Nonlinear evolution of resistive tearing mode instability with shear flow and viscosity

The nonlinear evolution of the tearing mode instability with equilibrium shear flow is investigated via numerical solutions of the time dependent, visco-resistive magnetohydrodynamic equations. The two-dimensional simulations in slab geometry, periodic in x-direction are initiated with solutions of the linearized MHD equations. Magnetic Reynolds number S was varied from 50 to 104, the flow parameter V was varied up to 1.0 in units of the average Alfven speed, and small viscosity (Sv < 106) was incorporated in the model. When the shear flow is small (V < 0.3) the tearing mode saturates within 100 Alfven times, while large flows (V > 0.3) induce temporal and spatial oscillations of the plasma with a period of ∼1 Alfven time regardless of the value of resistivity, viscosity or the size of the physical system in the non periodic direction. They are initiated within 20-50 Alfven times and persist through the simulation time (T > 100). The initiating time depends on the flow parameter, and the period is affected by the dissipation parameters. Analytical calculations, and close examination of their temporal and spatial evolution, suggest that the oscillations are Alfven waves that originate near the region where the magnetic field and flow are parallel and homogeneous. They propagate towards the resistive layer and are resonantly absorbed in a region of small local Alfven speed outside the resistive layer