  Vortices in protoplanetary disks have attracted attention since the discovery
of lopsided structures. One of the possible mechanisms for producing vortices
is the Rossby Wave Instability (RWI). In our previous work, we have performed
detailed linear stability analyses of the RWI with various initial conditions.
In this paper, we perform numerical simulations of the vortex formation by the
RWI in 2D barotropic disks using the Athena++ code. As initial conditions, we
consider axisymmetric disks with a Gaussian surface density bump of various
contrasts and half-widths. Perturbations grow as expected from the linear
stability analyses in the linear and weakly non-linear regimes. After the
saturation, multiple vortices are formed in accordance with the most unstable
azimuthal mode and coalesce one after another. In the end, only one
quasi-stationary vortex (the RWI vortex) remains, which migrates inward. During
the RWI evolution, the axisymmetric component approaches the stable
configuration. We find that the axisymmetric component reaches the marginally
stable state for the most unstable azimuthal mode at the saturation and the
marginally stable state for the m = 1 mode at the final vortex merger. We
investigate the structure and evolution of the RWI vortices. We obtain some
empirical relations between the properties of the RWI vortices and the initial
conditions. Using tracer particle analyses, we find that the RWI vortex can be
considered as a physical entity like a large fluid particle. Our results
provide a solid theoretical ground for quantitative interpretation of the
observed lopsided structures in protoplanetary disks.
