  We use a high order accuracy spectral code to carry out two-dimensional
time-dependent numerical simulations of vortices in accretion disks. In
particular, we examine the stability and the life time of vortices in
circumstellar disks around young stellar objects. The results show that
cyclonic vortices dissipate quickly, while anticyclonic vortices can survive in
the flow for many orbits. When more than one vortex is present, the
anticyclonic vortices interact through vorticity waves and merge together to
form larger vortices. The decay time of anticyclonic vortices is of the order
of 30-60 orbital periods (for a viscosity parameter alpha = 1.e-4), which is
sufficiently long to allow heavy dust particles to rapidly concentrate in the
core of anticyclonic vortices in protoplanetary disks. This dust concentration
increases the local density of centimeter-size grains, thereby favoring the
formation of larger scale objects which are then capable of efficiently
triggering a gravitational instability. The relatively long-lived vortices
found in this work may therefore play a key role in the formation process of
giant planets.
