Numerical simulation of helical magnetohydrodynamic turbulence

The three-dimensional incompressible magnetohydrodynamic (MHD) equations for rectangular geometry and periodic boundary conditions are solved numerically using the spectral method of Orszag & Patterson (1972). The calculations are restricted to a magnetic Prandtl number of one and to Gaussian random initial conditions with zero mean magnetic and momentum fields. We permit non-mirror-symmetric (helical) flows. In all cases, there is a continuous transfer of energy from the momentum field to the magnetic field. A proposed mechanism for this transfer involves the cascading of energy from the large scales of the momentum field to the small scales, thence a redistribution of energy between the momentum and magnetic fields by Alfvén waves, and, finally, an inverse cascade of energy from the small scales of the magnetic field to the large scales. This inverse cascade is found when magnetic helicity (〈a. b〉, where b = curl a is the magnetic induction) is present in the flow.