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The nonlinear evolution of the tearing mode instability with equilibrium shear flow is investigated via numerical solutions of the resistive magnetohydrodynamic 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 10{sup 2} to 10{sup 5}, a parameter V that measures the strength of the flow in units of the average Alfven speed was varied, and the viscosity as measured by the Reynolds number of S{sub v} satisfied S{sub v} > 10{sup 3}. 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 steam function distort in the direction of the equilibrium flow. The magnetic energy release decreased and the saturation time increased with V, for both small and large resistivity. The validity of the numerical solutions was tested by verifying that the total energy and the magnetic helicity were conserved. Total energy dissipation rate dE/dt decreases as the tearing mode approached its saturated state.

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