**1. Introduction**

The dynamics at the onset of turbulent fluid flow, as the parameters are varied, is one of the most puzzling issues of hydrodynamics. Subcritical flows are known to feature two regimes in competition, namely a laminar and a turbulent one. As the Reynolds number (their main control parameter) is varied, this competition takes the form of laminar-turbulent coexistence featuring some interesting analogies with phase transitions in thermodynamics. The onset of this coexistence in wall-bounded shear flows has been speculated to follow a statistical scenario called directed percolation (DP). It involves a critical point (a critical Reynolds number) in the vicinity of which fluctuations diverge algebraically [1,2]. The directed percolation scenario has gained theoretical importance because it appears as the usual rule for a one-dimensional systems obeying a set of specific properties, notably a unique absorbing state and short-range interactions [3,4]. However, it quickly proved difficult to isolate similar phenomena experimentally [5]. The main limitations happen to be finite-size effects, as well as the presence of defects [6–8] or issues revolving around nucleation rates [9,10]. The first experimental evidence for directed percolation in a two-dimensional physical system, with a complete set of critical exponents, occurred in electroconvection in nematic liquid crystals [11]. More recent experiments and numerical simulations with inert liquids were aimed at establishing the critical exponents relevant for the laminar-turbulent transition. The only meaningful experimental results are to be found in Ref. [12] for the flow inside an annulus driven by the revolutions of the outer wall, where all critical exponents match those of (1 + 1)-D DP. All other experimental attempts in effectively two-dimensional geometries have so far lead to ambiguous results [13,14]. A few numerical studies based on other geometries have also confirmed the DP hypothesis in one dimension, among them [15]. The most

notorious system displaying one-dimensional spatiotemporal intermittency (STI) is cylindrical pipe flow. Although (1 + 1)-D DP has been widely speculated and is found in the most recent modelling approaches [16–18], clean experimental evidence seems to require facilities of a size beyond anything engineerable [19]. The only convincing two-dimensional study to date based on the (underesolved) Navier–Stokes equations and supporting the DP hypothesis is found in Ref. [20]. There again, a cost compromise was necessary between accuracy of the Navier–Stokes solutions and size effects. There the set of critical exponents differs from their unidimensional counterpart and corresponds to (2 + 1)-D DP. The status of the application of (2 + 1)-D DP to other planar flows is still open: for plane Couette flow (pCf), finite-size effects wrongly predict to discontinuous scenarios [21], whereas plane Poiseuille flow (pPf) seems to display a two-stage behavior so far poorly understood [22–24]. At a finite distance from the critical point, these two planar flows feature more structured arrays of turbulent stripes, all oblique to the mean flow direction (see, e.g., [21,25–30] for recent reviews).

Given the current status of DP affairs in shear flows, new flow candidates where to probe the DP hypothesis are encouraged, irrespective of the effective dimension considered (one or two). In the present article, we revisit transition in annular Couette flow (aCf) in the light of critical scaling. This flow has a geometry similar to cylindrical pipe flow, however, with a solid cylinder at its centerline. The geometry is determined by the radius ratio *η* between the radius of the outer pipe and that of the inner one. This flow supports both turbulence [31] as well as a linearly stable base flow for all Reynolds number of interest, hence transition has to be of the subcritical type. Unlike annular pipe flow [32–34], no pressure gradient is applied, instead the fluid is entrained by the translating motion of the inner cylinder [35]. Earlier work by some of us [36] on this flow have lead to surprising results: although the transitional flow reported for *η* ≥ 0.5 consists of helical bands of turbulence wrapping around the inner rod, for lower values of *η*, a new regime of laminar-turbulent alternations was reported. This regime is characterized by slightly shorter streamwise correlations and non-oblique structures, explained by the azimuthal confinement and by the impossibility to host azimuthal large-scale flows [37]. The aim of the present article is to give a more detailed characterization of the novel low-*η* intermittent regime and of its onset. In particular, the azimuthal extension of aCf is investigated in a range of parameters beyond that used by Kunii et al. [36]. As will be seen, this new choice of geometrical parameters leads to new conclusions regarding the critical exponents. This new parametric study allows one to rationalize once and for all the quantitative comparison between original geometry and the extended one.

The plan of this article unfolds as follows: the geometry and the numerical methods are explained in Section 2, and the statistics of STI are reported in Section 3 and discussed in Section 4.
