Statistical and spectral properties of magnetic islands in reconnecting current sheets during two-ribbon flares

We perform a set of two dimensional resistive magnetohydrodynamic simulations to study the reconnection process occurring in current sheets that develop during solar eruptions. Reconnection commences gradually and produces small-scale structures inside the current sheet, which has one end anchored to the bottom boundary and the other end open. The main features we study include plasmoids (or plasma blobs) flowing in the sheet, and X-points between pairs of adjacent islands. The statistical properties of the fine structure and the dependence of the spectral energy on these properties are examined. The flux and size distribution functions of plasmoids roughly follow inverse square power laws at large scales. The mass distribution function is steep at large scales and shallow at small scales. The size distribution also shows that plasmoids are highly asymmetric soon after being formed, while older plasmoids tend to be more circular. The spectral profiles of magnetic and kinetic energy inside the current sheet are both consistent with a power law. The corresponding spectral indices γ are found to vary with the magnetic Reynolds number Rm of the system, but tend to approach a constant for large Rm (>105). The motion and growth of blobs change the spectral index. The growth of new islands causes the power spectrum to steepen, but it becomes shallower when old and large plasmoids leave the computational domain