Alignment of the scalar gradient in evolving magnetic fields

Abstract

We conduct simulations of turbulent mixing in the presence of a magnetic field, grown by the small-scale dynamo. We show that the scalar gradient field, $\nabla C$, which must be large for diffusion to operate, is strongly biased perpendicular to the magnetic field, ${\mathbf B}$. This is true both early-on, when the magnetic field is negligible, and at late times, when the field is strong enough to back react on the flow. This occurs because $\nabla C$ increases within the plane of a compressive motion, but ${\mathbf B}$ increases perpendicular to it. At late times the magnetic field resists compression, making it harder for scalar gradients to grow and likely slowing mixing.