Nonlinear transverse cascade and two-dimensional magnetohydrodynamic subcritical turbulence in plane shear flows

TL;DR

This paper investigates two-dimensional subcritical magnetohydrodynamic turbulence in shear flows, revealing a nonlinear transverse cascade driven by transient growth, which differs from traditional cascade concepts in MHD turbulence.

Contribution

It introduces a new perspective on MHD turbulence by highlighting the role of transient growth and a transverse energy redistribution process, contrasting with traditional cascade theories.

Findings

Turbulence is sustained by transient growth due to shear flow nonnormality.

Spectral anisotropy is key to the nonlinear dynamics of the turbulence.

The nonlinear process involves a transverse redistribution of spectral energies, differing from classical cascades.

Abstract

We find and investigate via numerical simulations self-sustained two-dimensional turbulence in a magnetohydrodynamic flow with a maximally simple configuration: plane, noninflectional (with a constant shear of velocity) and threaded by a parallel uniform background magnetic field. This flow is spectrally stable, so the turbulence is subcritical by nature and hence it can be energetically supported just by transient growth mechanism due to shear flow nonnormality. This mechanism appears to be essentially anisotropic in spectral (wavenumber) plane and operates mainly for spatial Fourier harmonics with streamwise wavenumbers less than a ratio of flow shear to the Alfv\'{e}n speed, $k_y < S/u_A$ (i.e., the Alfv\'{e}n frequency is lower than the shear rate). We focused on the analysis of the character of nonlinear processes and underlying self-sustaining scheme of the turbulence, i.e., on the interplay between linear transient growth and nonlinear processes, in spectral plane. Our study, being concerned with a new type of the energy-injecting process for turbulence -- the transient growth, represents an alternative to the main trends of MHD turbulence research. We find similarity of the nonlinear dynamics to the related dynamics in hydrodynamic flows -- to the \emph{bypass} concept of subcritical turbulence. The essence of the analyzed nonlinear MHD processes appears to be a transverse redistribution of kinetic and magnetic spectral energies in wavenumber plane [as occurs in the related hydrodynamic flow, see Horton et al., Phys. Rev. E {\bf 81}, 066304 (2010)] and differs fundamentally from the existing concepts of (anisotropic direct and inverse) cascade processes in MHD shear flows.