  Rotor-stator cavity flows are known to exhibit unsteady flow structures in
the form of circular and spiral rolls. While the origin of the spirals is well
understood, that of the circular rolls is not. In the present study the
axisymmetric flow in an aspect ratio $R/H=10$ cavity is revisited {numerically
using recent concepts and tools from bifurcation theory}. It is confirmed that
a linear instability takes place at a finite critical Reynolds number
$Re=Re_c$, and that there exists a subcritical branch of large amplitude
chaotic solutions. This motivates the search for subcritical finite-amplitude
solutions. The branch of periodic states born in a Hopf bifurcation at
$Re=Re_c$, identified using a Self-Consistent Method (SCM) and arclength
continuation, is found to be supercritical. The associated solutions only
exist, however, in a very narrow range of $Re$ and do not explain the
subcritical chaotic rolls. Another subcritical branch of periodic solutions is
found using the Harmonic Balance Method with an initial guess obtained by SCM.
In addition, edge states separating the steady laminar and chaotic regimes are
identified using a bisection algorithm. These edge states are bi-periodic in
time for most values of $Re$, {where} their dynamics is {analysed in detail}.
Both solution branches fold around at approximately the same value of $Re$,
which is lower than $Re_c$ yet still larger than the values reported in
experiments. This suggests that, at least in the absence of external forcing,
sustained chaotic rolls have their origin in the bifurcations from these
unstable solutions.
