**Xiangkai Xiao and Baofang Song \***

Center for Applied Mathematics, Tianjin University, Tianjin 300072, China; xiaoxk2018@tju.edu.cn

**\*** Correspondence: baofang\_song@tju.edu.cn

Received: 19 September 2020; Accepted: 13 October 2020; Published: 16 October 2020

**Abstract:** Channel flow turbulence exhibits interesting spatiotemporal complexities at transitional Reynolds numbers. In this paper, we investigated some aspects of the kinematics and dynamics of fully localized turbulent bands in large flow domains. We discussed the recent advancement in the understanding of the wave-generation at the downstream end of fully localized bands. Based on the discussion, we proposed a possible mechanism for the tilt direction selection. We measured the propagation speed of the downstream end and the advection speed of the low-speed streaks in the bulk of turbulent bands at various Reynolds numbers. Instead of measuring the tilt angle by treating an entire band as a tilted object as in prior studies, we proposed that, from the point of view of the formation and growth of turbulent bands, the tilt angle should be determined by the relative speed between the downstream end and the streaks in the bulk. We obtained a good agreement between our calculation of the tilt angle and the reported results in the literature at relatively low Reynolds numbers.

**Keywords:** turbulent bands; obliqueness; advection speed; wave generation; inflectional instability
