A type of large eddy simulation model is proposed which consists of three hierarchies, i.e. transport, magnetohydrodynamics (MHD) and turbulence. These classes are categorized by the poloidal and toroidal mode number (m, n). A (0, 0) mode represents transport, low (m, n) modes represent MHD and high (m, n) modes represent turbulence. Mutual interactions between three classes are possible via nonlinearities such as Reynolds stress, renormalized eddy viscosity and so on. As a starting point, a two-hierarchical model of MHD and turbulence is derived and applied for the analysis of magnetic island dynamics in the presence of a strong pressure gradient. It is found that the growth of the magnetic island is accelerated by the anomalous resistivity, whereas it causes the rotation of the magnetic island to decelerate.
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