*3.4. Stream-Wise Vortices*

Figure 7a shows the distribution of stream-wise vortices *<sup>x</sup>* at different times of *t* = 15, 55, and 114 of the P–N model. Figure 7b shows the distribution of stream-wise vortices *<sup>x</sup>* at different times of *t* = 15, 55, and 114 of the N–P model. Contours in three section planes at each time are given, and the contour increment was 0.1; the red color denotes *<sup>x</sup>* > 0, while the green color denotes *<sup>x</sup>* < 0.

$$
\partial \lrcorner \partial \lrcorner = \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner \partial \lnot \urcorner$$

**Figure 7.** Stream-wise vortices: (**a**) P–N model; (**b**) N–P model.

The intensity of stream-wise vortices became stronger and stronger with the evolution of vortex structures. Furthermore, different scales of stream-wise vortices came into being, the centers of vortices went up, and the influencing areas gradually diffused, followed by strong ejection and sweeping at the centers of these vortices. In addition, the sizes of stream-wise vortices increased continuously. According to Biot–Savart theory, the vortex tube is lengthened in the stream-wise direction, which amplifies the vortex intensity. At last, both stream-wise and span-wise velocities grow quickly, followed by dramatic ejection and sweeping, the formation of strong shear layers locally, and the flow becoming unstable. However, the main affected area is in the vicinity of the wall, which is the region near the wall where hydrodynamic instability occurs actively. Results of the vortex distribution agree with the research results of Shinneeb et al. [12].
