Chaotic behavior of Eulerian MHD turbulence
  We study the chaotic properties of a turbulent conducting fluid using direct
numerical simulation in the Eulerian frame. The maximal Lyapunov exponent is
measured for simulations with varying Reynolds number and magnetic Prandtl
number. We extend the Ruelle theory of hydrodynamic turbulence to
magnetohydrodynamic turbulence as a working hypothesis and find broad agreement
with results. In other simulations we introduce magnetic helicity and these
simulations show a diminution of chaos, which is expected to be eliminated at
maximum helicity. We also find that the difference between two initially close
fields grows linearly at late times, which was also recently found in
hydrodynamics. This linear growth rate is found to be dependent on the
dissipation rate of the relevant field. We discuss the important consequences
this linear growth has on predictability. 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.
