Single-mode nonlinear Langevin emulation of magnetohydrodynamic turbulence

TL;DR

This paper introduces a Langevin-based model to emulate a typical mode in incompressible MHD turbulence, capturing key properties and aligning with established decay laws, validated against numerical simulations.

Contribution

It presents a simple Langevin equation model that reproduces key features of MHD turbulence modes, including decay laws and symmetries, without considering dissipation scales.

Findings

Model aligns with von Kármán decay law

Reproduces Kolmogorov's symmetries in turbulence

Matches results from direct numerical simulations

Abstract

Based on the Langevin equation of Brownian motion, we present a simple model that emulates a typical mode in incompressible magnetohydrodynamic turbulence, providing a demonstration of several key properties. The model equation is consistent with von K\'arm\'an decay law and Kolmogorov's symmetries. We primarily focus on the behavior of inertial range modes although we also attempt to include some properties of the large scale modes. Dissipation scales are not considered. Results from the model are compared with results from published Direct Numerical Simulations.