Effect of hyperdiffusivity on turbulent dynamos with helicity

In numerical studies of turbulence, hyperviscosity is often used as a tool to extend the inertial subrange and to reduce the dissipative subrange. By analogy, hyperdiffusivity (or hyperresistivity) is sometimes used in magnetohydrodynamics. The underlying assumption is that only the small scales are affected by this manipulation. In the present paper, possible side effects on the evolution of the large-scale magnetic field are investigated. It is found that for turbulent flows with helicity, hyperdiffusivity causes the dynamo-generated magnetic field to saturate at a higher level than normal diffusivity. This result is successfully interpreted in terms of magnetic helicity conservation, which also predicts that full saturation is reached only after a time comparable to the large-scale magnetic (hyper)diffusion time.