  The transition to turbulence in Taylor-Couette flow often occurs via a
sequence of supercritical bifurcations to progressively more complex, yet
stable, flows. We describe a subcritical laminar-turbulent transition in the
counter-rotating regime mediated by an unstable intermediate state in a system
with an axial aspect ratio of $\Gamma=5.26$ and a radius ratio of $\eta=0.905$.
In this regime, flow visualization experiments and numerical simulations
indicate the intermediate state corresponds to an aperiodic flow featuring
interpenetrating spirals. Furthermore, the reverse transition out of turbulence
leads first to the same intermediate state, which is now stable, before
returning to an azimuthally-symmetric laminar flow. Time-resolved tomographic
particle image velocimetry is used to characterize the experimental flows;
these measurements compare favorably to direct numerical simulations with axial
boundary conditions matching those of the experiments.
