Nonlinear viscoresistive dynamics of the m=1 tearing instability

A numerical investigation of the viscoresistive evolution of the m=1 tearing instability is presented. Its linear growth rate is found to have various power law scalings in different viscoresistive regimes, in agreement with the theoretical results of Porcelli [Phys. Fluids 30, 1734 (1987)]. Our principal focus is on the nonlinear behavior of this instability at a high value of the stability parameter Δ' and for different values of the Prandtl number Pm. It is found that, depending on the Prandtl regime, and in association with a poloidal oscillation of the magnetic structure, a quadrupolar flow can be generated and/or destroyed outside the current sheet. The reconnection process appears to be influenced by the generation/inhibition dynamics of this external quadrupolar flow. At large enough times, this nonlinear quadrupolar flow can be partially advected in the poloidal direction at the Alfven velocity. However at high Pm values, such an advection is inhibited by viscosity and, as a consequence, the latter contributes to the reduction of the amplitude of the poloidal oscillations