Magnetized Kelvin-Helmholtz instability: theory and simulations in the Earth's magnetosphere context

The Kelvin-Helmholtz instability, proposed a long time ago for its role in and impact on the transport properties at magnetospheric flanks, has been widely investigated in the Earth's magnetosphere context. This review covers more than fifty years of theoretical and numerical efforts in investigating the evolution of Kelvin-Helmholtz vortices and how the rich nonlinear dynamics they drive allow solar wind plasma bubbles to enter into the magnetosphere. Special care is devoted to pointing out the main advantages and weak points of the different plasma models that can he adopted for describing the collisionless magnetospheric medium and in underlying the important role of the three-dimensional geometry of the system.