Nonlinear transverse cascade and two-dimensional magnetohydrodynamic subcritical turbulence in plane shear flows.
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 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 Alfvén speed, ky<S/uA (i.e., the Alfvén 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.
Department of Physics, Faculty of Exact and Natural Sciences, Tbilisi State University, Tbilisi 0179, Georgia.
G R
GR
Mamatsashvili
Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA.
D Z
DZ
Gogichaishvili
Institute of Geophysics, Tbilisi State University, Tbilisi 0193, Georgia and Abastumani Astrophysical Observatory, Ilia State University, Tbilisi 0162, Georgia.
G D
GD
Chagelishvili
Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712, USA.
W
W
Horton