Dynamic Alignment in Driven Magnetohydrodynamic Turbulence

Motivated by recent analytic predictions, we report numerical evidence showing that in driven incompressible magnetohydrodynamic turbulence the magnetic- and velocity-field fluctuations locally tend to align the directions of their polarizations. This dynamic alignment is stronger at smaller scales with the angular mismatch between the polarizations decreasing with the scale $\lambda$ approximately as ${\theta }_{\lambda }\propto {\lambda }^{1/4}$. This can naturally lead to a weakening of the nonlinear interactions and provide an explanation for the energy spectrum $E(k)\propto k^{-3/2}$ that is observed in numerical experiments of strongly magnetized turbulence.

Figure 1

Two-dimensional spectrum of MHD turbulence in the plane perpendicular to the guiding field ${\mathbf{B}}_0$. The numerical resolution is ${256}^3$, the Reynolds number is $\mathrm{Re}=800$, and the strength of the uniform guiding field is $B_0=5$. The turbulence is driven by a solenoidal random force at wave numbers $k=1,2$, as is explained in the text.

Figure 2

The alignment angle, defined in Eq. (7), compensated by the theoretical scaling $r^{1/4}$ ($B_0=5$, $\mathrm{Re}=800$). The inset demonstrates how the slope $d\theta /dr$ in the inertial range changes with the strength of the guiding field.