assymetric one is shown (above movie) when the magnetic induction equation is solved numerically.

When the initial magnetic field is chosen to be weak and uniform, magnetic flux "cigars" rapidly arise at certain (stagnation) points of the flow. Eventually, double flux cigars with opposite polarity appear next to the primary magnetic structures. The growth / decay of the flux cigars occurs simultaneously in all of the (eight) cells in the computational box (symmetry). This is not what happens when the assymetry occurs (end of the movie). There are cells where the "double-cigar" mode is still visible and cells where the secondary flux cigars are passing through zero (less supply of flux).

Download a .gz version of the movie.

Turbulent dynamo action

The full MHD compressible equations are taken into account to study (via numerical simulations) the turbulent dynamo action for an ABC flow. The inital magnetic field is chosen to be a very weak and random perturbation. The magnetic and fluid Reynolds numbers are chosen to be equal to 100. The movie shows the temporal evolution of the weak magnetic field (pink isosurfaces) during the turbulent growth phase (before saturation). Field lines with dark colour correspond to weak magnetic field regions and those with white colour to regions with higher field strength. The movie illustrates the stretching of the weak magnetic field lines that lead to an exponential growth of the magnetic energy when the flow enters the turbulent phase.

A .gz version of the movie is available here.