A statistical model of three-dimensional anisotropy and intermittency in strong Alfv\'enic turbulence

We propose a simple statistical model of three-dimensionally anisotropic, intermittent, strong Alfv\'enic turbulence, incorporating both critical balance and dynamic alignment. Our model is based on log-Poisson statistics for Elsasser-field increments along the magnetic field. We predict the scalings of Elsasser-field conditional two-point structure functions with point separations in all three directions in a coordinate system locally aligned with the direction of the magnetic field and of the fluctuating fields and obtain good agreement with numerical simulations. We also derive a scaling of the parallel coherence scale of the fluctuations, $l_\parallel \propto \lambda^{1/2}$, where $\lambda$ is the perpendicular scale. This is indeed observed for the bulk of the fluctuations in numerical simulations.