Nonlinear viscoresistive dynamics of the m= 1 tearing instability

Abstract

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 P_m. 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 Alfvén velocity. However at high P_m 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.