  We study the temporal evolution of umbral dots (UDs) using measurements from
the CRISP imaging spectropolarimeter at the Swedish 1-m Solar Telescope. Scans
of the magnetically sensitive 630 nm iron lines were performed under stable
atmospheric conditions for 71 min with a cadence of 63 s. These observations
allow us to investigate the magnetic field and velocity in and around UDs at a
resolution approaching 0.13". From the analysis of 339 UDs, we draw the
following conclusions: (1)UDs show clear hints of upflows, as predicted by
magnetohydrodynamic (MHD) simulations. By contrast, we could not find
systematic downflow signals. Only in very deep layers we detect localized
downflows around UDs, but they do not persist in time. (2) We confirm that UDs
exhibit weaker and more inclined fields than their surroundings, as reported
previously. However, UDs that have strong fields above 2000 G or are in the
decay phase show enhanced and more vertical fields. (3)There are enhanced
fields at the migration front of UDs detached from penumbral grains, as if
their motion were impeded by the ambient field. (4) Long-lived UDs travel
longer distances with slower proper motions. Our results appear to confirm some
aspects of recent numerical simulations of magnetoconvection in the umbra
(e.g., the existence of upflows in UDs), but not others (e.g., the systematic
weakening of the magnetic field at the position of UDs.)
