Local analysis of the canonical Hamiltonian model of reduced magnetohydrodynamics

The reduced magnetohydrodynamic equations can be written in non-canonical Hamiltonian form, which can then be transformed into a canonized system through the introduction of Clebsch-like parameterization. In this paper, we present our development of the ordinary differential model of the canonized system in a local domain as well as a strong nonlinear term −Q2J and our comparison of that system with a simple canonized system, including the linearized term −ΔQ (where Q is a Clebsch variable, J is the current density, and Δ is the two-dimensional Laplacian). By the numerical simulations of the obtained ordinary differential model, we observe a rapid growth of the current, J, even under the influence of the vorticity.