Leveling of MHD turbulence imbalance in shear flows

Abstract

We investigate magnetohydrodynamic (MHD) turbulence in plane shear flows with a streamwise background magnetic field in the super-Alfvénic regime. We show that the large-scale velocity shear suppresses turbulence imbalance, driving the system toward a balanced state -- the energies of counter-propagating Alfvén waves become essentially equal, even at initially perfectly imbalanced Alfvénic turbulence. This balancing is due to the shear-induced linear non-modal dynamics of Alfvén waves, including their transient growth and over-reflection. This linear route to balancing turbulence is new -- fundamentally different from nonlinear ones operative in shearless MHD turbulence -- and have direct implications for understanding balanced/imbalanced MHD turbulence in the solar wind, which is modeled as a shear flow in a thermodynamically complex plasma.

Figures (4)

• Figure 1: Evolution of the volume-averaged (a) kinetic $\left< E_k \right>$ and (b) magnetic $\left< E_m \right>$ energies of PAW, SAW and $k_{y}=0$ modes for the initially imposed PAWs. (c) Kinetic energy of the basic mode together with that of the $k_y=0$ modes. (d) The same evolution of the wave energies as in (a) and (b), but at early times and normalized by the initial values. (e) The same as in (d) but for initially imposed SAWs.
• Figure 2: Evolution of (a) the volume-averaged Elsässer energies $\langle (Z_p^{\pm})^2\rangle$ and $\langle (Z_s^{\pm})^2 \rangle$ for PAWs (blue) and SAWs (red), respectively, for the initially imposed only PAWs, (b) the ratios $f_{p}$ and $f_{s}$ (see text) and (c) the normalized cross-helicity with small time-average 0.04 in the turbulent state.
• Figure 3: Spectra of $|\bar{\bm{Z}}^{\pm}_p|^2$ (left) and $|\bar{\bm Z}^{\pm}_s|^2$ (right) in the $(k_x, k_y)$-plane at $k_z =2$ in the turbulent state.
• Figure 4: 1D spectra of $|\bar{\bm Z}^{\pm}_p|^2$ and $|\bar{\bm Z}^{\pm}_s|^2$ represented as a function of (a) $k_x$, (b) $k_y$ and (c) $k_z$ being integrated in each case over the other two wavenumbers.