# A local approach to the study of energy transfers in incompressible magnetohydrodynamic turbulence

## TL;DR

This paper introduces a local, exact approach to analyze energy transfers in incompressible MHD turbulence using local averages and a derived local Karman-Howarth-Monin relation, validated with numerical simulation data.

## Contribution

The work develops a local, non-homogeneous framework for studying energy transfers in MHD turbulence, extending traditional statistical methods without assuming homogeneity or isotropy.

## Key findings

- Local Karman-Howarth-Monin relation holds well in simulations.
- Wide tails in PDFs indicate strong localized transfer events.
- Structures of strong transfers are filament-like or sheet-like, associated with vorticity or electric current.

## Abstract

We present a local approach to the study of scale-to-scale energy transfers in magnetohydrodynamic (MHD) turbulence. This approach is based on performing local averages of the physical fields, which amounts to filtering scales smaller than some parameter $\ell$. A key step in this work is the derivation of a local K\'arm\'an-Howarth-Monin relation which provides a local form of Politano and Pouquet's 4/3-law, without any assumption of homogeneity or isotropy. Our approach is exact, non-random, and we show its connection to the usual statistical results of turbulence. Its implementation on data obtained via a three dimensional direct numerical simulation of the forced, incompressible MHD equations from the John Hopkins turbulence database constitutes the main part of our study. First, we show that the local K\'arm\'an-Howarth-Monin relation holds well. The space statistics of local cross-scale transfers is studied next, their means and standard deviations being maximum at inertial scales, and their probability density functions (PDFs) displaying very wide tails. Events constituting the tails of the PDFs are shown to form structures of strong transfers, either positive or negative, and which can be observed over the whole available range of scales. As $\ell$ is decreased, these structures become more and more localized in space while contributing to an increasing fraction of the mean energy cascade rate. Finally, we highlight their quasi 1D (filament-like) or quasi 2D (sheet/ribbon-lke) nature, and show that they appear in areas of strong vorticity or electric current density.