  Rings and gaps are routinely observed in the dust continuum emission of
protoplanetary discs (PPDs). How they form and evolve remains debated. Previous
studies have demonstrated the possibility of spontaneous gas rings and gaps
formation in wind-launching disks. Here, we show that such gas substructures
are unstable to the Rossby Wave Instability (RWI) through numerical
simulations. Specifically, shorter wavelength azimuthal modes develop earlier,
and longer wavelength ones dominate later, forming elongated (arc-like)
anti-cyclonic vortices in the rings and (strongly magnetized) cyclonic vortices
in the gaps that persist until the end of the simulation. Highly elongated
vortices with aspect ratios of 10 or more are found to decay with time in our
non-ideal MHD simulation, in contrast with the hydro case. This difference
could be caused by magnetically induced motions, particularly strong meridional
circulations with large values of the azimuthal component of the vorticity,
which may be incompatible with the columnar structure preferred by vortices.
The cyclonic and anti-cyclonic RWI vortices saturate at moderate levels,
modifying but not destroying the rings and gaps in the radial gas distribution
of the disk. In particular, they do not shut off the poloidal magnetic flux
accumulation in low-density regions and the characteristic meridional flow
patterns that are crucial to the ring and gap formation in wind-launching
disks. Nevertheless, the RWI and their associated vortices open up the
possibility of producing non-axisymmetric dust features observed in a small
fraction of protoplanetary disks through non-ideal MHD, although detailed dust
treatment is needed to explore this possibility.
