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 \leq 0.1 local orbit periods ) develop strong vorticity perturbations that roll up into vortices that have small aspect ratios ( \chi \leq 2 ) and short lifetimes ( \sim a few orbits ) .
Longer thermal time-scales give rise to vortices with larger aspect ratios ( 6 \leq \chi \leq 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 .