  The statistics of velocity fluctuations of turbulent Taylor-Couette flow are
examined. The rotation rate of the inner and outer cylinder are varied while
keeping the Taylor number fixed to $1.49 \times 10^{12}$
($\mathcal{O}(\text{Re})=10^6$). The azimuthal velocity component of the flow
is measured using laser Doppler anemometry (LDA). For each experiment
$5\times10^6$ datapoints are acquired and carefully analysed. Using extended
self-similarity (ESS) \cite{ben93b} the longitudinal structure function
exponents are extracted, and are found to weakly depend on the ratio of the
rotation rates. For the case where only the inner cylinder rotates the results
are in good agreement with results measured by Lewis and Swinney \cite{lew99}
using hot-film anemometry. The power spectra shows clear -5/3 scaling for the
intermediate angular velocity ratios $-\omega_o/\omega_i \in \{0.6, 0.8,
1.0\}$, roughly -5/3 scaling for $-\omega_o/\omega_i \in \{0.2, 0.3, 0.4,
2.0\}$, and no clear scaling law can be found for $-\omega_0/\omega_i = 0$
(inner cylinder rotation only); the local scaling exponent of the spectra has a
strong frequency dependence. We relate these observations to the shape of the
probability density function of the azimuthal velocity and the presence of a
neutral line.
