Growth and decay of isolated turbulent band in Plane-Couette flow

The transition of plane Couette flow is numerically investigated in a large computational domain. It is found that the averaged period of the transient growth reduces slowly with the decrease of the Reynolds number (Re) except when Re is close to a threshold value of 286. During the decay process, the band contracts from its both ends with a statistical constant velocity, but keeps its center, width, and tilt angle statistically unchanged. For self-sustained turbulent band, three growth styles are observed. At moderate Re, the isolated band extends obliquely as what happens in plane Poiseuille flow. With the increase of Re, transverse split occurs and the band breaks into several attached segments, forming a shape of `F'. Further increasing Re leads to a longitudinal split, i.e. the isolated band becomes wider at first and then splits into two parallel bands.