  If sufficiently irradiated by its central star, a protoplanetary disks falls
into an equilibrium state exhibiting vertical shear. This state may be subject
to a hydrodynamical instability, the `vertical shear instability' (VSI), whose
breakdown into turbulence transports a moderate amount of angular momentum
while also facilitating planet formation, possibly via the production of
small-scale vortices. In this paper, we show that VSI modes (a) exhibit
arbitrary spatial profiles and (b) remain nonlinear solutions to the
incompressible local equations, no matter their amplitude. The modes are
themselves subject to parasitic Kelvin-Helmholtz instability, though the disk
rotation significantly impedes the parasites and permits the VSI to attain
large amplitudes (fluid velocities < 10% the sound speed). This `delay' in
saturation probably explains the prominence of the VSI linear modes in global
simulations. More generally, the parasites may set the amplitude of VSI
turbulence in strongly irradiated disks. They are also important in breaking
the axisymmetry of the flow, via the unavoidable formation of vortices. The
vortices, however, are not aligned with the orbital plane and thus express a
pronounced $z$-dependence. We also briefly demonstrate that the vertical shear
has little effect on the magnetorotational instability, whereas magnetic fields
easily quench the VSI, a potential issue in the ionised surface regions of the
disk and also at larger radii.
