Nonlinear transverse cascade and two-dimensional magnetohydrodynamic subcritical turbulence in plane shear flows
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We find and investigate via numerical simulations self-sustained two-dimensional turbulence in a magnetohy-drodynamic 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 a transient growth mechanism due to shear flow non-normality. This mechanism appears to be essentially anisotropic in the spectral (wave-number) plane and operates mainly for spatial Fourier harmonics with streamwise wave numbers less than the ratio of flow shear to Alfven speed, k(y) < S/u(A) (i.e., the Alfven frequency is lower than the shear rate). We focus on analysis of the character of nonlinear processes and the underlying self-sustaining scheme of the turbulence, i.e., on the interplay between linear transient growth and nonlinear processes, in the spectral plane. Our study, being concerned with a new type of energy-injecting process for turbulence-the transient growth-represents an alternative to the main trends of magnetohydrodynamic (MHD) turbulence research. We find similarity of the nonlinear dynamics to the related dynamics in hydrodynamic flows: to the 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 the wave-number plane [as occurs in the related hydrodynamic flow; see Horton et al., Phys. Rev. E 81, 066304 (2010)] and differs fundamentally from the existing concepts of (anisotropic direct and inverse) cascade processes in MHD shear flows.