Fully turbulent Taylor–Couette flow between independently rotating cylinders is investigated experimentally in a wide-gap configuration ($\unicode[STIX]{x1D702}=0.5$) around the maximum transport of angular momentum. In that regime turbulent Taylor vortices are present inside the gap, leading to a pronounced axial dependence of the flow. To account for this dependence, we measure the radial and azimuthal velocity components in horizontal planes at different cylinder heights using particle image velocimetry. The ratio of angular velocities of the cylinder walls $\unicode[STIX]{x1D707}$, where the torque maximum appears, is located in the low counter-rotating regime ($\unicode[STIX]{x1D707}_{max}(\unicode[STIX]{x1D702}=0.5)=-0.2$). This point coincides with the smallest radial gradient of angular velocity in the bulk and the detachment of the neutral surface from the outer cylinder wall, where the azimuthal velocity component vanishes. The structure of the flow is further revealed by decomposing the flow field into its large-scale and turbulent contributions. Applying this decomposition to the kinetic energy, we can analyse the formation process of the turbulent Taylor vortices in more detail. Starting at pure inner cylinder rotation, the vortices are formed and strengthened until $\unicode[STIX]{x1D707}=-0.2$ quite continuously, while they break down rapidly for higher counter-rotation. The same picture is shown by the decomposed Nusselt number, and the range of rotation ratios, where turbulent Taylor vortices can exist, shrinks strongly in comparison to investigations at much lower shear Reynolds numbers. Moreover, we analyse the scaling of the Nusselt number and the wind Reynolds number with the shear Reynolds number, finding a communal transition at approximately $Re_{S}\approx 10^{5}$ from classical to ultimate turbulence with a transitional regime lasting at least up to $Re_{S}\geqslant 2\times 10^{5}$. Including the axial dispersion of the flow into the calculation of the wind amplitude, we can also investigate the wind Reynolds number as a function of the rotation ratio $\unicode[STIX]{x1D707}$, finding a maximum in the low counter-rotating regime slightly larger than $\unicode[STIX]{x1D707}_{max}$. Based on our study it becomes clear that the investigation of counter-rotating Taylor–Couette flows strongly requires an axial exploration of the flow.

We experimentally and numerically investigate the angular momentum transport in turbulent Taylor-Couette flow for independently rotating cylinders at a small radius ratio of η = 0.357 for various shear Reynolds numbers (4.5 × 10 3 ≤ Re S ≤ 1.2 × 10 5 ) and ratios of angular velocitiesmomentum transport in terms of the pseudo-Nusselt number N u ω does not show a pure power law scaling with the forcing Re S and features non-constant effective scaling between 1.3 × 10 4 ≤ Re S ≤ 4 × 10 4 . This transition lies in the classical turbulent regime and is caused by the curvature-dependent limited capacity of the outer cylinder to emit small-scale plumes at a sufficient rate to equalize the angular momentum in the bulk. For counter-rotating cylinders, a maximum in the torque occurs at µ max = −0.123 ± 0.030. The origin of this maximum can be attributed to a strengthening of turbulent Taylor vortices, which is revealed by the flow visualization technique. In addition, different flow states at µ max concerning the wavelength of the large-scale vortices have been detected. The experimental and numerical results for the Nusselt number show a very good agreement.

In this study, we discuss the observed flow regimes in Taylor–Couette flow of radius ratio η = 0.1 for various Reynolds numbers up to 1.5 × 10 4 . We investigate the flow using a visualization method. The flow states in the centrifugally unstable flow are investigated in the case of counter-rotating cylinders and pure inner cylinder rotation. Beside classical known flow states as Taylor-vortex flow and wavy vortex flow, we observe a variety of new flow structures in the cylindrical annulus, especially for the transition to turbulence. Coexisting turbulent and laminar regions inside the system are observed. Turbulent spots and turbulent bursts are observed, as well as an irregular Taylor-vortex flow and non-stationary turbulent vortices. Especially, a single axially aligned columnar vortex between the inner and outer cylinder is found. The principal regimes observed in flow between independently rotating cylinders are summarized in a flow-regime diagram. This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal Philosophical Transactions paper (part 2)’.