Fractality feature in incompressible three-dimensional magnetohydrodynamic turbulence

High-resolution direct numerical simulation data for three-dimensional magnetohydrodynamic (MHD) turbulence based on the 1024(3)-modes in a periodic box are used to study the statistical properties of turbulence. In this paper, the presence of intermittency in MHD turbulence is investigated through the analysis of the Probability Distribution Function (PDF) for Elsasser fields and total energy fluctuations. The energy PDFs exhibit similarity over all scales of the turbulent system since they show no substantial qualitative change in shape as the scale of the fluctuations varies. This is in sharp and surprising contrast to the well-known behavior of PDFs of turbulent field fluctuations of, for example, velocity, and magnetic and Elsasser fields. The PDFs have exponential tails and satisfy the function P(| delta X |) similar to exp(-A | delta X | (mu)). Numerically, we extract the exponent mu and find that it is constant for monofractal behavior as the scale of length varies. The compensated structure functions exhibit self-similarity for the respective fluctuations, and it is a reliable way in turbulence.