  Discovered in 1909 the Evershed effect represents strong mass outflows in
sunspot penumbra, where the magnetic field of sunspots is filamentary and
almost horizontal. These flows play important role in sunspots and have been
studied in detail using large ground-based and space telescopes, but the basic
understanding of its mechanism is still missing. We present results of
realistic numerical simulations of the Sun's subsurface dynamics, and argue
that the key mechanism of this effect is in non-linear magnetoconvection that
has properties of traveling waves in the presence of strong, highly inclined
magnetic field. The simulations reproduce many observed features of the
Evershed effect, including the high-speed "Evershed clouds", the filamentary
structure of the flows, and the non-stationary quasi-periodic behavior. The
results provide a synergy of previous theoretical models and lead to an
interesting prediction of a large-scale organization of the outflows.
