Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows

TL;DR

This study compares the internal dynamics and proliferation mechanisms of turbulent stripes in plane-Poiseuille and plane-Couette flows, revealing fundamental differences in their growth and splitting processes despite similar overall patterns.

Contribution

It provides a detailed analysis of the distinct mechanisms driving stripe proliferation in pressure-driven and shear-driven planar flows, highlighting the role of symmetry and internal growth processes.

Findings

Stripe creation is stochastic in Couette flow and deterministic in Poiseuille flow.

Stripe splitting mechanisms differ: tail shedding in Poiseuille and stripe division in Couette.

Symmetry influences the number of laminar-turbulent interfaces in the flows.

Abstract

The first long-lived turbulent structures observable in planar shear flows take the form of localized stripes, inclined with respect to the mean flow direction. The dynamics of these stripes are central to transition, and recent studies proposed an analogy to directed percolation where the stripes' proliferation is ultimately responsible for turbulence to become sustained. In the present study we focus on the internal stripe dynamics as well as on the eventual stripe expansion, and we compare the underlying mechanisms in pressure and shear driven planar flows, respectively plane-Poiseuille and plane-Couette flow. Despite the similarities of the overall laminar-turbulence patterns, the stripe proliferation processes in the two cases are fundamentally different. Starting from the growth and sustenance of individual stripes, we find that in plane-Couette flow new streaks are created stochastically throughout the stripe whereas in plane-Poiseuille flow streak creation is deterministic and occurs locally at the downstream tip. Because of the up/downstream symmetry, Couette stripes, in contrast to Poiseuille stripes, have two weak and two strong laminar turbulent interfaces. These differences in symmetry as well as in internal growth give rise to two fundamentally different stripe splitting mechanisms. In plane-Poiseuille flow splitting is connected to the elongational growth of the original stripe, and it results from a break-off / shedding of the stripe's tail. In plane-Couette flow splitting follows from a broadening of the original stripe and a division along the stripe into two slimmer stripes.