Description
Space- and solar-plasma physics continue to pose major challenges for the characterization of turbulence in these systems. Satellite observations of solar-wind-plasma turbulence have shown a fluid energy spectrum with an inertial range with a -5/3 exponent. However, the magnetic-energy spectrum displays MHD- and sub-ion-scale power-law ranges, the former consistent with the -5/3 power, but the latter characterized by an exponent that is approximately -2.8. These observations have examined (a) the multiscaling of velocity- and magnetic-field structure functions and (b) the alignment of velocity- and magnetic-field fluctuations. One study has found simple scaling of magnetic structure–functions in the sub-ion range, but multiscaling in the MHD range. By carrying out simulations of three-dimensional (3D) Hall magnetohydrodynamics (HMHD) turbulence, we show that it provides a natural framework for understanding solar-wind turbulence, and its dependence on non-dimensional parameters in the sub-ion scale. We present several statistical properties of 3D HMHD turbulence and compare them with their counterparts in solar-wind turbulence. We compute (a) the wave-number dependence of spectra and the scale-dependent Alfven ratio on ion-cyclotron and whistler waves and (b) different measures of the intermittency and multiscaling. The power-laws in the energy spectra are under influences of the Alfven ratio, magnetic Prandtl number, and others. We present relationships between the power-laws and these parameters. Intermittency and multiscaling natures are typically characterized by probability distribution functions and structure functions of magnetic field and current density field. We present the intermittency and multiscaling natures not only by the analysis of magnetic and current density fields, but also by relating these quantities to ion-cyclotron modes and whistler modes.
Our analysis can be related to space- and solar-plasma observations, some of which report relevant multi-fractal, multiscaling nature of turbulence. A comparison of such observatory reports with our simulation results with various settings highlights essences of multiscaling nature of turbulence.