The effect of viscosity on the resistive tearing mode with the presence of shear flow

Abstract

The effect of small viscosity on the ‘‘constant ψ’’ tearing mode in the presence of shear flow is analyzed using the boundary‐layer approach. It is found that the influence of viscosity depends upon the parameter G’(0)/F’(0), where G’(0) and F’(0) denote the flow shear and magnetic field shear at the magnetic null plane, respectively. When ‖G’(0)/F’(0)‖≪1, the tearing mode growth rate is suppressed by the viscosity, but not completely stabilized. When ‖G’(0)/F’(0)‖∼O(1) and the viscosity is comparable to the resistivity, the growth rate vanishes as [1−G’(0)2/F’(0)2]1/3, when G’(0)2→F’(0)2 from below. In the case where 1−[G’(0)2/F’(0)2]<0 matching cannot be achieved and the tearing mode vanishes.