  We investigate the stability, nonlinear development and equilibrium structure
of vortices in a background shearing Keplerian flow. We make use of
high-resolution global two-dimensional compressible hydrodynamic simulations.
We introduce the concept of nonlinear adjustment to describe the transition of
unbalanced vortical fields to a long-lived configuration. We discuss the
conditions under which vortical perturbations evolve into long-lived persistent
structures and we describe the properties of these equilibrium vortices. The
properties of equilibrium vortices appear to be independent from the initial
conditions and depend only on the local disk parameters. In particular we find
that the ratio of the vortex size to the local disk scale height increases with
the decrease of the sound speed, reaching values well above the unity. The
process of spiral density wave generation by the vortex, discussed in our
previous work, appear to maintain its efficiency also at nonlinear amplitudes
and we observe the formation of spiral shocks attached to the vortex. The
shocks may have important consequences on the long term vortex evolution and
possibly on the global disk dynamics. Our study strengthens the arguments in
favor of anticyclonic vortices as the candidates for the promotion of planetary
formation. Hydrodynamic shocks that are an intrinsic property of persistent
vortices in compressible Keplerian flows are an important contributor to the
overall balance. These shocks support vortices against viscous dissipation by
generating local potential vorticity and should be responsible for the eventual
fate of the persistent anticyclonic vortices. Numerical codes have be able to
resolve shock waves to describe the vortex dynamics correctly.
