Magneto-hyperbolic instability: a new instability due to hyperbolic instability and phase shift by Alfven waves

The linear stability of vortices which possess hyperbolic stagnation points and are subjected to weak magnetic field is studied by local and modal stability analysis. The base flow is the two-dimensional Taylor-Green vortices. The local stability analysis shows that strong instability emerges near the heteroclinic streamlines connecting the hyperbolic stagnation points. Unstable regions form bands in a parameter space. These features are similar to those of strato-hyperbolic instability discovered recently (Suzuki et al., 2018). The modal stability analysis is performed numerically using the Krylov method. In addition to the magneto-rotational instability, asymmetric instability which is closely related to the local instability is observed. The corresponding eigenmodes have large amplitude near the heteroclinic streamlines and are again similar to those of strato-hyperbolic instability. This new instability is due to the hyperbolic instability and phase shift by the Alfven waves, the latter being replaced by the internal gravity waves in the strato-hyperbolic instability. Thus it is named as magneto-hyperbolic instability.