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Statistical properties of the Sun's photospheric turbulent magnetic field,especially those of the Active Regions (ARs), have been studied using theline-of-sight data from magnetograms taken by SOHO and several otherinstruments (see e.g. Abramenko et al (2002, 2003),Abramenko and Yurchyshyn(2010)). This includes structure functions and their exponents, flatness curvesand correlation functions. In these works, the dependence of structure functionexponents ($\zeta_p$) of the order of the structure functions ($\it{p}$) wasmodeled using a non-intermittent K41 model. It is now well known that the ARsare highly turbulent and are associated with strong intermittent events. Inthis paper we compare some of the observations from Abramenko et al (2003) withthe log-Poisson model (Biskamp 2003) used for modeling intermittent MHDturbulent flows. Next, we analyze the structure function data obtained from thedirect numerical simulations (DNS) of homogeneous, incompressible 3D-MHDturbulence in three cases: sustained by forcing, freely decaying and a flowinitially driven and later allowed to decay (case 3). The respective DNSreplicate the properties seen in the plots of $\zeta_p$ against $\it{p}$ ofARs. We also reproduce the trends and changes observed in intermittency inflatness [Abramenko and Yurchyshyn (2010)] and correlation functions [Abramenkoet al (2003)] of ARs. It is suggested from this analysis that an AR in theonset phase of a flare can be treated as a forced 3D-MHD turbulent system inits simplest form and that the flaring stage is representative of decaying3D-MHD turbulence. It is also inferred that significant changes inintermittency from the initial onset phase of a flare to its final peak flaringphase, are related to the time taken by the system to reach the initial onsetphase.

Modeling Statistical Properties of Solar Active Regions through DNS of 3D-MHD Turbulence