Modelling and analytic studies of sheared flow effects on tearing modes

The effects of flow shear on the stability of a (2,1) tearing mode are examined using numerical and analytic studies on a number of model systems. For a cylindrical reduced magnetohydrodynamic (MHD) model, linear computations using the CUTIE code show that sheared axial flows have a destabilizing effect, while sheared poloidal flows tend to reduce the growth rate of the mode. These effects are independent of the direction of the flow. For helical flows the sign of the shear in the flow matters. This symmetry breaking is also seen in the nonlinear regime where the island saturation level is found to depend on the sign of the flows. In the absence of flow, the CUTIE simulations show that the linear mode is more stable in a two fluid as compared to a single fluid model. However, in the presence of sheared axial flows a negative sheared flow is more destabilizing while a positive sheared flow is more stabilizing, compared to the single fluid model. In contrast to the cylindrical model, simulations in a toroidal model, using the MHD code NEAR, always show a stabilizing effect in the presence of a sheared toroidal flow. This is understood analytically in terms of a flow induced 'Shafranov' like shift in the profiles of the equilibrium current that results in a stabilizing change in Delta' and the saturated island size.