  For a circular magnetic nanodot in a vortex ground state we study how the
critical velocity $v_c$ of the vortex core reversal depends on the magnitude
$H$ of a bias magnetic field applied perpendicularly to the dot plane. We find
that, similarly to the case $H$ = 0, the critical velocity does not depend on
the size of the dot. The critical velocity is dramatically reduced when the
negative (i.e. opposite to the vortex core direction) bias field approaches the
value, at which a \emph{static} core reversal takes place. A simple analytical
model shows good agreement with our numerical result.
