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

TL;DR

This study investigates how turbulent spots develop into stripe patterns in plane Poiseuille flow using direct numerical simulations at different Reynolds numbers, revealing differences in pattern formation and turbulence decay.

Contribution

It demonstrates the formation of stripe patterns from turbulent spots in plane Poiseuille flow at specific Reynolds numbers through large-scale simulations.

Findings

Stripe patterns form inside turbulent spots.

Turbulent eddies decay faster at lower Reynolds number.

The structure of developed spots differs between Re_tau=56 and 64.

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 ${\rm Re}_\tau = 56$.