Turbulence strength in ultimate Taylor-Couette turbulence

Abstract

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 $4.0\times 10^8<\text{Ta}<9.0\times 10^{10}$.

15 pages, 8 figures, J. Fluid Mech. (In press)

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