  Recent spectro-polarimetric observations of a sunspot showed the formation of
bipolar magnetic patches in the mid penumbra and their propagation toward the
outer penumbral boundary. The observations were interpreted as being caused by
sea-serpent magnetic fields near the solar surface (Sainz Dalda & Bellot Rubio
2008). In this Letter, we develop a 3D radiative MHD numerical model to explain
the sea-serpent structure and the wave-like behavior of the penumbral magnetic
field lines. The simulations reproduce the observed behavior, suggesting that
the sea-serpent phenomenon is a consequence of magnetoconvection in a strongly
inclined magnetic field. It involves several physical processes: filamentary
structurization, high-speed overturning convective motions in strong, almost
horizontal magnetic fields with partially frozen field lines, and traveling
convective waves. The results demonstrate a correlation of the bipolar magnetic
patches with high-speed Evershed downflows in the penumbra. This is the first
time that a 3D numerical model of the penumbra results in downward directed
magnetic fields, an essential ingredient of sunspot penumbrae that has eluded
explanation until now.
