Development of a turbulent spot into a stripe pattern in plane Poiseuille flow

Abstract: A structure consisting of quasi-laminar and turbulent regions in a stripe pattern, which can be found in a transitional plane channel flow, is called `turbulent stripe'. In the previous works, the emergence of this structure was confirmed only in the case of decreasing Reynolds number from turbulent regime. In the present study, its formation from a turbulent spot has been investigated using a direct numerical simulation in a relatively large-scale computational domain of $L_x \times L_y \times L_z = 731.4\delta \times 2\delta \times 365.7\delta$ at ${\rm Re}\tau = 56$ and $L_x \times L_y \times L_z = 640\delta \times 2\delta \times 320\delta$ at ${\rm Re}\tau = 64$. We observed the stripe pattern of quasi-laminar and turbulent regions inside of the spot. However, the turbulent eddies decayed more rapidly for ${\rm Re}\tau = 56$ than those for ${\rm Re}\tau = 64$.. The developed spot at ${\rm Re}\tau = 64$. was found to be different form from that at ${\rm Re}\tau = 56$.