Intermittency and Alignment in Strong RMHD Turbulence

Abstract: We develop an analytic model of intermittent, three-dimensional, strong, reduced magnetohydrodynamic turbulence with zero cross helicity. We take the fluctuation amplitudes to have a log-Poisson distribution and incorporate into the model a new phenomenology of scale-dependent dynamic alignment. The log-Poisson distribution in our model is characterized by two parameters. To calculate these parameters, we make use of three assumptions: that the energy cascade rate is independent of scale within the inertial range, that the most intense coherent structures at scale $\lambda$ are sheet-like with a volume filling factor proportional to $\lambda$, and that most of the cascade power arises from interactions between exceptionally intense fluctuations and much weaker fluctuations. We then compute the scalings of the power spectrum, the kurtosis, higher-order structure functions, and three different average alignment angles. These scalings appear to be consistent with numerous results from direct numerical simulations.