*3.1. The Flow Structure*

Many studies have noticed the wave-like form of the bulk of turbulent bands [6,7,9,24], i.e., regularly aligned and distributed streaks along the band. In Figure 5a, the streamwise velocity fluctuations are plotted as the colormap in the *x*-*z* plane at *y* = −0.5 (blue color shows low speed and red shows high speed region). Low-speed streaks (blue) are nearly parallel to the streamwise direction and show nearly a periodic pattern. On the upstream edge, high-speed streaks (red) can be observed but do not show a strong periodic pattern as the low-speed streaks. It should be noted that the tilt angle, with respect to the streamwise direction, of the steaks in the bulk is significantly lower than that at the head. Both low speed and high-speed streaks are nearly parallel to the streamwise direction. However, it still can be noticed that these two groups of streaks exhibit opposite tilt directions. The four dashed lines mark the positions of four cut planes perpendicular to the wall, in which streamwise velocity fluctuations are plotted to visualize the structure of the band in the wall-normal direction (see Figure 5b–e). A two-layer structure can be observed, which can be expected from the symmetry of the base flow about the channel center-plane. Each layer consists of staggered high- and low-speed streaks, and, in each layer, high-speed streaks are located near the wall and low-speed streaks near the channel center-plane. Figure 5e and the part between *s* = 20 and 50 in Figure 5d show that, on the upstream, high-speed streaks are the dominate structures. On the downstream, low-speed streaks dominate (see Figure 5b and the part between *s* = 0 and 20 in Figure 5c). In between, high-speed and low-speed streaks are comparable (see the part between *s* = 20 and 50 in Figure 5c and between *s* = 0 and 20 in Figure 5d), and this is the most energetic and turbulent region.

Xiao and Song [24] showed that the generated streaks move away from the head in the frame of reference co-moving with the head, and that streaks decay at the tail of the band. To show this process explicitly, we selected a low-speed streak and tracked it (see Figure 6). The tracking lasted for hundreds of time units until the streak reaches the tail of the band, without a significant change in the shape of the streak.

**Figure 5.** (**a**) Streamwise velocity fluctuations of a band at *Re* = 750 plotted in the *x*-*z* plane at *y* = −0.5. The four dashed lines mark the positions of four cut planes perpendicular to the wall, in which streamwise velocity fluctuations are plotted in (**b**–**e**). The *s*-axis goes from top-left to bottom-right along the lines. The two arrows, at *s* = 10 and 40, respectively, show the sequence of (**b**–**e**). The length in *y* direction is stretched by a factor of 3.

**Figure 6.** Tracking of a low-speed streak (enclosed by a parallelogram) at *Re* = 750 in the frame of reference co-moving with the head. (**a**) *t* = 600; (**b**) *t* = 680; (**c**) *t* = 760; (**d**) *t* = 840.
