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 resistive magnetohydrodynamic (MHD) equations. The two-dimensional simulations are in slab geometry, are periodic in the x direction, and are initiated with solutions of the linearized MHD equations. The magnetic Reynolds number S was varied from 102 to 105, a parameter V that measures the strength of the flow in units of the average Alfvén speed was varied from 0 to 0.5, and the viscosity as measured by the Reynolds number Sν satisfied Sν≥103. When the shear flow is small (V≤0.3) the tearing mode saturates within one resistive time, while for larger flows the nonlinear saturation develops on a longer time scale. The two-dimensional spatial structure of both the flux function and the streamfunction distort in the direction of the equilibrium flow. The magnetic energy release decreases and the saturation time increases with V for both small and large resistivity. Shear flow decreases the saturated magnetic island width, and generates currents far from the tearing layer. The validity of the numerical solutions was tested by verifying that the total energy and the magnetic helicity are conserved. The results of the present study suggest that equilibrium shear flow may improve the confinment of tokamak plasma.