  We study periodically driven Taylor-Couette turbulence, i.e. the flow
confined between two concentric, independently rotating cylinders. Here, the
inner cylinder is driven sinusoidally while the outer cylinder is kept at rest
(time-averaged Reynolds number is $Re_i = 5 \times 10^5$). Using particle image
velocimetry (PIV), we measure the velocity over a wide range of modulation
periods, corresponding to a change in Womersley number in the range $15 \leq Wo
\leq 114$. To understand how the flow responds to a given modulation, we
calculate the phase delay and amplitude response of the azimuthal velocity.
  In agreement with earlier theoretical and numerical work, we find that for
large modulation periods the system follows the given modulation of the
driving, i.e. the system behaves quasi-stationary. For smaller modulation
periods, the flow cannot follow the modulation, and the flow velocity responds
with a phase delay and a smaller amplitude response to the given modulation. If
we compare our results with numerical and theoretical results for the laminar
case, we find that the scalings of the phase delay and the amplitude response
are similar. However, the local response in the bulk of the flow is independent
of the distance to the modulated boundary. Apparently, the turbulent mixing is
strong enough to prevent the flow from having radius-dependent responses to the
given modulation.
