Dimensional reduction in freely decaying turbulent non-helical magnetic fields

TL;DR

This paper demonstrates that self-similarity and inverse transfer phenomena in decaying turbulent non-helical magnetic fields are consistent across all dimensions, linking them to a gauge-invariant squared vector potential akin to 2D MHD inverse cascade.

Contribution

It reveals the universal self-similarity and inverse transfer mechanisms in turbulent magnetic fields across all dimensions, connecting them to gauge-invariant quantities.

Findings

Inverse transfer occurs in all dimensions.

Self-similarity property is dimension-independent.

Inverse cascade mechanism is linked to a gauge-invariant squared vector potential.

Abstract

We show that the self-similarity property of decaying turbulent non-helical magnetic fields is the same in all dimensions. It is shown that these fields produce an inverse transfer in all dimensions. It is also shown that this phenomenon in a certain gauge can be assigned to a time independent value of the squared vector potential. This mechanism is similar to what happens in the well known inverse cascade in two dimensional magnetohydrodynamics.