  We study the temporal evolution of downflows observed at the lateral edges of
penumbral filaments in a sunspot located very close to the disk center. Our
analysis is based on a sequence of nearly diffraction-limited scans of the Fe I
617.3 nm line taken with the CRisp Imaging Spectro-Polarimeter at the Swedish 1
m Solar Telescope. We compute Dopplergrams from the observed intensity profiles
using line bisectors and filter the resulting velocity maps for subsonic
oscillations. Lateral downflows appear everywhere in the center-side penumbra
as small, weak patches of redshifts next to or along the edges of blueshifted
flow channels. These patches have an intermittent life and undergo mergings and
fragmentations quite frequently. The lateral downflows move together with the
hosting filaments and react to their shape variations, very much resembling the
evolution of granular convection in the quiet Sun. There is a good relation
between brightness and velocity of the flow structures in the center-side
penumbra, with downflows being darker than upflows on average, which is again
reminiscent of quiet Sun convection. These results point to the existence of
overturning convection in sunspot penumbrae, with elongated cells forming
filaments where the flow is upward but very inclined, and weak lateral downward
flows. In general, the circular polarization profiles emerging from the lateral
downflows do not show sign reversals, although sometimes we detect three-lobed
profiles which are suggestive of opposite magnetic polarities in the pixel.
