The nonlinear evolution of weakly coupled double tearing modes (DTMs) with and without sheared toroidal flow is systematically investigated with the three-dimensional, toroidal-geometry, and nonlinear magneto-hydro-dynamics code CLT. Due to the explosive growth of the weakly coupled DTMs, the pressure crashes are much more severe than those caused by the strongly coupled DTMs. The weakly coupled DTMs can easily be decoupled by sheared toroidal flow, and then the mutually driven term between the two tearing modes becomes periodically positive and negative, leading to periodic growth. The interaction slows the rotation between the two tearing modes when the phase difference is close to 180°. When the islands are sufficiently large, the interaction can overcome the decoupling effect of the shear flow, and the two tearing modes then lock with each other. Due to the different coupling effects of the two tearing modes, the threshold island width or perturbed magnetic field for mode-locking increases with increasing separation. The coupling effect between the two tearing modes is also related to the resistivity. If the resistivity is high, the coupling effect between the two tearing modes can be huge. A stronger shear flow is needed to decouple them, and even a small island can lead to mode-locking in high-resistivity plasma.
This paper investigates the nonlinear behavior of weakly coupled double tearing modes (DTMs) with and without sheared toroidal flow. The study shows that weakly coupled DTMs can lead to severe pressure crashes, but sheared flow can decouple them, causing periodic growth. The interaction between the modes can also slow their rotation and eventually lead to mode-locking, depending on factors like island width and resistivity.