Nonlinear Terms of MHD Equations for Homogeneous Magnetized Shear Flow

TL;DR

This paper derives the full nonlinear MHD equations for incompressible magnetized shear flow, highlighting their role in turbulence creation, wave amplification, and implications for accretion disk viscosity, with potential for numerical simulation.

Contribution

It provides a comprehensive derivation of nonlinear terms in MHD equations for shear flow, enabling better understanding of turbulence and wave dynamics in magnetized fluids.

Findings

Nonlinear terms lead to turbulence and spectral density of MHD waves.

Linearized equations describe wave amplification and magnetorotational instability.

Discussion on numerical simulation prospects for weak turbulence and accretion disk viscosity.

Abstract

We have derived the full set of MHD equations for incompressible shear flow of a magnetized fluid and considered their solution in the wave-vector space. The linearized equations give the famous amplification of slow magnetosonic waves and describe the magnetorotational instability. The nonlinear terms in our analysis are responsible for the creation of turbulence and self-sustained spectral density of the MHD (Alfven and pseudo-Alfven) waves. Perspectives for numerical simulations of weak turbulence and calculation of the effective viscosity of accretion disks are shortly discussed in k-space.