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Abstract

We use experiments and direct numerical simulations to probe the phase space of
low-curvature Taylor–Couette flow in the vicinity of the ultimate regime. The cylinder
radius ratio is fixed at η = ri/ro = 0.91, where ri (ro) is the inner (outer) cylinder radius.
Non-dimensional shear drivings (Taylor numbers Ta) in the range 107 ≤ Ta ≤ 1011 are
explored for both co- and counter-rotating configurations. In the Ta range 108 ≤ Ta ≤ 1010,
we observe two local maxima of the angular momentum transport as a function of the
cylinder rotation ratio, which can be described as either ‘co-’ or ‘counter-rotating’ due to
their location or as ‘broad’ or ‘narrow’ due to their shape. We confirm that the broad peak
is accompanied by the strengthening of the large-scale structures, and that the narrow
peak appears once the driving (Ta) is strong enough. As first evidenced in numerical
simulations by Brauckmann et al. (J. Fluid Mech., vol. 790, 2016, pp. 419–452), the broad
peak is produced by centrifugal instabilities and that the narrow peak is a consequence of
shear instabilities. We describe how the peaks change with Ta as the flow becomes more
turbulent. Close to the transition to the ultimate regime when the boundary layers (BLs)
become turbulent, the usual structure of counter-rotating Taylor vortex pairs breaks down
and stable unpaired rolls appear locally. We attribute this state to changes in the underlying
roll characteristics during the transition to the ultimate regime. Further changes in the flow
structure around Ta ≈ 1010 cause the broad peak to disappear completely and the narrow
peak to move. This second transition is caused when the regions inside the BLs which are
locally smooth regions disappear and the whole boundary layer becomes active.