  We present the results of 2D and 3D hydrodynamic simulations of idealized
protoplanetary discs that examine the formation and evolution of vortices by
the vertical shear instability (VSI). In agreement with recent work, we find
that discs with radially decreasing temperature profiles and short thermal
relaxation time-scales, are subject to the axisymmetric VSI. In three
dimensions, the resulting velocity perturbations give rise to
quasi-axisymmetric potential vorticity perturbations that break-up into
discrete vortices, in a manner that is reminiscent of the Rossby wave
instability. Discs with very short thermal evolution time-scales (i.e.
{\tau}<0.1 local orbit periods) develop strong vorticity perturbations that
roll up into vortices that have small aspect ratios ({\chi}<2) and short
lifetimes (~ a few orbits). Longer thermal time-scales give rise to vortices
with larger aspect ratios (6<{\chi}<10), and lifetimes that depend on the
entropy gradient. A steeply decreasing entropy profile leads to vortex
lifetimes that exceed the simulation run times of hundreds of orbital periods.
Vortex lifetimes in discs with positive or weakly decreasing entropy profiles
are much shorter, being 10s of orbits at most, suggesting that the subcritical
baroclinic instability plays an important role in sustaining vortices against
destruction through the elliptical instability. Applied to the outer regions of
protoplanetary discs, where the VSI is most likely to occur, our results
suggest that vortices formed by the VSI are likely to be short lived
structures.
