Intermittency and Alignment in Strong RMHD Turbulence

Abstract:

Intermittency is one of the critical unsolved problems in solar-wind turbulence. Intermittency is important not just because it affects the observable properties of turbulence in the inertial range, but also because it modifies the nature of turbulent dissipation at small scales. In this talk, I will present recent work by colleagues A. Schekochihin, A. Mallet, and myself that focuses on the development of intermittency within the inertial range of solar-wind turbulence. We restrict our analysis to the transverse, non-compressive component of the turbulence. Previous work has shown that this component of the turbulence is anisotropic, varying most rapidly in directions perpendicular to the magnetic field. We argue that, deep within the inertial range, this component of the turbulence is well modeled by the equations of reduced magnetohydrodynamics (RMHD). We then 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 two assumptions: that the energy cascade rate is independent of scale within the inertial range and that the most intense coherent structures at scale lambda are sheet-like with a volume filling factor proportional to lambda. We then compute the scalings of the power spectrum, the kurtosis, higher-order structure functions, and three different average alignment angles. We also carry out a direct numerical simulation of RMHD turbulence. The scalings in our model are similar to the scalings in this simulation as well as the structure-function scalings observed in the slow solar wind.