  We provide experimental measurements for the effective scaling of the
Taylor-Reynolds number within the bulk $\text{Re}_{\lambda,\text{bulk}}$, based
on local flow quantities as a function of the driving strength (expressed as
the Taylor number Ta), in the ultimate regime of Taylor-Couette flow. The data
are obtained through flow velocity field measurements using Particle Image
Velocimetry (PIV). We estimate the value of the local dissipation rate
$\epsilon(r)$ using the scaling of the second order velocity structure
functions in the longitudinal and transverse direction within the inertial
range---without invoking Taylor's hypothesis. We find an effective scaling of
$\epsilon_{\text{bulk}} /(\nu^{3}d^{-4})\sim \text{Ta}^{1.40}$, (corresponding
to $\text{Nu}_{\omega,\text{bulk}} \sim \text{Ta}^{0.40}$ for the dimensionless
local angular velocity transfer), which is nearly the same as for the global
energy dissipation rate obtained from both torque measurements
($\text{Nu}_{\omega} \sim \text{Ta}^{0.40}$) and Direct Numerical Simulations
($\text{Nu}_{\omega} \sim \text{Ta}^{0.38}$). The resulting Kolmogorov length
scale is then found to scale as $\eta_{\text{bulk}}/d \sim \text{Ta}^{-0.35}$
and the turbulence intensity as $I_{\theta,\text{bulk}} \sim
\text{Ta}^{-0.061}$. With both the local dissipation rate and the local
fluctuations available we finally find that the Taylor-Reynolds number
effectively scales as Re$_{\lambda,\text{bulk}}\sim \text{Ta}^{0.18}$ in the
present parameter regime of $4.0 \times 10^8 < \text{Ta} < 9.0 \times 10^{10}$.
