Nonlinear transverse cascade and sustenance of MRI-turbulence in Keplerian disks with an azimuthal magnetic field

TL;DR

This paper reveals a new nonlinear transverse cascade process in Fourier space that sustains MRI-driven turbulence in Keplerian disks with azimuthal magnetic fields, emphasizing the interplay of linear growth and nonlinear redistribution.

Contribution

It introduces the concept of a nonlinear transverse cascade as a key process for MRI turbulence sustenance, differing from traditional cascade mechanisms.

Findings

Turbulence is maintained by interplay of linear MRI growth and transverse cascade.

The vital area in Fourier space is crucial for turbulence sustenance.

The mechanism is robust across different simulation box aspect ratios.

Abstract

We investigate magnetohydrodynamic turbulence driven by the magnetorotational instability (MRI) in Keplerian disks with a nonzero net azimuthal magnetic field using shearing box simulations. As distinct from most previous studies, we analyze turbulence dynamics in Fourier (${\bf k}$-) space to understand its sustenance. The linear growth of MRI with azimuthal field has a transient character and is anisotropic in Fourier space, leading to anisotropy of nonlinear processes in Fourier space. As a result, the main nonlinear process appears to be a new type of angular redistribution of modes in Fourier space -- the \emph{nonlinear transverse cascade} -- rather than usual direct/inverse cascade. We demonstrate that the turbulence is sustained by interplay of the linear transient growth of MRI (which is the only energy supply for the turbulence) and the transverse cascade. These two processes operate at large length scales, comparable to box size and the corresponding small wavenumber area, called \emph{vital area} in Fourier space is crucial for the sustenance, while outside the vital area direct cascade dominates. The interplay of the linear and nonlinear processes in Fourier space is generally too intertwined for a vivid schematization. Nevertheless, we reveal the \emph{basic subcycle} of the sustenance that clearly shows synergy of these processes in the self-organization of the magnetized flow system. This synergy is quite robust and persists for the considered different aspect ratios of the simulation boxes. The spectral characteristics of the dynamical processes in these boxes are qualitatively similar, indicating the universality of the sustenance mechanism of the MRI-turbulence.