INTERMITTENCY AND ALIGNMENT IN STRONG RMHD TURBULENCE

We develop an analytic model of intermittent, three-dimensional, strong, reduced magnetohydro- dynamic (RMHD) 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 between the Elsasser variables z ± . We find that the structure function h|�z ± | n i scales as λ 1−β n , wherez ± is the variation in z ± across a distance λ perpendicular to the mag- netic field. We calculate the value of β to be ≃ 0.69 based on our assumptions that the energy cascade rate is independent of λ within the inertial range, that the most intense coherent structures are two-dimensional with a volume filling factor ∝ λ, and that most of the cascade power arises from interactions between exceptionally intense fluctuations and much weaker fluctuations. Two conse- quences of this structure-function scaling are that the total-energy power spectrum is ∝ k −1.52 ⊥ and that the kurtosis of the fluctuations is ∝ λ −0.27 . Our model resolves the problem that alignment an- gles defined in different ways exhibit different scalings. Specifically, we find that the energy-weighted average angle between the velocity and magnetic-field fluctuations is ∝ λ 0.21 , the energy-weighted av- erage angle betweenz + andz − is ∝ λ 0.10 , and the average angle betweenz + andz − without energy weighting is ∝ (ln(L/λ)) −1/2 when L/λ ≫ 1, where L is the outer scale. These scalings appear to be consistent with numerous results from direct numerical simulations. Subject headings: magnetohydrodynamics — turbulence — plasmas — solar wind