Resistive tearing instability with equilibrium shear flow

The effect of equilibrium velocity shear on the resistive tearing instability has been systematically studied, using the boundary layer approach. Both the ‘‘constant-ψ’’ tearing mode, which has a growth rate that scales as S−3/5, and the ‘‘nonconstant-ψ’’ tearing mode Δ′(αS)−1/3≫1, which has a growth rate that scales as S−1/3, are analyzed in the presence of flow. Here S is the usual ratio of the resistive diffusion and Alfvén times. It is found that the shear flow has a significant influence on both the external ideal region and the internal resistive region. In the external ideal region, the shear flow can dramatically change the value of the matching quantity Δ′. In the internal resistive region, the tearing mode is sensitive to the flow shear at the magnetic null plane: G′(0). When G′(0) is comparable to the magnetic field shear, F′(0), the scalings of the constant-ψ tearing mode are changed and the Δ′0 instability criterion is removed, provided G′(0)G″(0)−F′(0)F″(0)≠0. The scalings of the nonconstant-ψ tearing mode remain unchanged. When the flow shear is larger than the magnetic field shear at the magnetic null plane, both tearing modes are stabilized. Finally, the transition to ideal instability is discussed.