Scaling Properties of Three-Dimensional Magnetohydrodynamic Turbulence

The scaling properties of three-dimensional magnetohydrodynamic turbulence with finite magnetic helicity are obtained from direct numerical simulations using ${512}^3$ modes. The results indicate that the turbulence does not follow the Iroshnikov-Kraichnan phenomenology. The scaling exponents of the structure functions can be described by a modified She-Leveque model ${\zeta }_p=p/9+1-(1/3{)}^{p/3}$, corresponding to basic Kolmogorov scaling and sheetlike dissipative structures. In particular, we find ${\zeta }_2\simeq 0.7$, consistent with the energy spectrum $E_k\sim k^{-5\mathrm{}/3}$ as observed in the solar wind, and ${\zeta }_3\simeq 1$, confirming a recent analytical result.