Numerical study on a canonized Hamiltonian system representing reduced magnetohydrodynamics and its comparison with two-dimensional Euler system

Abstract

Introducing a Clebsch-like parameterization, we have formulated a canonical Hamiltonian system on a symplectic leaf of reduced magnetohydrodynamics. An interesting structure of the equations is in that the Lorentz-force, which is a quadratic nonlinear term in the conventional formulation, appears as a linear term -{\Delta}Q, just representing the current density (Q is a Clebsch variable, and {\Delta} is the two-dimensional Laplacian); omitting this term reduces the system into the two-dimensional Euler vorticity equation of a neutral fluid. A heuristic estimate shows that current sheets grow exponentially (even in a fully nonlinear regime) together with the action variable P that is conjugate to Q. By numerical simulation, the predicted behavior of the canonical variables, yielding exponential growth of current sheets, has been demonstrated.