**4. Results and Discussion**

The main DNS at *Rew* ≤ 1600 for which a laminar–turbulent intermittency was clearly confirmed through the preliminary analysis is presented in this section, and the characteristics of the localized turbulence are discussed. Table 2 summarizes the numerical conditions, including the friction Reynolds number *Re<sup>τ</sup>* that was obtained. As in the preliminary analysis, the radius ratio was *η* = 0.1, and the computational domain was extended only in *x*; however, the grid resolution was not changed. Because *Re<sup>τ</sup>* is lower than that of the preliminary analysis, the grid spacing in terms of the wall units was finer. The table also shows the grid resolutions based on the friction velocity *uτ* under each condition:

$$
u\_{\tau} = \frac{\eta u\_{\tau, \rm in} + u\_{\tau, \rm out}}{\eta + 1},\tag{5}$$

where *uτ*,*in* and *uτ*,*out* are defined by the corresponding wall shear stress, *τ*in, and *τ*out, as well as by the relation *τ* = *ρu*<sup>2</sup> *<sup>τ</sup>*, from which inner units can be defined. For a low Reynolds-number regime of *Rew* < 1600, which is of interest in this study, the grid spacings of Δ*x*<sup>+</sup> < 8, Δ*r*<sup>+</sup> min <sup>&</sup>lt; 0.2, <sup>Δ</sup>*r*<sup>+</sup> max < 3, and Δ*z*<sup>+</sup> < 4 are comparable to or higher in resolution than those in previous studies [35,37,53]. The initial conditions during each analysis adopted a turbulent field with a one-step-higher Reynolds number, but reduced the Reynolds number adiabatically. In other words, the study was carried out carefully such that the sudden drop in the Reynolds number will not be a proximate cause of laminarization.

**Table 2.** Numerical conditions for the main DNS with a long domain. The grid resolutions of (Δ*x*, Δ*r*, Δ*θ*) are described in their dimensionless form based on *u<sup>τ</sup>* and *μ*/*ρ*. The minimum and maximum Δ*r* of the radial direction, in which we used non-uniform grids, are shown. † Laminar values from a laminarized case.

