Chaos in a Two-Dimensional Magneto-Hydrodynamic System

The flow of an electrolyte in a shallow square horizontal cavity subject to a steady current between opposite sides in the presence of an array of external magnets is simulated using a two dimensional lattice Boltzmann equation method for different values of the Chandrasekhar number. The flow is in a viscous regime for small values of Ch and in an advective one for larger values. In this last regime and in a steady state, a fixed number of pairs of initially close ideal tracer particles are added to the flow. We find that the average distance between each pair grows exponentially in time. Then, an average Lyapunov exponent that grows as a power law of the Chandrasekhar number can be defined.