Alignment of Velocity and Magnetic Fluctuations in Simulations of Anisotropic MHD Turbulence

There has been recent theoretical interest in the effect of the alignment of velocity and magnetic fluctuations in three-dimensional (3D) MHD turbulence with a large-scale magnetic field [Boldyrev 2005, 2006]. This theory predicts that the angle $\theta$ between the velocity and magnetic fluctuation vectors has a scaling of $\theta \propto \lambda^{1/4}$, where $\lambda$ is the spatial scale of the fluctuations. There have also been simulations on 3D forced MHD turbulence that supports this prediction [Mason {\em et al.} 2006, 2007]. The scaling has also been tested against observations of solar wind turbulence [Podesta {\em et al.} 2007]. We report here simulation results based on decaying 2D turbulence. The scaling of $\theta \propto \lambda^{1/4}$ and Iroshnikov-Kraichnan scaling has also been observed within a range of time interval and spatial scales, despite the fact that Boldyrev's theory was developed for fully 3D turbulence in the presence of a strong external field. As the external field is reduced in magnitude and becomes comparable to the magnitude of magnetic fluctuations or lower, the scale-dependent alignment is weakened. Implications for observations of solar wind turbulence will be discussed.