  We propose a first-principles model for self-assembled magnetic surface
structures on the water-air interface reported in earlier experiments
\cite{snezhko2,snezhko4}. The model is based on the Navier-Stokes equation for
liquids in shallow water approximation coupled to Newton equations for
interacting magnetic particles suspended on the water-air interface. The model
reproduces most of the observed phenomenology, including spontaneous formation
of magnetic snake-like structures, generation of large-scale vortex flows,
complex ferromagnetic-antiferromagnetic ordering of the snake, and
self-propulsion of bead-snake hybrids. The model provides valuable insights
into self-organization phenomena in a broad range of non-equilibrium magnetic
and electrostatic systems with competing interactions.
