Driven magnetic particles on a fluid surface: pattern assisted surface flows.

Magnetic microparticles suspended on the liquid-air interface and subjected to an alternating magnetic field exhibit spontaneous formation of dynamic localized snake patterns. These patterns are accompanied by four large-scale hydrodynamic vortices located at the opposite ends of the snake patterns. We report detailed studies of these large-scale vortices and their relationship to the collective response of magnetic particles in the presence of an alternating magnetic field. We present a model based on the amplitude equation for surface waves coupled to the large-scale hydrodynamic mean flow equation. The model describes both the formation of the dynamic snake patterns and the induced structure of the experimentally observed hydrodynamic flows.