Chaotic behaviour of Eulerian MHD turbulence

We study the chaos of a turbulent conducting fluid using direct numerical simulation in the Eulerian frame. We predict that the Lyapunov exponent, which measures the exponential separation of initially close solutions of the magnetohydrodynamic equations, is proportional to the inverse of the Kolmogorov microscale time and also obtain new results for this relation in hydrodynamic turbulence, specifically deriving a previously unknown co-efficient. These predictions agree with simulation results. The simulations also show a diminution of chaos from the introduction of magnetic helicity, which is expected to be eliminated at maximum helicity. Linear growth of the difference between fields was recently found in hydrodynamics and we find here that it extends to the magnetic and velocity fields, with growth rates dependent on the dissipation rate of the relevant field. We infer that the chaos in the system is totally dominated by the velocity field and connect this work to real magnetic systems such as solar weather and confined plasmas.