Toroidal flow effects in 3/2 and 2/1 resistive modes nonlinearly driven by a 1/1 internal kink

The nonlinear drive from an unstable m/n=1/1 internal kink mode to reconnecting modes on surrounding low order rational surfaces is studied with a varying imposed toroidal flow shear in equilibria which accurately model the DIII-D tokamak.~ The flow is linear in poloidal flux, and is varied from 0 to $\Omega \tau _A \approx 0.1$.~ The simulations are described in three stages; the linear, nonlinearly driven and nonlinearly saturated stages.~ In the linear stage the independent modes exhibit classic flow effects.~ In the nonlinear driven stage, while below the threshold for locking, small components driven by toroidal coupling exhibit damping and phase shifts with small torques.~ In the nonlinear saturated stage the n=0 flow is strongly modified as various components lock to each other and phases exhibit long timescale oscillations, the details of which depend on the linear stability and equilibrium flow.~ The nonlinear 3-D resistive magnetohydrodynamic code NIMROD is used for the analysis, which includes the effects of strong anisotropic heat conduction.