Instabilities and vortex dynamics in shear flow of magnetized plasmas

Gradient-driven instabilities and the subsequent nonlinear evolution of generated vortices in sheared E×B flows are investigated for magnetized plasmas with and without gravity (magnetic curvature) and magnetic shear by using theory and implicit particle simulations. In the linear eigenmode analysis, the instabilities considered are the Kelvin–Helmholtz (K–H) instability and the resistive interchange instability. The presence of the shear flow can stabilize these instabilities. The dynamics of the K–H instability and the vortex dynamics can be uniformly described by the initial flow pattern with a vorticity localization parameter ε. The observed growth of the K–H modes is exponential in time for linearly unstable modes, secular for the marginal mode, and absent until driven nonlinearly for linearly stable modes. The distance between two vortex centers experiences rapid merging while the angle θ between the axis of the vortices and the external shear flow increases. These vortices proceed toward their overall coalescence, while shedding small-scale vortices and waves. The main features of vortex dynamics, the nonlinear coalescence and the tilt or the rotational instabilities of vortices, are shown to be given by using a low-dimension Hamiltonian representation for interacting vortex cores in the shear flow.